Thinning of antenna arrays has been a popular topic for the last several decades. With increasing computational power, this optimization task acquired a new hue. This paper suggests a genetic algorithm as an instrument for antenna array thinning. The algorithm with a deliberately chosen fitness function allows synthesizing thinned linear antenna arrays with low peak sidelobe level (SLL) while maintaining the half-power beamwidth (HPBW) of a full linear antenna array. Based on results from existing papers in the field and known approaches to antenna array thinning, a classification of thinning types is introduced. The optimal thinning type for a linear thinned antenna array is determined on the basis of a maximum attainable SLL. The effect of thinning coefficient on main directional pattern characteristics, such as peak SLL and HPBW, is discussed for a number of amplitude distributions.

Most of the existing direction of arrival (DOA) estimation algorithms are applied under the assumption that the array manifold is ideal. In practical engineering applications, the existence of non-ideal conditions such as mutual coupling between array elements, array amplitude and phase errors, and array element position errors leads to defects in the array manifold, which makes the performance of the algorithm decline rapidly or even fail. In order to solve the problem of DOA estimation in the presence of amplitude and phase errors and array element position errors, this paper introduces the first-order Taylor expansion equivalent model of the received signal under the uniform linear array from the Bayesian point of view. In the solution, the amplitude and phase error parameters and the array element position error parameters are regarded as random variables obeying the Gaussian distribution. At the same time, the expectation-maximization algorithm is used to update the probability distribution parameters, and then the two error parameters are solved alternately to obtain more accurate DOA estimation results. Finally, the effectiveness of the proposed algorithm is verified by simulation and experiment.

Jamming suppression is traditionally achieved through the use of spatial filters based on array signal processing theory. In order to achieve better jamming suppression performance, many studies have applied blind source separation (BSS) to jamming suppression. BSS can achieve the separation and extraction of the individual source signals from the mixed signal received by the array. This paper proposes a perspective to recognize BSS as spatial band-pass filters (SBPFs) for jamming suppression applications. The theoretical derivation indicates that the processing of mixed signals by BSS can be perceived as the application of a set of SBPFs that gate the source signals at various angles. Simulations are performed using radar jamming suppression as an example. The simulation results suggest that BSS and SBPFs produce approximately the same effects. Simulation results are consistent with theoretical derivation results.

According to the measurement principle of the traditional interferometer, a narrowband signal model is established and used, however, for wideband signals or multiple signals, this model is invalid. For the problems of direction finding with interferometer for wideband signals and multiple signals scene, a frequency domain phase interferometer is proposed and the concrete implementation scheme is given. The proposed method computes the phase difference in frequency domain, and finds multi-target results with judging the spectrum amplitude changing, and uses the frequency phase difference to compute the arrival angle. Theoretical analysis and simulation results show that the proposed method effectively solves the problem of the angle estimation with phase interferometer for wideband signals, and has good performance in multiple signals scene with non-overlapping spectrum or partially overlapping. In addition, the wider the signal bandwidth, the better direction finding performance of this algorithm.

The theory of compressed sensing (CS) provides a new chance to reduce the data acquisition time and improve the data usage factor of the stepped frequency radar system. In light of the sparsity of radar target reflectivity, two imaging methods based on CS, termed the CS-based 2D joint imaging algorithm and the CS-based 2D decoupled imaging algorithm, are proposed. These methods incorporate the coherent mixing operation into the sparse dictionary, and take random measurements in both range and azimuth directions to get high resolution radar images, thus can remarkably reduce the data rate and simplify the hardware design of the radar system while maintaining imaging quality. Experimentsfrom both simulated data and measured data in the anechoic chamber show that the proposed imaging methods can get more focused images than the traditional fast Fourier transform method. Wherein the joint algorithm has stronger robustness and can provide clearer inverse synthetic aperture radar images, while the decoupled algorithm is computationally more efficient but has slightly degraded imaging quality, which can be improved by increasing measurements or using a robuster recovery algorithm nevertheless

In this paper, we propose a beam space coversion (BSC)-based approach to achieve a single near-field signal localization under uniform circular array (UCA). By employing the centro-symmetric geometry of UCA, we apply BSC to extract the two-dimensional (2-D) angles of near-field signal in the Vandermonde form, which allows for azimuth and elevation angle estimation by utilizing the improved estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm. By substituting the calculated 2-D angles into the direction vector of near-field signal, the range parameter can be consequently obtained by the 1-D multiple signal classification (MUSIC) method. Simulations demonstrate that the proposed algorithm can achieve a single near-field signal localization, which can provide satisfactory performance and reduce computational complexity.

Traditional multi-band frequency selective surface (FSS) approaches are hard to achieve a perfect resonance response in a wide band due to the limit of the onset grating lobe frequency determined by the array. To solve this problem, an approach of combining elements in different period to build a hybrid array is presented. The results of series of numerical simulation show that multi-periodicity combined element FSS, which are designed using this approach, usually have much weaker grating lobes than the traditional FSS. Furthermore, their frequency response can be well predicted through the properties of their member element FSS. A prediction method for estimating the degree of expected grating lobe energy loss in designing multi-band FSS using this approach is provided.

The non-minimum phase feature of tail-controlled missile airframes is analyzed. Three selection strategies for desired performance indexes are presented. An acceleration autopilot design methodology based on output feedback and optimization is proposed. Performance and robustness comparisons between the two-loop and classical three-loop topologies are made. Attempts to improve the classical three-loop topology are discussed. Despite the same open-loop structure, the classical three-loop autopilot shows distinct characteristics from a two-loop autopilot with PI compensator. Both the two-loop and three-loop topologies can stabilize a static unstable missile. However, the finite actuator resource is the crucial factor dominating autopilot function.

The wheel brake system safety is a complex problem which refers to its technical state, operating environment, human factors, etc., in aircraft landing taxiing process. Usually, professors consider system safety with traditional probability techniques based on the linear chain of events. However, it could not comprehensively analyze system safety problems, especially in operating environment, interaction of subsystems, and human factors. Thus, we consider system safety as a control problem based on the system-theoretic accident model, the processes (STAMP) model and the system theoretic process analysis (STPA) technique to compensate the deficiency of traditional techniques. Meanwhile, system safety simulation is considered as system control simulation, and Monte Carlo methods are used which consider the range of uncertain parameters and operation deviation to quantitatively study system safety influence factors in control simulation. Firstly, we construct the STAMP model and STPA feedback control loop of the wheel brake system based on the system functional requirement. Then four unsafe control actions are identified, and causes of them are analyzed. Finally, we construct the Monte Carlo simulation model to analyze different scenarios under disturbance. The results provide a basis for choosing corresponding process model variables in constructing the context table and show that appropriate brake strategies could prevent hazards in aircraft landing taxiing.

To address the issue of neglecting scenarios involving joint operations and collaborative drone swarm operations in air combat target intent recognition. This paper proposes a transfer learning-based intention prediction model for drone formation targets in air combat. This model recognizes the intentions of multiple aerial targets by extracting spatial features among the targets at each moment. Simulation results demonstrate that, compared to classical intention recognition models, the proposed model in this paper achieves higher accuracy in identifying the intentions of drone swarm targets in air combat scenarios.

In wideband noncooperative interference cancellation, the reference signals obtained through auxiliary antennas are weighted to cancel with the interference signal. The correlation between the reference signal and the interference signal determines interference cancellation performance, while the auxiliary antenna array affects the correlation by influencing the amplitude and phase of the reference signals. This paper analyzes the effect of auxiliary antenna array on multiple performances of wideband noncooperative interference cancellation. Firstly, the array received signal model of wideband interference is established, and the weight vector coupled with the auxiliary antennas array manifold is solved by spectral analysis and eigen-subspace decomposition. Then, multiple performances which include cancellation resolution, grating null, wideband interference cancellation ratio (ICR), and convergence rate are quantitatively characterized with the auxiliary antenna array. It is obtained through analysis that the performances mutually restrict the auxiliary antenna array. Higher cancellation resolution requires larger array aperture, but when the number of auxiliary antennas is fixed, larger array aperture results in more grating nulls. When the auxiliary antennas are closer to the main antenna, the wideband ICR is improved, but the convergence rate is reduced. The conclusions are verified through simulation of one-dimensional uniform array and two-dimensional nonuniform array. The experiments of three arrays are compared, and the results conform well with simulation and support the theoretical analysis.

A specialized Hungarian algorithm was developed here for the maximum likelihood data association problem with two implementation versions due to presence of false alarms and missed detections. The maximum likelihood data association problem is formulated as a bipartite weighted matching problem. Its duality and the optimality conditions are given. The Hungarian algorithm with its computational steps, data structure and computational complexity is presented. The two implementation versions, Hungarian forest (HF) algorithm and Hungarian tree (HT) algorithm, and their combination with the naïve auction initialization are discussed. The computational results show that HT algorithm is slightly faster than HF algorithm and they are both superior to the classic Munkres algorithm.

Performance-based warranties (PBWs) are widely used in industry and manufacturing. Given that PBW can impose financial burdens on manufacturers, rational maintenance decisions are essential for expanding profit margins. This paper proposes an optimization model for PBW decisions for systems affected by Gamma degradation processes, incorporating periodic inspection. A system performance degradation model is established. Preventive maintenance probability and corrective renewal probability models are developed to calculate expected warranty costs and system availability. A benefits function, which includes incentives, is constructed to optimize the initial and subsequent inspection intervals and preventive maintenance thresholds, thereby maximizing warranty profit. An improved sparrow search algorithm is developed to optimize the model, with a case study on large steam turbine rotor shafts. The results suggest the optimal PBW strategy involves an initial inspection interval of approximately 20 months, with subsequent intervals of about four months, and a preventive maintenance threshold of approximately 37.39 mm wear. When compared to common cost-minimization-based condition maintenance strategies and PBW strategies that do not differentiate between initial and subsequent inspection intervals, the proposed PBW strategy increases the manufacturer’s profit by 1% and 18%, respectively. Sensitivity analyses provide managerial recommendations for PBW implementation. The PBW strategy proposed in this study significantly increases manufacturers’ profits by optimizing inspection intervals and preventive maintenance thresholds, and manufacturers should focus on technological improvement in preventive maintenance and cost control to further enhance earnings.

In this paper, we study the orthogonal time frequency space signal transmission over multi-path channel in the presence of phase noise (PHN) at both sides of millimeter wave (mmWave) communication links. The statistics characteristics of the PHN-induced common phase error and inter-Doppler interference are investigated. Then, a column-shaped pilot structure is designed, and training pilots are used to realize linear-complexity PHN tracking and compensation. Numerical results demonstrate that the proposed scheme enables the signal to noise ratio loss to be restrained within 1 dB in contrast to the no PHN case.

In this paper, the newly-derived maximum correntropy Kalman filter (MCKF) is re-derived from the M-estimation perspective, where the MCKF can be viewed as a special case of the M-estimations and the Gaussian kernel function is a special case of many robust cost functions. Based on the derivation process, a unified form for the robust Gaussian filters (RGF) based on M-estimation is proposed to suppress the outliers and non-Gaussian noise in the measurement. The RGF provides a unified form for one Gaussian filter with different cost functions and a unified form for one robust filter with different approximating methods for the involved Gaussian integrals. Simulation results show that RGF with different weighting functions and different Gaussian integral approximation methods has robust anti-jamming performance.

This paper presents a path planning approach for rotary unmanned aerial vehicles (R-UAVs) in a known static rough terrain environment. This approach aims to find collision-free and feasible paths with minimum altitude, length and angle variable rate. First, a three-dimensional (3D) modeling method is proposed to reduce the computation burden of the dynamic models of R-UAVs. Considering the length, height and tuning angle of a path, the path planning of R-UAVs is described as a tri-objective optimization problem. Then, an improved multi-objective particle swarm optimization algorithm is developed. To render the algorithm more effective in dealing with this problem, a vibration function is introduced into the collided solutions to improve the algorithm efficiency. Meanwhile, the selection of the global best position is taken into account by the reference point method. Finally, the experimental environment is built with the help of the Google map and the 3D terrain generator World Machine. Experimental results under two different rough terrains from Guilin and Lanzhou of China demonstrate the capabilities of the proposed algorithm in finding Pareto optimal paths.

Numerous works prove that existing neighbor-averaging graph neural networks (GNNs) cannot efficiently catch structure features, and many works show that injecting structure, distance, position, or spatial features can significantly improve the performance of GNNs, however, injecting high-level structure and distance into GNNs is an intuitive but untouched idea. This work sheds light on this issue and proposes a scheme to enhance graph attention networks (GATs) by encoding distance and hop-wise structure statistics. Firstly, the hop-wise structure and distributional distance information are extracted based on several hop-wise ego-nets of every target node. Secondly, the derived structure information, distance information, and intrinsic features are encoded into the same vector space and then added together to get initial embedding vectors. Thirdly, the derived embedding vectors are fed into GATs, such as GAT and adaptive graph diffusion network (AGDN) to get the soft labels. Fourthly, the soft labels are fed into correct and smooth (C&S) to conduct label propagation and get final predictions. Experiments show that the distance and hop-wise structures encoding enhanced graph attention networks (DHSEGATs) achieve a competitive result.

To utilizing the characteristic of radar cross section (RCS) of the low detectable aircraft, a special path planning algorithm to eluding radars by the variable RCS is presented. The algorithm first gives the RCS changing model of low detectable aircraft, then establishes a threat model of a ground-based air defense system according to the relations between RCS and the radar range coverage. By the new cost functions of the flight path, which consider both factors of the survival probability and the distance of total route, this path planning method is simulated based on the Dijkstra algorithm, and the planned route meets the flight capacity constraints. Simulation results show that using the effective path planning algorithm, the low detectable aircraft can give full play to its own advantage of stealth to achieve the purpose of silent penetration.

To analyze the behavioral model of the command, control, communication, computer, intelligence, surveillance, reconnaissance (C4ISR) architecture, we propose an executable modeling and analyzing approach to it. First, the meta concept model of the C4ISR architecture is introduced. According to the meta concept model, we construct the executable meta models of the C4ISR architecture by extending the meta models of fUML. Then, we define the concrete syntax and executable activity algebra (EAA) semantics for executable models. The semantics functions are introduced to translating the syntax description of executable models into the item of EAA. To support the execution of models, we propose the executable rules which are the structural operational semantics of EAA. Finally, an area air defense of the C4ISR system is used to illustrate the feasibility of the approach.

Performance degradation or system resource exhaustion can be attributed to inadequate computing resources as a result of software aging. In the real world, the workload of a web server varies with time, which will cause a nonlinear aging phenomenon. The nonlinear property often makes analysis and modelling difficult. Workload is one of the important factors influencing the speed of aging. This paper quantitatively analyzes the workload-aging relation and proposes a framework for aging control under varying workloads. In addition, this paper proposes an approach that employs prior information of workloads to accurately forecast incoming system exhaustion. The workload data are used as a threshold to divide the system resource usage data into multiple sections, while in each section the workload data can be treated as a constant. Each section is described by an individual autoregression (AR) model. Compared with other AR models, the proposed approach can forecast the aging process with a higher accuracy.

The exploration of unmanned aerial vehicle (UAV) swarm systems represents a focal point in the research of multi-agent systems, with the investigation of their fission-fusion behavior holding significant theoretical and practical value. This review systematically examines the methods for fission-fusion of UAV swarms from the perspective of multi-agent systems, encompassing the composition of UAV swarm systems and fission-fusion conditions, information interaction mechanisms, and existing fission-fusion approaches. Firstly, considering the constituent units of UAV swarms and the conditions influencing fission-fusion, this paper categorizes and introduces the UAV swarm systems. It further examines the effects and limitations of fission-fusion methods across various categories and conditions. Secondly, a comprehensive analysis of the prevalent information interaction mechanisms within UAV swarms is conducted from the perspective of information interaction structures. The advantages and limitations of various mechanisms in the context of fission-fusion behaviors are summarized and synthesized. Thirdly, this paper consolidates the existing implementation research findings related to the fission-fusion behavior of UAV swarms, identifies unresolved issues in fission-fusion research, and discusses potential solutions.Finally, the paper concludes with a comprehensive summary and systematically outlines future research opportunities.

A system of systems (SoS) composes a set of independent constituent systems (CSs), where the degree of authority to control the independence of CSs varies, depending on different SoS types. Key researchers describe four SoS types with descending levels of central authority: directed, acknowledged, collaborative and virtual. Although the definitions have been recognized in SoS engineering, what is challenging is the difficulty of translating these definitions into models and simulation environments. Thus, we provide a goal-based method including a mathematical baseline to translate these definitions into more effective agent-based modeling and simulations. First, we construct the theoretical models of CS and SoS. Based on the theoretical models, we analyze the degree of authority influenced by SoS characteristics. Next, we propose a definition of SoS types by quantitatively explaining the degree of authority. Finally, we recognize the differences between acknowledged SoS and collaborative SoS using a migrating waterfowl flock by an agent-based model (ABM) simulation. This paper contributes to the SoS body of knowledge by increasing our understanding of the degree of authority in an SoS, so we may identify suitable SoS types to achieve SoS goals by modeling and simulation.

Fog computing has emerged as an important technology which can improve the performance of computation-intensive and latency-critical communication networks. Nevertheless, the fog computing Internet-of-Things (IoT) systems are susceptible to malicious eavesdropping attacks during the information transmission, and this issue has not been adequately addressed. In this paper, we propose a physical-layer secure fog computing IoT system model, which is able to improve the physical layer security of fog computing IoT networks against the malicious eavesdropping of multiple eavesdroppers. The secrecy rate of the proposed model is analyzed, and the quantum galaxy–based search algorithm (QGSA) is proposed to solve the hybrid task scheduling and resource management problem of the network. The computational complexity and convergence of the proposed algorithm are analyzed. Simulation results validate the efficiency of the proposed model and reveal the influence of various environmental parameters on fog computing IoT networks. Moreover, the simulation results demonstrate that the proposed hybrid task scheduling and resource management scheme can effectively enhance secrecy performance across different communication scenarios.

A three-dimensional path-planning approach has been developed to coordinate multiple fixed-wing unmanned aerial vehicles (UAVs) while avoiding collisions. The hierarchical path-planning architecture that divides the path-planning process into two layers is proposed by designing the velocity-obstacle strategy for satisfying timeliness and effectiveness. The upper-level layer focuses on creating an efficient Dubins initial path considering the dynamic constraints of the fixed wing. Subsequently, the lower-level layer detects potential collisions and adjusts its flight paths to avoid collisions by using the three-dimensional velocity obstacle method, which describes the maneuvering space of collision avoidance as the intersection space of half space. To further handle the dynamic and collision-avoidance constraints, a priority mechanism is designed to ensure that the adjusted path is still feasible for fixed-wing UAVs. Simulation experiments demonstrate the effectiveness of the proposed method.

In the field of automatic target recognition and tracking, traditional image complexity metrics, such as statistical variance and signal-to-noise ratio, all focus on single-frame images. However, there are few researches about the complexity of image sequence. To solve this problem, a criterion of evaluating image sequence complexity is proposed. Firstly, to characterize this criterion quantitatively, two metrics for measuring the complexity of image sequence, namely feature space similarity degree of global background (FSSDGB) and feature space occultation degree of local background (FSODLB) are developed. Here, FSSDGB reflects the ability of global background to introduce false alarms based on feature space, and FSODLB represents the difference between target and local background based on feature space. Secondly, the feature space is optimized by the grey relational method and relevant features are removed so that FSSDGB and FSODLB are more reasonable to establish complexity of single-frame images. Finally, the image sequence complexity is not a linear sum of the single-frame image complexity. Target tracking errors often occur in high-complexity images and the tracking effect of low-complexity images is very well. The nonlinear transformation based on median (NTM) is proposed to construct complexity of image sequence. The experimental results show that the proposed metric is more valid than other metrics, such as sequence correlation (SC) and interframe change degree (IFCD), and it is highly relevant to the actual performance of automatic target tracking algorithms.

In consideration of the field-of-view (FOV) angle constraint, this study focuses on the guidance problem with impact time control. A deep reinforcement learning guidance method is given for the missile to obtain the desired impact time and meet the demand of FOV angle constraint. On basis of the framework of the proportional navigation guidance, an auxiliary control term is supplemented by the distributed deep deterministic policy gradient algorithm, in which the reward functions are developed to decrease the time-to-go error and improve the terminal guidance accuracy. The numerical simulation demonstrates that the missile governed by the presented deep reinforcement learning guidance law can hit the target successfully at appointed arrival time.

Accurate modeling and parameter estimation of sea clutter are fundamental for effective sea surface target detection. With the improvement of radar resolution, sea clutter exhibits a pronounced heavy-tailed characteristic, rendering traditional distribution models and parameter estimation methods less effective. To address this, this paper proposes a dual compound-Gaussian model with inverse Gaussian texture (CG-IG) distribution model and combines it with an improved Adam algorithm to introduce a method for parameter correction. This method effectively fits sea clutter with heavy-tailed characteristics. Experiments with real measured sea clutter data show that the dual CG-IG distribution model, after parameter correction, accurately describes the heavy-tailed phenomenon in sea clutter amplitude distribution, and the overall mean square error of the distribution is reduced.

In this paper, an online midcourse guidance method for intercepting high-speed maneuvering targets is proposed. Firstly, the affine system is used to build a dynamic model and analyze the state constraints. The midcourse guidance problem is transformed into a continuous time optimization problem. Secondly, the problem is transformed into a discrete convex programming problem by affine control variable relaxation, Gaussian pseudospectral discretization and constraints linearization. Then, the off-line midcourse guidance trajectory is generated before midcourse guidance. It is used as the initial reference trajectory for online correction of midcourse guidance. An online guidance framework is used to eliminate the error caused by calculation of guidance instruction time. And the design of discrete points decreases with flight time to improve the solving efficiency. In addition, it is proposed that the terminal guidance capture is used innovatively space to judge the success of midcourse guidance. Numerical simulation shows the feasibility and effectiveness of the proposed method.

The consensus problem of the distributed attitude synchronization in the spacecraft formation flying is considered. Firstly, the attitude dynamics of a rigid body spacecraft is described by modified Rodriguez parameters (MRPs). Then global stable distributed cooperative attitude control laws are proposed for different cases. In the first case, the control law guarantees the state consensus during the attitude synchronization. In the second case, the control law ensures both the attitudes synchronizing to a desired constant attitude and the angular velocities converging at zero. In the third case, an attitude consensus control law with bounded control input is proposed. Finally, the effectiveness and validity of the control laws are demonstrated by simulations of six rigid bodies formation flying.

Magnetic field gradient tensor measurement is an important technique to obtain position information of magnetic objects. When using magnetic field sensors to measure magnetic field gradient as the coefficients of tensor, field differentiation is generally approximated by field difference. As a result, magnetic objects positioning by magnetic field gradient tensor measurement always involves an inherent error caused by sensor sizes, leading to a reduction in detectable distance and detectable angle. In this paper, the inherent positioning error caused by magnetic field gradient tensor measurement is calculated and corrected by iterations based on the systematic position error distribution patterns. The results show that, the detectable distance range and the angle range of an ac magnetic object (2.44 Am$ \bf^2 $ @1 kHz) can be increased from (0.45 m, 0.75 m), (0$ ^\circ $, 25$ ^\circ $) to (0.30 m, 0.80 m), (0$ ^\circ $, 80$ ^\circ $), respectively.

Two improved structures of high resolution digital pulse width modulator (DPWM) control circuit are proposed. Embedded digital clock manager (DCM) blocks and digital programmable delay circuits are employed as the basic resources to construct the field-programmable gate array (FPGA)-based DPWM implementations. Detailed schemes are illustrated and the circuits have been successfully implemented on the Artix-7 FPGA device developed by Xilinx. Experimental results show that when the basic clock operates at the frequency of 200 MHz, the resolutions of the two approaches can reach 625 ps and 500 ps, respectively. Besides, the presented schemes possess other merits including flexible resolution, strong versatility and relatively good stability.

It is unpractical to learn the optimal structure of a big Bayesian network (BN) by exhausting the feasible structures, since the number of feasible structures is super exponential on the number of nodes. This paper proposes an approach to layer nodes of a BN by using the conditional independence testing. The parents of a node layer only belong to the layer, or layers who have priority over the layer. When a set of nodes has been layered, the number of feasible structures over the nodes can be remarkably reduced, which makes it possible to learn optimal BN structures for bigger sizes of nodes by accurate algorithms. Integrating the dynamic programming (DP) algorithm with the layering approach, we propose a hybrid algorithm—layered optimal learning (LOL) to learn BN structures. Benefitted by the layering approach, the complexity of the DP algorithm reduces to O(ρ2^n-1) from O(n2^n-1), where ρ < n. Meanwhile, the memory requirements for storing intermediate results are limited to $O(C_{k^\# }^{{{k^\# } \over 2}})$ from $O(C_n^{{n \over 2}} )$, where k^# < n. A case study on learning a standard BN with 50 nodes is conducted. The results demonstrate the superiority of the LOL algorithm, with respect to the Bayesian information criterion (BIC) score criterion, over the hill-climbing, max-min hill-climbing, PC, and three-phrase dependency analysis algorithms.

Complex systems widely exist in nature and human society. There are complex interactions between system elements in a complex system, and systems show complex features at the macro level, such as emergence, self-organization, uncertainty, and dynamics. These complex features make it difficult to understand the internal operation mechanism of complex systems. Networked modeling of complex systems is a favorable means of understanding complex systems. It not only represents complex interactions but also reflects essential attributes of complex systems. This paper summarizes the research progress of complex systems modeling and analysis from the perspective of network science, including networked modeling, vital node analysis, network invulnerability analysis, network disintegration analysis, resilience analysis, complex network link prediction, and the attacker-defender game in complex networks. In addition, this paper presents some points of view on the trend and focus of future research on network analysis of complex systems.