Current Issue

18 October 2021, Volume 32 Issue 5
New Developments on FDD and FTC Techniques
Unified control and detection framework and its applications: a review, some new results, and future perspectives
Steven Xianchuan DING, Linlin LI, Bin JIANG
2021, 32(5):  995-1013.  doi:10.23919/JSEE.2021.000085
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Initiated three decades ago, integrated design of controllers and fault detectors has continuously attracted research attention. The recent development of the unified control and detection framework with an observer-based residual generator in its core gives a more general form of the previous works. Its applications to residual centred modelling of uncertain control systems, fault detection in feedback control systems with uncertainties, fault-tolerant control (FTC) as well as control performance degradation monitoring, detection and recovery are introduced. In conclusion, some future perspectives are proposed.

Event-triggered leader-following formation control for multi-agent systems under communication faults: application to a fleet of unmanned aerial vehicles
Juan Antonio VAZQUEZ TREJO, Adrien GUENARD, Manuel ADAM-MEDINA, Jean-Christophe PONSART, Laurent CIARLETTA, Damiano ROTONDO, Didier THEILLIOL
2021, 32(5):  1014-1022.  doi:10.23919/JSEE.2021.000086
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The main contribution of this paper is the design of an event-triggered formation control for leader-following consensus in second-order multi-agent systems (MASs) under communication faults. All the agents must follow the trajectories of a virtual leader despite communication faults considered as smooth time-varying delays dependent on the distance between the agents. Linear matrix inequalities (LMIs)-based conditions are obtained to synthesize a controller gain that guarantees stability of the synchronization error. Based on the closed-loop system, an event-triggered mechanism is designed to reduce the control law update and information exchange in order to reduce energy consumption. The proposed approach is implemented in a real platform of a fleet of unmanned aerial vehicles (UAVs) under communication faults. A comparison between a state-of-the-art technique and the proposed technique has been provided, demonstrating the performance improvement brought by the proposed approach.

Reconfigurability evaluation method for input-constrained control systems
Yuanyuan TU, Dayi WANG, Wenbo LI
2021, 32(5):  1023-1030.  doi:10.23919/JSEE.2021.000087
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This paper proposes a quantitative reconfigurability evaluation method for control systems with actuator saturation and additive faults from the perspective of system stability. Placing the saturated feedback law in the convex hull of a group of auxiliary linear controls, the sufficient reconfigurability conditions for the system under additive faults are derived using invariant sets. These conditions are then expressed as linear matrix inequalities (LMIs) and applied to quantify the degree of reconfigurability for the fault system. The largest fault magnitude for which the system can be stabilized, the largest initial state domain from which all the trajectories are convergent, and the minimum final state domain to which the trajectories will converge are investigated. The effectiveness of the proposed method is illustrated through an application example.

Distributed fuzzy fault-tolerant consensus of leader-follower multi-agent systems with mismatched uncertainties
Sader MALIKA, Fuyong WANG, Zhongxin LIU, Zengqiang CHEN
2021, 32(5):  1031-1040.  doi:10.23919/JSEE.2021.000088
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In this paper, the distributed fuzzy fault-tolerant tracking consensus problem of leader-follower multi-agent systems (MASs) is studied. The objective system includes actuator faults, mismatched parameter uncertainties, nonlinear functions, and exogenous disturbances under switching communication topologies. To solve this problem, a distributed fuzzy fault-tolerant controller is proposed for each follower by adaptive mechanisms to track the state of the leader. Furthermore, the fuzzy logic system is utilized to approximate the unknown nonlinear dynamics. An error estimator is introduced between the mismatched parameter matrix and the input matrix. Then, a selective adaptive law with relative state information is adopted and applied. When calculating the Lyapunov function’s derivative, the coupling terms related to consensus error and mismatched parameter uncertainties can be eliminated. Finally, a numerical simulation is given to validate the effectiveness of the proposed protocol.

A fault-tolerant control method for distributed flight control system facing wing damage
Yuwei CUI, Aijun LI, Xianfeng MENG
2021, 32(5):  1041-1052.  doi:10.23919/JSEE.2021.000089
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With the strong battlefield application environment of the next generation fighter, based on the design of distributed vehicle management system, a fault diagnosis and fault-tolerant control (FTC) method for wing surface damage is proposed in this paper. Aiming at three kinds of wing damage modes, this paper proposes a diagnosis method based on the fault decision tree and forms a fault decision tree for wing damage from the aspects of sample database construction, feature parameter extraction, and fault decision tree construction. Based on the fault diagnosis results, the longitudinal control law based on dynamic inverse and the lateral-directional robust control laws based on linear quadratic regulator (LQR) are proposed. From the simulation examples, the fault diagnosis algorithm based on the decision tree can complete the judgment of three wing surface damage modes within 2 ms, and the FTC law can make the fighter quickly return to a stable flight state after a short transient of 1 s, which achieves the fault-tolerant goal.

PID-type fault-tolerant prescribed performance control of fixed-wing UAV
Ziquan YU, Youmin ZHANG, Bin JIANG
2021, 32(5):  1053-1061.  doi:10.23919/JSEE.2021.000090
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This paper introduces a fault-tolerant control (FTC) design for a faulty fixed-wing unmanned aerial vehicle (UAV). To constrain tracking errors against actuator faults, error constraint inequalities are first transformed to a new set of variables based on prescribed performance functions. Then, the commonly used and powerful proportional-integral-derivative (PID) control concept is employed to filter the transformed error variables. To handle the fault-induced nonlinear terms, a composite learning algorithm consisting of neural network and disturbance observer is incorporated for increasing flight safety. It is shown by Lyapunov stability analysis that the tracking errors are strictly constrained within the specified error bounds. Experimental results are presented to verify the feasibility of the developed FTC scheme.

Memristive network-based genetic algorithm and its application to image edge detection
Yongbin YU, Chenyu YANG, Quanxin DENG, Tashi NYIMA, Shouyi LIANG, Chen ZHOU
2021, 32(5):  1062-1070.  doi:10.23919/JSEE.2021.000091
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This paper proposes a mem-computing model of memristive network-based genetic algorithm (MNGA) by building up the relationship between the memristive network (MN) and the genetic algorithm (GA), and a new edge detection algorithm where image pixels are defined as individuals of population. First, the computing model of MNGA is designed to perform mem-computing, which brings new possibility of the hardware implementation of GA. Secondly, MNGA-based edge detection integrating image filter and GA operator deployed by MN is proposed. Finally, simulation results demonstrate that the figure of merit (FoM) of our model is better than the latest memristor-based swarm intelligence. In summary, a new way is found to build proper matching of memristor to GA and aid image edge detection.

An efficient adaptive space partitioning algorithm for electromagnetic scattering calculation of complex 3D models
Minjie HUANG, Yaoming ZHOU, Yongchao WANG, Zhongtie LIU
2021, 32(5):  1071-1082.  doi:10.23919/JSEE.2021.000092
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The space partitioning algorithm based on the rounding and addressing operations has been proved to be an efficient space partitioning algorithm with the potential for real-time calculation. An improvement on this kind of space partitioning algorithms for solving complex 3D models is presented. Numerical examples show that the efficiency of the improved algorithm is better than that of the original method. When the size of most target elements is smaller than the size of spatial grids, the efficiency of the improved method can be more than four times of that of the original method. An adaptive method of space partitioning based on the improved algorithm is developed by taking the surface element density or the curvature as the threshold for deep partitioning and conducting the deep partitioning using the octree method. A computer program implementation for applying the method in some typical applications is discussed, and the performance in terms of the efficiency, reliability, and resource use is evaluated. Application testing shows that the results of the adaptive spacing partitioning are more convenient for the follow-up use than that of the basic uniform space partitioning. Furthermore, when it is used to calculate the electromagnetic scattering of complex targets by the ray tracing (RT) method, the adaptive space partitioning algorithm can reduce the calculation time of the RT process by more than 40% compared with the uniform space segmentation algorithm.

Dataset of human motion status using IR-UWB through-wall radar
Zhengliang ZHU, Degui YANG, Junchao ZHANG, Feng TONG
2021, 32(5):  1083-1096.  doi:10.23919/JSEE.2021.000093
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Ultra-wideband (UWB) through-wall radar has a wide range of applications in non-contact human information detection and monitoring. With the integration of machine learning technology, its potential prospects include the physiological monitoring of patients in the hospital environment and the daily monitoring at home. Although many target detection methods of UWB through-wall radar based on machine learning have been proposed, there is a lack of an opensource dataset to evaluate the performance of the algorithm. This published dataset is measured by impulse radio UWB (IR-UWB) through-wall radar system. Three test subjects are measured in different environments and several defined motion status. Using the presented dataset, we propose a human-motion-status recognition method using a convolutional neural network (CNN), and the detailed dataset partition method and the recognition process flow are given. On the well-trained network, the recognition accuracy of testing data for three kinds of motion status is higher than 99.7%. The dataset presented in this paper considers a simple environment. Therefore, we call on all organizations in the UWB radar field to cooperate to build opensource datasets to further promote the development of UWB through-wall radar.

Learning a discriminative high-fidelity dictionary for single channel source separation
Yuanrong TIAN, Xing WANG
2021, 32(5):  1097-1110.  doi:10.23919/JSEE.2021.000094
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Sparse-representation-based single-channel source separation, which aims to recover each source’s signal using its corresponding sub-dictionary, has attracted many scholars’ attention. The basic premise of this model is that each sub-dictionary possesses discriminative information about its corresponding source, and this information can be used to recover almost every sample from that source. However, in a more general sense, the samples from a source are composed not only of discriminative information but also common information shared with other sources. This paper proposes learning a discriminative high-fidelity dictionary to improve the separation performance. The innovations are threefold. Firstly, an extra sub-dictionary was combined into a conventional union dictionary to ensure that the source-specific sub-dictionaries can capture only the purely discriminative information for their corresponding sources because the common information is collected in the additional sub-dictionary. Secondly, a task-driven learning algorithm is designed to optimize the new union dictionary and a set of weights that indicate how much of the common information should be allocated to each source. Thirdly, a source separation scheme based on the learned dictionary is presented. Experimental results on a human speech dataset yield evidence that our algorithm can achieve better separation performance than either state-of-the-art or traditional algorithms.

M-FCN based sea-surface weak target detection
Meiyan PAN, Jun SUN, Yuhao YANG, Dasheng LI, Junpeng YU
2021, 32(5):  1111-1118.  doi:10.23919/JSEE.2021.000095
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This paper focuses on the sea-surface weak target detection based on memory-fully convolutional network (M-FCN) in strong sea clutter. Firstly, the constant false alarm rate (CFAR) detection method utilizes a low threshold with high probability of false alarm to detect sea-surface weak targets after non-coherent integration. Reducing the detection threshold can generate a large number of false alarms while increasing the detection rate, and how to suppress a large number of false alarms is the key to improve the performance of weak target detection. Then, the detection result of the low threshold is operated to construct the target matrix suitable for the size of fully convolutional networks and the convolution operator form. Finally, the M-FCN architecture is designed to learn the different accumulation characteristics of the target and the sea clutter between different frames. For improving the detection performance, the historical multi-frame information is memorized by the network, and the end-to-end structure is established to detect sea-surface weak target automatically. Experimental results on measured data demonstrate that the M-FCN method outperforms the traditional track before detection (TBD) method and reduces false alarm tracks by 35.1%, which greatly improves the track quality.

Online adaptive dwell scheduling based on dynamic template for PAR
Qianqian TAN, Ting CHENG, Xi LI
2021, 32(5):  1119-1129.  doi:10.23919/JSEE.2021.000096
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An adaptive dwell scheduling algorithm for phased array radar (PAR) is proposed in this paper. The concept of online dynamic template is introduced, based on which a general pulse interleaving technique for PAR is put forward. The pulse interleaving condition of the novel pulse interleaving is more intuitive and general. The traditional adaptive dwell scheduling algorithm combined with the general novel pulse interleaving technique results in the online adaptive dwell scheduling based on dynamic template for PAR is given. The proposed algorithm is suitable for radar tasks with multiple pulse repetition intervals (PRIs), which can be utilized in the actual radar system. For the purpose of further improving the scheduling efficiency, an efficient version is proposed. Simulation results demonstrate the effectiveness of the proposed algorithm and the efficient one. The proposed efficient algorithm can improve the time utilization ratio (TUR) by 9%, the hit value ratio (HVR) by 3.5%, and reduce the task drop ratio (TDR) by 6% in comparison with existing dwell scheduling algorithms considering pulse interleaving in PAR and the proposed efficient one.

Quasi-LFM radar waveform recognition based on fractional Fourier transform and time-frequency analysis
Cunxiang XIE, Limin ZHANG, Zhaogen ZHONG
2021, 32(5):  1130-1142.  doi:10.23919/JSEE.2021.000097
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Recent advances in electronics have increased the complexity of radar signal modulation. The quasi-linear frequency modulation (quasi-LFM) radar waveforms (LFM, Frank code, P1?P4 code) have similar time-frequency distributions, and it is difficult to identify such signals using traditional time-frequency analysis methods. To solve this problem, this paper proposes an algorithm for automatic recognition of quasi-LFM radar waveforms based on fractional Fourier transform and time-frequency analysis. First of all, fractional Fourier transform and the Wigner-Ville distribution (WVD) are used to determine the number of main ridgelines and the tilt angle of the target component in WVD. Next, the standard deviation of the target component's width in the signal's WVD is calculated. Finally, an assembled classifier using neural network is built to recognize different waveforms by automatically combining the three features. Simulation results show that the overall recognition rate of the proposed algorithm reaches 94.17% under 0 dB. When the training data set and the test data set are mixed with noise, the recognition rate reaches 89.93%. The best recognition accuracy is achieved when the size of the training set is taken as 400. The algorithm complexity can meet the requirements of real-time recognition.

Sparse flight spotlight mode 3-D imaging of spaceborne SAR based on sparse spectrum and principal component analysis
Kai ZHOU, Daojing LI, Anjing CUI, Dong HAN, He TIAN, Haifeng YU, Jianbo DU, Lei LIU, Yu ZHU, Running ZHANG
2021, 32(5):  1143-1151.  doi:10.23919/JSEE.2021.000098
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The spaceborne synthetic aperture radar (SAR) sparse flight 3-D imaging technology through multiple observations of the cross-track direction is designed to form the cross-track equivalent aperture, and achieve the third dimensionality recognition. In this paper, combined with the actual triple star orbits, a sparse flight spaceborne SAR 3-D imaging method based on the sparse spectrum of interferometry and the principal component analysis (PCA) is presented. Firstly, interferometric processing is utilized to reach an effective sparse representation of radar images in the frequency domain. Secondly, as a method with simple principle and fast calculation, the PCA is introduced to extract the main features of the image spectrum according to its principal characteristics. Finally, the 3-D image can be obtained by inverse transformation of the reconstructed spectrum by the PCA. The simulation results of 4.84 km equivalent cross-track aperture and corresponding 1.78 m cross-track resolution verify the effective suppression of this method on high-frequency sidelobe noise introduced by sparse flight with a sparsity of 49% and random noise introduced by the receiver. Meanwhile, due to the influence of orbit distribution of the actual triple star orbits, the simulation results of the sparse flight with the 7-bit Barker code orbits are given as a comparison and reference to illuminate the significance of orbit distribution for this reconstruction results. This method has prospects for sparse flight 3-D imaging in high latitude areas for its short revisit period.

Review on strategies of space-based optical space situational awareness
Yunpeng HU, Kebo LI, Yan’gang LIANG, Lei CHEN
2021, 32(5):  1152-1166.  doi:10.23919/JSEE.2021.000099
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Space-based optical (SBO) space surveillance has attracted widespread interest in the last two decades due to its considerable value in space situation awareness (SSA). SBO observation strategy, which is related to the performance of space surveillance, is the top-level design in SSA missions reviewed. The recognized real programs about SBO SAA proposed by the institutions in the U.S., Canada, Europe, etc., are summarized firstly, from which an insight of the development trend of SBO SAA can be obtained. According to the aim of the SBO SSA, the missions can be divided into general surveillance and space object tracking. Thus, there are two major categories for SBO SSA strategies. Existing general surveillance strategies for observing low earth orbit (LEO) objects and beyond-LEO objects are summarized and compared in terms of coverage rate, revisit time, visibility period, and image processing. Then, the SBO space object tracking strategies, which has experienced from tracking an object with a single satellite to tracking an object with multiple satellites cooperatively, are also summarized. Finally, this paper looks into the development trend in the future and points out several problems that challenges the SBO SSA.

Joint optimization of inspection, maintenance, and spare ordering policy considering defective products loss
Mengying HAN, Jianhua YANG, Xiao ZHAO
2021, 32(5):  1167-1179.  doi:10.23919/JSEE.2021.000100
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This paper proposes a joint inspection-based maintenance and spare ordering optimization policy that considers the problem of integrated inspection, preventive maintenance, spare ordering, and quality control for a four-state single-unit manufacturing system. When an inspection detects a minor defect, a second phase inspection is initiated and a regular order is placed. Product quality begins to deteriorate when the system undergoes a severe defect. To counter this, an advanced replacement of the minor defective system is carried out at the $J{\rm{th}}$ second phase inspection. If a severe defect is recognized prior to the $J{\rm{th}}$ inspection, or if system failure occurs, preventive or corrective replacement is executed. The timeliness of replacement depends on the availability of spare. We adopt two modes of ordering: a regular order and an emergency order. Meanwhile, a threshold level is introduced to determine whether an emergency order is preferred even when the regular order is already ordered but has not yet arrived. The optimal joint inspection-based maintenance and spare ordering policy is formulated by minimizing the expected cost per unit time. A simulation algorithm is proposed to obtain the optimal two-phase inspection interval, threshold level and advanced replacement interval. Results from several numerical examples demonstrate that, in terms of the expected cost per unit time, our proposed model is superior to some existing models.

A blockchain bee colony double inhibition labor division algorithm for spatio-temporal coupling task with application to UAV swarm task allocation
Husheng WU, Hao LI, Renbin XIAO
2021, 32(5):  1180-1199.  doi:10.23919/JSEE.2021.000101
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It is difficult for the double suppression division algorithm of bee colony to solve the spatio-temporal coupling or have higher dimensional attributes and undertake sudden tasks. Using the idea of clustering, after clustering tasks according to spatio-temporal attributes, the clustered groups are linked into task sub-chains according to similarity. Then, based on the correlation between clusters, the child chains are connected to form a task chain. Therefore, the limitation is solved that the task chain in the bee colony algorithm can only be connected according to one dimension. When a sudden task occurs, a method of inserting a small number of tasks into the original task chain and a task chain reconstruction method are designed according to the relative relationship between the number of sudden tasks and the number of remaining tasks. Through the above improvements, the algorithm can be used to process tasks with spatio-temporal coupling and burst tasks. In order to reflect the efficiency and applicability of the algorithm, a task allocation model for the unmanned aerial vehicle (UAV) group is constructed, and a one-to-one correspondence between the improved bee colony double suppression division algorithm and each attribute in the UAV group is proposed. Task assignment has been constructed. The study uses the self-adjusting characteristics of the bee colony to achieve task allocation. Simulation verification and algorithm comparison show that the algorithm has stronger planning advantages and algorithm performance.

An integrated simulation system for operating solar sail spacecraft
Yaru ZHENG, Qinglong LI, Ming XU, Yunfeng DONG
2021, 32(5):  1200-1211.  doi:10.23919/JSEE.2021.000102
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An integrated simulation system for solar sail spacecraft with individually controllable elements (SSICE) is investigated in this paper, including the modelling of power management, thermal control, attitude control, umbra prediction, and orbit prediction subsystems. Considering the self-control and reactivity subsystems, an agent based method is applied to develop the subsystem models. Each subsystem is an individual agent component, which manages itself autonomously and reacts to the requirements from other agents. To reduce computing burden on a specified computer and improve the suitability and flexibility of the integrated simulation system, a distributed framework is employed in the system by deploying agent components on different computers. The data transmission among agents is based on the transmission control protocol/Internet protocol (TCP/IP). A practical example of sun pointing is used to test the operating effect of the integrated system and the working condition of subsystems. The simulation results verify that the integrated system has higher sun pointing accuracy, quicker dynamical response to variations of the lighting, attitude and temperature and fewer computing resources with effective and accurate subsystems. The integrated system proposed in this paper can be applied to solar sail design, operation, and mission planning.

An iterated local coordinate-exchange algorithm for constructing experimental designs for multi-dimensional constrained spaces
Yang YOU, Guang JIN, Zhengqiang PAN, Rui GUO
2021, 32(5):  1212-1220.  doi:10.23919/JSEE.2021.000103
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Iterated local search (ILS) is used to construct the optimal experimental designs for multi-dimensional constrained spaces, in which the inner loop is based on the stochastic coordinate-exchange (SCE) algorithm. Every time a local optimal solution is found by the SCE algorithm, the perturbation operator is applied to it, and then a new solution is explored in the areas where the exchange of coordinates may produce improvement, so as to retain the features and attributes of the current optimal solution and avoid the defects of random restart. We implement the iterated local coordinate-exchange algorithm for experimental designs in the multi-dimensional constrained spaces. In addition, sensitivity analysis was conducted to analyze the impacts of the parameters on the performance of the proposed algorithm. Also we compared the performance of the proposed algorithm to the SCE algorithm using the random restart strategy. The analysis shows that the proposed algorithm is better than the SCE algorithm in terms of efficiency and quality, especially in the experimental designs for high-dimensional constrained space.

Reliability analysis of k-out-of-n system with load-sharing and failure propagation effect
Ying CHEN, Qichao MA, Ze WANG, Yingyi LI
2021, 32(5):  1221-1231.  doi:10.23919/JSEE.2021.000104
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In complex systems, functional dependency and physical dependency may have a coupling effect. In this paper, the reliability of a k-out-of-n system is analyzed considering load-sharing effect and failure mechanism (FM) propagation. Three types of FMs are considered and an accumulative damage model is proposed to illustrate the system behavior of the k-out-of-n system and the coupling effect between load-sharing effect and FM propagation effect. A combinational algorithm based on Binary decision diagram (BDD) and Monte-Carlo simulation is presented to evaluate the complex system behavior and reliability of the k-out-of-n system. A current stabilizing system that consists of a 3-out-of-6 subsystem with FM propagation effect is presented as a case to illustrate the complex behavior and to verify the applicability of the proposed method. Due to the coupling effect change, the main mechanism and failure mode will be changed, and the system lifetime is shortened. Reasons are analyzed and results show that different sensitivity factors of three different FMs lead to the change of the development rate, thus changing the failure scenario. Neglecting the coupling effect may lead to an incomplete and ineffective measuring and monitoring plan. Design strategies must be adopted to make the FM propagation insensitive to load-sharing effect.

A method to realize NAVSOP by utilizing GNSS authorized signals
Ying YUAN, Feng YU, Yang CHEN, Niancheng ZHANG
2021, 32(5):  1232-1245.  doi:10.23919/JSEE.2021.000105
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Navigation via signals of opportunity (NAVSOP) is able to realize positioning by making use of hundreds of different signals that are all around us. A method to realize NAVSOP for low earth orbit (LEO) satellites is proposed in this paper, in which the global navigation satellite system (GNSS) authorized signals are utilized as the signal of opportunity (SOP). At first, the carrier recovery technique is studied under the premise that the pseudo-code is unknown. Secondly, a method based on characteristics of Doppler frequency shift is proposed to recognize the navigation satellites. Thirdly, the extended Kalman filter (EKF) is utilized to estimate the orbital parameters by using carrier phase measurements. Finally, the proposed method is evaluated by using signals generated by a satellite navigation data simulator. The simulation results show that the proposed method can successfully realize navigation via GNSS authorized signals.

Belief reliability modeling and analysis for planetary reducer considering multi-source uncertainties and wear
Yun LI, Kaige JIANG, Ting ZENG, Wenbin CHEN, Xiaoyang LI, Deyong LI, Zhiqiang ZHANG
2021, 32(5):  1246-1262.  doi:10.23919/JSEE.2021.000106
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The planetary reducer is a common type of transmission mechanism, which can provide high transmission accuracy and has been widely used, and it is usually required with high reliability of transmission characteristics in practice. During the manufacturing and usage stages of planetary reducers, uncertainties are ubiquitous and wear is inevitable, which affect the transmission characteristics and the reliability of planetary reducers. In this paper, belief reliability modeling and analysis considering multi-uncertainties and wear are proposed for planetary reducers. Firstly, based on the functional principle and the influence of wear, the performance margin degradation model is established using the hysteresis error as the key performance parameter, where the degradation is mainly caused by the accumulated wear. After that, multi-source uncertainties are analyzed and quantified separately, including manufacturing errors, uncertainties in operational and environmental conditions, and uncertainties in performance thresholds. Finally, the belief reliability model is established based on the performance margin degradation model. A case study of a planetary reducer is applied and the reliability sensitivity analysis is implemented to show the practicability of the proposed method. The results show that the proposed method can provide some suggestions to the design and manufacturing phases of the planetary reducer.