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24 December 2022, Volume 33 Issue 6
ELECTRONICS TECHNOLOGY
Approximate CN scheme and its open region problems for metamaterial rotational symmetric simulation
Peiyu WU, Han YU, Yenan HU, Yongjun XIE, Haolin JIANG
2022, 33(6):  1081-1087.  doi:10.23919/JSEE.2022.000135
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In order to simulate metamaterial rotational symmetric open region problems, unconditionally stable perfectly match layer (PML) implementation is proposed in the body of revolution (BOR) finite-difference time-domain (FDTD) lattice. More precisely, the proposed algorithm is implemented by the Crank-Nicolson (CN) Douglas-Gunn (DG) procedure for BOR metamaterial simulation. The constitutive relationship of metamaterial can be expressed by the Drude model and calculated by the piecewise linear recursive convolution (PLRC) approach. The effectiveness including absorption, efficiency, and accuracy is demonstrated through the numerical example. It can be concluded that the proposed implementation is to take the advantages of the CNDG-PML procedure, PLRC approach, and BOR-FDTD algorithm in terms of considerable accuracy, enhanced absorption and remarkable efficiency. Meanwhile, it can be demonstrated that the proposed scheme can maintain its unconditional stability when the time step exceeds the Courant-Friedrichs-Levy (CFL) condition.

Deep learning for fast channel estimation in millimeter-wave MIMO systems
Siting LYU, Xiaohui LI, Tao FAN, Jiawen LIU, Mingli SHI
2022, 33(6):  1088-1095.  doi:10.23919/JSEE.2022.000126
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Channel estimation has been considered as a key issue in the millimeter-wave (mmWave) massive multi-input multi-output (MIMO) communication systems, which becomes more challenging with a large number of antennas. In this paper, we propose a deep learning (DL)-based fast channel estimation method for mmWave massive MIMO systems. The proposed method can directly and effectively estimate channel state information (CSI) from received data without performing pilot signals estimate in advance, which simplifies the estimation process. Specifically, we develop a convolutional neural network (CNN)-based channel estimation network for the case of dimensional mismatch of input and output data, subsequently denoted as channel (H) neural network (HNN). It can quickly estimate the channel information by learning the inherent characteristics of the received data and the relationship between the received data and the channel, while the dimension of the received data is much smaller than the channel matrix. Simulation results show that the proposed HNN can gain better channel estimation accuracy compared with existing schemes.

Super-resolution DOA estimation for correlated off-grid signals via deep estimator
Shuang WU, Ye YUAN, Weike ZHANG, Naichang YUAN
2022, 33(6):  1096-1107.  doi:10.21629/JSEE.2022.00074
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This paper develops a deep estimator framework of deep convolution networks (DCNs) for super-resolution direction of arrival (DOA) estimation. In addition to the scenario of correlated signals, the quantization errors of the DCN are the major challenge. In our deep estimator framework, one DCN is used for spectrum estimation with quantization errors, and the remaining two DCNs are used to estimate quantization errors. We propose training our estimator using the spatial sampled covariance matrix directly as our deep estimator’s input without any feature extraction operation. Then, we reconstruct the original spatial spectrum from the spectrum estimate and quantization errors estimate. Also, the feasibility of the proposed deep estimator is analyzed in detail in this paper. Once the deep estimator is appropriately trained, it can recover the correlated signals’ spatial spectrum fast and accurately. Simulation results show that our estimator performs well in both resolution and estimation error compared with the state-of-the-art algorithms.

Two-dimensional directional modulation with dual-mode vortex beam for security transmission
Changju ZHU, Maozhong SONG, Xiaoyu DANG, Qiuming ZHU
2022, 33(6):  1108-1118.  doi:10.23919/JSEE.2022.000136
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A two-dimensional directional modulation (DM) technology with dual-mode orbital angular momentum (OAM) beam is proposed for physical-layer security of the relay unmanned aerial vehicle (UAV) tracking transmission. The elevation and azimuth of the vortex beam are modulated into the constellation, which can form the digital waveform with the encoding modulation. Since the signal is direction-dependent, the modulated waveform is purposely distorted in other directions to offer a security technology. Two concentric uniform circular arrays (UCAs) with different radii are excited to generate dual vortex beams with orthogonality for the composite signal, which can increase the demodulation difficulty. Due to the phase propagation characteristics of vortex beam, the constellation at the desired azimuth angle will change continuously within a wavelength. A desired single antenna receiver can use the propagation phase compensation and an opposite helical phase factor for the signal demodulation in the desired direction. Simulations show that the proposed OAM-DM scheme offers a security approach with direction sensitivity transmission.

Multi-fidelity Bayesian algorithm for antenna optimization
Jianxing LI, An YANG, Chunming TIAN, Le YE, Badong CHEN
2022, 33(6):  1119-1126.  doi:10.23919/JSEE.2022.000137
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In this work, the multi-fidelity (MF) simulation driven Bayesian optimization (BO) and its advanced form are proposed to optimize antennas. Firstly, the multiple objective targets and the constraints are fused into one comprehensive objective function, which facilitates an end-to-end way for optimization. Then, to increase the efficiency of surrogate construction, we propose the MF simulation-based BO (MFBO), of which the surrogate model using MF simulation is introduced based on the theory of multi-output Gaussian process. To further use the low-fidelity (LF) simulation data, the modified MFBO (M-MFBO) is subsequently proposed. By picking out the most potential points from the LF simulation data and re-simulating them in a high-fidelity (HF) way, the M-MFBO has a possibility to obtain a better result with negligible overhead compared to the MFBO. Finally, two antennas are used to testify the proposed algorithms. It shows that the HF simulation-based BO (HFBO) outperforms the traditional algorithms, the MFBO performs more effectively than the HFBO, and sometimes a superior optimization result can be achieved by reusing the LF simulation data.

Micro-Doppler feature extraction of micro-rotor UAV under the background of low SNR
Weikun HE, Jingbo SUN, Xinyun ZHANG, Zhenming LIU
2022, 33(6):  1127-1139.  doi:10.23919/JSEE.2022.000138
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Micro-Doppler feature extraction of unmanned aerial vehicles (UAVs) is important for their identification and classification. Noise and the motion state of the UAV are the main factors that may affect feature extraction and estimation precision of the micro-motion parameters. The spectrum of UAV echoes is reconstructed to strengthen the micro-motion feature and reduce the influence of the noise on the condition of low signal to noise ratio (SNR). Then considering the rotor rate variance of UAV in the complex motion state, the cepstrum method is improved to extract the rotation rate of the UAV, and the blade length can be intensively estimated. The experiment results for the simulation data and measured data show that the reconstruction of the spectrum for the UAV echoes is helpful and the relative mean square root error of the rotating speed and blade length estimated by the proposed method can be improved. However, the computation complexity is higher and the heavier computation burden is required.

DEFENCE ELECTRONICS TECHNOLOGY
Debiased conversion measurements based target tracking with direction cosine measurements
Lifu LI, Ting CHENG
2022, 33(6):  1140-1150.  doi:10.23919/JSEE.2022.000139
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Phased array radar ’s measurements include two direction cosine and range measurements, which can be obtained in the direction cosine coordinates. State equation of the target is nonlinear with the measurements and in order to solve the nonlinear problem, debiased conversion measurements based target tracking with direction cosine and range measurements in direction cosine coordinates named DCMKF-PreDcos is proposed first in this paper, where the predicted information is introduced to calculate the converted measurement errors ’ statistical characteristics to eliminate the correlation between measurement noise and the converted measurement errors covariance. When range rate information can be obtained further, based on the above DCMKF-PreDcos ’ filtering result, the sequential filtering is adopted to process the additional range rate measurement and the DCMKF-PreDcos algorithm with extra range rate information is given. The predicted information is also introduced to calculate the involved statistical characteristics of converted measurements. The effectiveness of the proposed algorithms is shown in simulation results.

Mainlobe jamming suppression via improved BSS method for rotated array radar
Hailong ZHANG, Gong ZHANG, Biao XUE, Jiawen YUAN
2022, 33(6):  1151-1158.  doi:10.23919/JSEE.2022.000129
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This study deals with the problem of mainlobe jamming suppression for rotated array radar. The interference becomes spatially nonstationary while the radar array rotates, which causes the mismatch between the weight and the snapshots and thus the loss of target signal to noise ratio (SNR) of pulse compression. In this paper, we explore the spatial divergence of interference sources and consider the rotated array radar anti-mainlobe jamming problem as a generalized rotated array mixed signal (RAMS) model firstly. Then the corresponding algorithm improved blind source separation (BSS) using the frequency domain of robust principal component analysis (FD-RPCA-BSS) is proposed based on the established rotating model. It can eliminate the influence of the rotating parts and address the problem of loss of SNR . Finally, the measured peak-to-average power ratio (PAPR) of each separated channel is performed to identify the target echo channel among the separated channels. Simulation results show that the proposed method is practically feasible and can suppress the mainlobe jamming with lower loss of SNR.

SYSTEMS ENGINEERING
A deep reinforcement learning method for multi-stage equipment development planning in uncertain environments
Peng LIU, Boyuan XIA, Zhiwei YANG, Jichao LI, Yuejin TAN
2022, 33(6):  1159-1175.  doi:10.23919/JSEE.2022.000140
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Equipment development planning (EDP) is usually a long-term process often performed in an environment with high uncertainty. The traditional multi-stage dynamic programming cannot cope with this kind of uncertainty with unpredictable situations. To deal with this problem, a multi-stage EDP model based on a deep reinforcement learning (DRL) algorithm is proposed to respond quickly to any environmental changes within a reasonable range. Firstly, the basic problem of multi-stage EDP is described, and a mathematical planning model is constructed. Then, for two kinds of uncertainties (future capability requirements and the amount of investment in each stage), a corresponding DRL framework is designed to define the environment, state, action, and reward function for multi-stage EDP. After that, the dueling deep Q-network (Dueling DQN) algorithm is used to solve the multi-stage EDP to generate an approximately optimal multi-stage equipment development scheme. Finally, a case of ten kinds of equipment in 100 possible environments, which are randomly generated, is used to test the feasibility and effectiveness of the proposed models. The results show that the algorithm can respond instantaneously in any state of the multi-stage EDP environment and unlike traditional algorithms, the algorithm does not need to re-optimize the problem for any change in the environment. In addition, the algorithm can flexibly adjust at subsequent planning stages in the event of a change to the equipment capability requirements to adapt to the new requirements.

Survey on autonomous task scheduling technology for Earth observation satellites
Jian WU, Yuning CHEN, Yongming HE, Lining XING, Yangrui HU
2022, 33(6):  1176-1189.  doi:10.23919/JSEE.2022.000141
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How to make use of limited onboard resources for complex and heavy space tasks has attracted much attention. With the continuous improvement on satellite payload capacity and the increasing complexity of observation requirements, the importance of satellite autonomous task scheduling research has gradually increased. This article first gives the problem description and mathematical model for the satellite autonomous task scheduling and then follows the steps of “satellite autonomous task scheduling, centralized autonomous collaborative task scheduling architecture, distributed autonomous collaborative task scheduling architecture, solution algorithm". Finally, facing the complex and changeable environment situation, this article proposes the future direction of satellite autonomous task scheduling.

A multiple heterogeneous UAVs reconnaissance mission planning and re-planning algorithm
Lei HU, Boqi XI, Guoxing YI, Hui ZHAO, Jiapeng ZHONG
2022, 33(6):  1190-1207.  doi:10.23919/JSEE.2022.000142
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Reconnaissance mission planning of multiple unmanned aerial vehicles (UAVs) under an adversarial environment is a discrete combinatorial optimization problem which is proved to be a non-deterministic polynomial (NP)-complete problem. The purpose of this study is to research intelligent multi-UAVs reconnaissance mission planning and online re-planning algorithm under various constraints in mission areas. For numerous targets scattered in the wide area, a reconnaissance mission planning and re-planning system is established, which includes five modules, including intelligence analysis, sub-mission area division, mission sequence planning, path smoothing, and online re-planning. The intelligence analysis module depicts the attribute of targets and the heterogeneous characteristic of UAVs and computes the number of sub-mission areas on consideration of voyage distance constraints. In the sub-mission area division module, an improved K-means clustering algorithm is designed to divide the reconnaissance mission area into several sub-mission areas, and each sub-mission is detected by the UAV loaded with various detective sensors. To control reconnaissance cost, the sampling and iteration algorithms are proposed in the mission sequence planning module, which are utilized to solve the optimal or approximately optimal reconnaissance sequence. In the path smoothing module, the Dubins curve is applied to smooth the flight path, which assure the availability of the planned path. Furthermore, an online re-planning algorithm is designed for the uncertain factor that the UAV is damaged. Finally, reconnaissance planning and re-planning experiment results show that the algorithm proposed in this paper are effective and the algorithms designed for sequence planning have a great advantage in solving efficiency and optimality.

Faster-than-Nyquist signaling based on filter bank multicarrier modulation with joint optimization
Hui CHE, Dingxiang PENG, Fachang GUO, Yong BAI
2022, 33(6):  1208-1223.  doi:10.23919/JSEE.2022.000143
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Multi-carrier faster-than-Nyquist (MFTN) can improve the spectrum efficiency (SE). In this paper, we first analyze the benefit of time frequency packing MFTN (TFP-MFTN). Then, we propose an efficient digital implementation for TFP-MFTN based on filter bank multicarrier modulation. The time frequency packing ratio pair in our proposed implementation scheme is optimized with the SE criterion. Next, the joint optimization for the coded modulation MFTN based on extrinsic information transfer (EXIT) chart is performed. The Monte-Carlo simulations are carried out to verify performance gain of the joint inner and outer code optimization. Simulation results demonstrate that the TFP-MFTN has a 0.8 dB and 0.9 dB gain comparing to time packing MFTN (TP-MFTN) and higher order Nyquist at same SE, respectively; the TFP-MFTN with optimized low density parity check (LDPC) code has a 2.9 dB gain comparing to that with digital video broadcasting (DVB) LDPC. Compared with previous work on TFP-MFTN (SE=1.55 bit/s/Hz), the SE of our work is improved by 29% and our work has a 4.1 dB gain at BER=1×10?5.

Risk transmission evaluation for parallel construction of warships based on IFCM and the cloud model
Jun GONG, Tao HU, Lu YAO
2022, 33(6):  1224-1237.  doi:10.23919/JSEE.2022.000144
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To cope with multi-directional transmission coupling, spreading, amplification, and chain reaction of risks during multi-project parallel construction of warships, a risk transmission evaluation method is proposed, which integrates an intuitionistic cloud model with a fuzzy cognitive map. By virtue of expectancy $ {\rm{Ex}} $ , entropy ${\rm{En}}$ , and hyper entropy ${\rm{He}}$ , the risk fuzziness and randomness of the knowledge of experts are organically combined to develop a method for converting bi-linguistic variable decision-making information into the quantitative information of the intuitionistic normal cloud (INC) model. Subsequently, the threshold function and weighted summation operation in the traditional fuzzy cognitive map is converted into the INC ordered weighted averaging operator to create the risk transmission model based on the intuitionistic fuzzy cognitive map (IFCM) and the algorithm for solving it. Subsequently, the risk influence sequencing method based on INC and the risk rating method based on nearness are proposed on the basis of Monte Carlo simulation in order to realize the mutual conversion of the qualitative and quantitative information in the risk evaluation results. Example analysis is presented to verify the effectiveness and practicality of the methods.

Evaluation of global navigation satellite system spoofing efficacy
Yue WANG, Fuping SUN, Jinming HAO, Lundong ZHANG, Xian WANG
2022, 33(6):  1238-1257.  doi:10.23919/JSEE.2022.000145
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The spoofing capability of Global Navigation Satellite System (GNSS) represents an important confrontational capability for navigation security, and the success of planned missions may depend on the effective evaluation of spoofing capability. However, current evaluation systems face challenges arising from the irrationality of previous weighting methods, inapplicability of the conventional multi-attribute decision-making method and uncertainty existing in evaluation. To solve these difficulties, considering the validity of the obtained results, an evaluation method based on the game aggregated weight model and a joint approach involving the grey relational analysis and technique for order preference by similarity to an ideal solution (GRA-TOPSIS) are firstly proposed to determine the optimal scheme. Static and dynamic evaluation results under different schemes are then obtained via a fuzzy comprehensive assessment and an improved dynamic game method, to prioritize the deceptive efficacy of the equipment accurately and make pointed improvement for its core performance. The use of judging indicators, including Spearman rank correlation coefficient and so on, combined with obtained evaluation results, demonstrates the superiority of the proposed method and the optimal scheme by the horizontal comparison of different methods and vertical comparison of evaluation results. Finally, the results of field measurements and simulation tests show that the proposed method can better overcome the difficulties of existing methods and realize the effective evaluation.

CONTROL THEORY AND APPLICATION
Design and implementation of data-driven predictive cloud control system
Runze GAO, Yuanqing XIA, Li DAI, Zhongqi SUN, Yufeng ZHAN
2022, 33(6):  1258-1268.  doi:10.23919/JSEE.2022.000146
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The rapid increase of the scale and the complexity of the controlled plants bring new challenges such as computing power and storage for conventional control systems. Cloud computing is concerned as a powerful solution to handle complex large-scale control missions by using sufficient computing resources. However, the computing ability enables more complex devices and more data to be involved and most of the data have not been fully utilized. Meanwhile, it is even impossible to obtain an accurate model of each device in the complex control systems for the model-based control algorithms. Therefore, motivated by the above reasons, we propose a data-driven predictive cloud control system. To achieve the proposed system, a practical data-driven predictive cloud control testbed is established and together a cloud-edge communication scheme is developed. Finally, the simulations and experiments demonstrate the effectiveness of the proposed system.

Dynamic affine formation control of networked under-actuated quad-rotor UAVs with three-dimensional patterns
Yang XU, Weiming ZHENG, Delin LUO, Haibin DUAN
2022, 33(6):  1269-1285.  doi:10.23919/JSEE.2022.000147
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This paper focuses on the solution to the dynamic affine formation control problem for multiple networked under-actuated quad-rotor unmanned aerial vehicles (UAVs) to achieve a configuration that preserves collinearity and ratios of distances for a target configuration. In particular, it is investigated that the quad-rotor UAVs are steered to track a reference linear velocity while maintaining a desired three-dimensional target formation. Firstly, by integrating the properties of the affine transformation and the stress matrix, the design of the target formation is convenient and applicable for various three-dimensional geometric patterns. Secondly, a distributed control method is proposed under a hierarchical framework. By introducing an intermediary control input for each quad-rotor UAV in the position loop, the necessary thrust input and the desired attitude are extracted. In the attitude loop, the desired attitude represented by the unit quaternion is tracked by the designed torque input. Both conditions of linear velocity unavailability and mutual collision avoidance are also tackled. In terms of Lyapunov theory, it is prooved that the overall closed-loop error system is asymptotically stable. Finally, two illustrative examples are simulated to validate the effectiveness of the proposed theoretical results.

Fiber resonator using negative-curvature anti-resonant fiber with temperature stability
Honghao MA, Hui LI, Changkun FENG, Lishuang FENG, Shoufei GAO, Yingying WANG, Pu WANG
2022, 33(6):  1286-1293.  doi:10.23919/JSEE.2022.000148
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The coupling efficiency of hollow-core fiber changes with temperature, which leads to the decrease of the finesse ( F ) of fiber resonator and limits the performance of the resonant fiber optic gyroscope (R-FOG) system. Negative-curvature anti-resonant fiber (ARF) can maintain single-mode characteristics under the condition of large mode field diameter, achieve efficient and stable fiber coupling, and significantly improve the consistency of the F of the spatial coupling resonator in variable temperature environment. A new type of ARF with a mode field diameter (MFD) of 25 μm is used to fabricate a fiber resonator with a length of 5.14 m. In the range of 25 °C?75 °C, the averageF is 31.45. The ARF resonator is used to construct an R-FOG system that shows long-term bias stability (3600 s) of 3.1 °/h at room temperature, 4.6 °/h at 75 °C. To our knowledge, this is the best reported index of hollow-core fiber resonator and R-FOG system within the temperature variation range of 50 °C test.

An optimal guidance method for free-time orbital pursuit-evasion game
Chengming ZHANG, Yanwei ZHU, Leping YANG, Xin ZENG
2022, 33(6):  1294-1308.  doi:10.23919/JSEE.2022.000149
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With the development of space rendezvous and proximity operations (RPO) in recent years, the scenarios with non-cooperative spacecraft are attracting the attention of more and more researchers. A method based on the costate normalization technique and deep neural networks is presented to generate the optimal guidance law for free-time orbital pursuit-evasion game. Firstly, the 24-dimensional problem given by differential game theory is transformed into a three-parameter optimization problem through the dimension-reduction method which guarantees the uniqueness of solution for the specific scenario. Secondly, a close-loop interactive mechanism involving feedback is introduced to deep neural networks for generating precise initial solution. Thus the optimal guidance law is obtained efficiently and stably with the application of optimization algorithm initialed by the deep neural networks. Finally, the results of the comparison with another two methods and Monte Carlo simulation demonstrate the efficiency and robustness of the proposed optimal guidance method.

Sliding mode fault tolerant consensus control for multi-agent systems based on super-twisting observer
Pu YANG, Xukai HU, Zixin WANG, Zhiqing ZHANG
2022, 33(6):  1309-1319.  doi:10.23919/JSEE.2022.000150
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The fault-tolerant consensus problem for leader-following nonlinear multi-agent systems with actuator faults is mainly investigated. A new super-twisting sliding mode observer is constructed to estimate the velocity and undetectable fault information simultaneously. The time-varying gain is introduced to solve the initial error problem and peak value problem, which makes the observation more accurate and faster. Then, based on the estimated results, an improved sliding mode fault-tolerant consensus control algorithm is designed to compensate the actuator faults. The protocol can guarantee the finite-time consensus control of multi-agent systems and suppress chattering. Finally, the effectiveness and the superiority of the observer and control algorithm are proved by some simulation examples of the multi-aircraft system.

Torque estimation for robotic joint with harmonic drive transmission based on system dynamic characteristics
Minghong ZHU, Shu XIAO, Fei YU
2022, 33(6):  1320-1331.  doi:10.23919/JSEE.2022.000151
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In the applications of joint control and robot movement, the joint torque estimation has been treated as an effective technique and widely used. Researches are made to analyze the kinematic and compliance model of the robot joint with harmonic drive to acquire high precision torque output. Through analyzing the structures of the harmonic drive and experiment apparatus, a scheme of the proposed joint torque estimation method based on both the dynamic characteristics and unscented Kalman filter (UKF) is designed and built. Based on research and scheme, torque estimation methods in view of only harmonic drive compliance model and compliance model with the Kalman filter are simulated as guidance and reference to promote the research on the torque estimation technique. Finally, a promoted torque estimation method depending on both harmonic drive compliance model and UKF is designed, and simulation results compared with the measurements of a commercial torque sensor, have verified the effectiveness of the proposed method.

RELIABILITY
Search for d-MPs without duplicates in two-terminal multistate networks based on MPs
Bei XU, Yining FANG, Guanghan BAI, Yun’an ZHANG, Junyong TAO
2022, 33(6):  1332-1341.  doi:10.23919/JSEE.2022.000152
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The reliability evaluation of a multistate network is primarily based on d-minimal paths/cuts (d-MPs/d-MCs). However, being a nondeterminism polynomial hard (NP-hard) problem, searching for all d-MPs is a rather challenging task. In existing implicit enumeration algorithms based on minimal paths (MPs), duplicate d-MP candidates may be generated. An extra step is needed to locate and remove these duplicate d-MP candidates, which costs significant computational effort. This paper proposes an efficient method to prevent the generation of duplicate d-MP candidates for implicit enumeration algorithms for d-MPs. First, the mechanism of generating duplicate d-MP candidates in the implicit enumeration algorithms is discussed. Second, a direct and efficient avoiding-duplicates method is proposed. Third, an improved algorithm is developed, followed by complexity analysis and illustrative examples. Based on the computational experiments comparing with two existing algorithms, it is found that the proposed method can significantly improve the efficiency of generating d-MPs for a particular demand level d.

Component reallocation and system replacement maintenance based on availability and cost in series systems
Yuqiang FU, Xiaoyang MA
2022, 33(6):  1342-1353.  doi:10.23919/JSEE.2022.000153
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Component reallocation (CR) is receiving increasing attention in many engineering systems with functionally interchangeable and unbalanced degradation components. This paper studies a CR and system replacement maintenance policy of series repairable systems, which undergoes minimal repairs for each emergency failure of components, and considers constant downtime and cost of minimal repair, CR and system replacement. Two binary mixed integer nonlinear programming models are respectively established to determine the assignment of CR, and the uptime right before CR and system replacement with the objective of minimizing the system average maintenance cost and maximizing the system availability. Further, we derive the optimal uptime right before system replacement with maximization of the system availability, and then give the relationship between the system availability and the component failure rate. Finally, numerical examples show that the CR and system replacement maintenance policy can effectively reduce the system average maintenance cost and improve the system availability, and further give the sensitivity analysis and insights of the CR and system replacement maintenance policy.