This paper presents an Eulerian-Lagrangian algorithm for direct numerical simulation(DNS)of particle-laden flows.The algorithm is applicable to perform simulations of dilute suspensions of small inertial particles in ...This paper presents an Eulerian-Lagrangian algorithm for direct numerical simulation(DNS)of particle-laden flows.The algorithm is applicable to perform simulations of dilute suspensions of small inertial particles in turbulent carrier flow.The Eulerian framework numerically resolves turbulent carrier flow using a parallelized,finite-volume DNS solver on a staggered Cartesian grid.Particles are tracked using a point-particle method utilizing a Lagrangian particle tracking(LPT)algorithm.The proposed Eulerian-Lagrangian algorithm is validated using an inertial particle-laden turbulent channel flow for different Stokes number cases.The particle concentration profiles and higher-order statistics of the carrier and dispersed phases agree well with the benchmark results.We investigated the effect of fluid velocity interpolation and numerical integration schemes of particle tracking algorithms on particle dispersion statistics.The suitability of fluid velocity interpolation schemes for predicting the particle dispersion statistics is discussed in the framework of the particle tracking algorithm coupled to the finite-volume solver.In addition,we present parallelization strategies implemented in the algorithm and evaluate their parallel performance.展开更多
Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algeb...Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algebras and tri-associative algebras.We introduce the notion of a quad-dendriform algebra,which is a splitting of a di-associative algebra.We show that a relative averaging operator on dendriform algebras gives rise to a quad-dendriform algebra.Furthermore,we introduce the notion of six-dendriform algebras,which are splittings of the tri-associative algebras,and demonstrate that homomorphic relative averaging operators induce six-dendriform algebras.展开更多
This paper introduces a novel nature-inspired metaheuristic algorithm called the Gekko japonicus algorithm.The algo-rithm draws inspiration mainly from the predation strategies and survival behaviors of the Gekko japo...This paper introduces a novel nature-inspired metaheuristic algorithm called the Gekko japonicus algorithm.The algo-rithm draws inspiration mainly from the predation strategies and survival behaviors of the Gekko japonicus.The math-ematical model is developed by simulating various biological behaviors of the Gekko japonicus,such as hybrid loco-motion patterns,directional olfactory guidance,implicit group advantage tendencies,and the tail autotomy mechanism.By integrating multi-stage mutual constraints and dynamically adjusting parameters,GJA maintains an optimal balance between global exploration and local exploitation,thereby effectively solving complex optimization problems.To assess the performance of GJA,comparative analyses were performed against fourteen state-of-the-art metaheuristic algorithms using the CEC2017 and CEC2022 benchmark test sets.Additionally,a Friedman test was performed on the experimen-tal results to assess the statistical significance of differences between various algorithms.And GJA was evaluated using multiple qualitative indicators,further confirming its superiority in exploration and exploitation.Finally,GJA was utilized to solve four engineering optimization problems and further implemented in robotic path planning to verify its practical applicability.Experimental results indicate that,compared to other high-performance algorithms,GJA demonstrates excep-tional performance as a powerful optimization algorithm in complex optimization problems.We make the code publicly available at:https://github.com/zhy1109/Gekko-japonicusalgorithm.展开更多
The Intrusion Detection System(IDS)is a security mechanism developed to observe network traffic and recognize suspicious or malicious activities.Clustering algorithms are often incorporated into IDS;however,convention...The Intrusion Detection System(IDS)is a security mechanism developed to observe network traffic and recognize suspicious or malicious activities.Clustering algorithms are often incorporated into IDS;however,conventional clustering-based methods face notable drawbacks,including poor scalability in handling high-dimensional datasets and a strong dependence of outcomes on initial conditions.To overcome the performance limitations of existing methods,this study proposes a novel quantum-inspired clustering algorithm that relies on a similarity coefficient-based quantum genetic algorithm(SC-QGA)and an improved quantum artificial bee colony algorithm hybrid K-means(IQABC-K).First,the SC-QGA algorithmis constructed based on quantum computing and integrates similarity coefficient theory to strengthen genetic diversity and feature extraction capabilities.For the subsequent clustering phase,the process based on the IQABC-K algorithm is enhanced with the core improvement of adaptive rotation gate and movement exploitation strategies to balance the exploration capabilities of global search and the exploitation capabilities of local search.Simultaneously,the acceleration of convergence toward the global optimum and a reduction in computational complexity are facilitated by means of the global optimum bootstrap strategy and a linear population reduction strategy.Through experimental evaluation with multiple algorithms and diverse performance metrics,the proposed algorithm confirms reliable accuracy on three datasets:KDD CUP99,NSL_KDD,and UNSW_NB15,achieving accuracy of 98.57%,98.81%,and 98.32%,respectively.These results affirm its potential as an effective solution for practical clustering applications.展开更多
In this paper,we propose a new privacy-aware transmission scheduling algorithm for 6G ad hoc networks.This system enables end nodes to select the optimum time and scheme to transmit private data safely.In 6G dynamic h...In this paper,we propose a new privacy-aware transmission scheduling algorithm for 6G ad hoc networks.This system enables end nodes to select the optimum time and scheme to transmit private data safely.In 6G dynamic heterogeneous infrastructures,unstable links and non-uniform hardware capabilities create critical issues regarding security and privacy.Traditional protocols are often too computationally heavy to allow 6G services to achieve their expected Quality-of-Service(QoS).As the transport network is built of ad hoc nodes,there is no guarantee about their trustworthiness or behavior,and transversal functionalities are delegated to the extreme nodes.However,while security can be guaranteed in extreme-to-extreme solutions,privacy cannot,as all intermediate nodes still have to handle the data packets they are transporting.Besides,traditional schemes for private anonymous ad hoc communications are vulnerable against modern intelligent attacks based on learning models.The proposed scheme fulfills this gap.Findings show the probability of a successful intelligent attack reduces by up to 65%compared to ad hoc networks with no privacy protection strategy when used the proposed technology.While congestion probability can remain below 0.001%,as required in 6G services.展开更多
This paper proposes an equivalent modeling method for photovoltaic(PV)power stations via a particle swarm optimization(PSO)K-means clustering(KMC)algorithm with passive filter parameter clustering to address the compl...This paper proposes an equivalent modeling method for photovoltaic(PV)power stations via a particle swarm optimization(PSO)K-means clustering(KMC)algorithm with passive filter parameter clustering to address the complexities,simulation time cost and convergence problems of detailed PV power station models.First,the amplitude–frequency curves of different filter parameters are analyzed.Based on the results,a grouping parameter set for characterizing the external filter characteristics is established.These parameters are further defined as clustering parameters.A single PV inverter model is then established as a prerequisite foundation.The proposed equivalent method combines the global search capability of PSO with the rapid convergence of KMC,effectively overcoming the tendency of KMC to become trapped in local optima.This approach enhances both clustering accuracy and numerical stability when determining equivalence for PV inverter units.Using the proposed clustering method,both a detailed PV power station model and an equivalent model are developed and compared.Simulation and hardwarein-loop(HIL)results based on the equivalent model verify that the equivalent method accurately represents the dynamic characteristics of PVpower stations and adapts well to different operating conditions.The proposed equivalent modeling method provides an effective analysis tool for future renewable energy integration research.展开更多
Engineering optimization problems are often characterized by high dimensionality,constraints,and complex,multimodal landscapes.Traditional deterministic methods frequently struggle under such conditions,prompting incr...Engineering optimization problems are often characterized by high dimensionality,constraints,and complex,multimodal landscapes.Traditional deterministic methods frequently struggle under such conditions,prompting increased interest in swarm intelligence algorithms.Among these,the Cuckoo Search(CS)algorithm stands out for its promising global search capabilities.However,it often suffers from premature convergence when tackling complex problems.To address this limitation,this paper proposes a Grouped Dynamic Adaptive CS(GDACS)algorithm.Theenhancements incorporated intoGDACS can be summarized into two key aspects.Firstly,a chaotic map is employed to generate initial solutions,leveraging the inherent randomness of chaotic sequences to ensure a more uniform distribution across the search space and enhance population diversity from the outset.Secondly,Cauchy and Levy strategies replace the standard CS population update.This strategy involves evaluating the fitness of candidate solutions to dynamically group the population based on performance.Different step-size adaptation strategies are then applied to distinct groups,enabling an adaptive search mechanism that balances exploration and exploitation.Experiments were conducted on six benchmark functions and four constrained engineering design problems,and the results indicate that the proposed GDACS achieves good search efficiency and produces more accurate optimization results compared with other state-of-the-art algorithms.展开更多
With the rapid development of intelligent navigation technology,efficient and safe path planning for mobile robots has become a core requirement.To address the challenges of complex dynamic environments,this paper pro...With the rapid development of intelligent navigation technology,efficient and safe path planning for mobile robots has become a core requirement.To address the challenges of complex dynamic environments,this paper proposes an intelligent path planning framework based on grid map modeling.First,an improved Safe and Smooth A*(SSA*)algorithm is employed for global path planning.By incorporating obstacle expansion and cornerpoint optimization,the proposed SSA*enhances the safety and smoothness of the planned path.Then,a Partitioned Dynamic Window Approach(PDWA)is integrated for local planning,which is triggered when dynamic or sudden static obstacles appear,enabling real-time obstacle avoidance and path adjustment.A unified objective function is constructed,considering path length,safety,and smoothness comprehensively.Multiple simulation experiments are conducted on typical port grid maps.The results demonstrate that the improved SSA*significantly reduces the number of expanded nodes and computation time in static environmentswhile generating smoother and safer paths.Meanwhile,the PDWA exhibits strong real-time performance and robustness in dynamic scenarios,achieving shorter paths and lower planning times compared to other graph search algorithms.The proposedmethodmaintains stable performance across maps of different scales and various port scenarios,verifying its practicality and potential for wider application.展开更多
Existing feature selection methods for intrusion detection systems in the Industrial Internet of Things often suffer from local optimality and high computational complexity.These challenges hinder traditional IDS from...Existing feature selection methods for intrusion detection systems in the Industrial Internet of Things often suffer from local optimality and high computational complexity.These challenges hinder traditional IDS from effectively extracting features while maintaining detection accuracy.This paper proposes an industrial Internet ofThings intrusion detection feature selection algorithm based on an improved whale optimization algorithm(GSLDWOA).The aim is to address the problems that feature selection algorithms under high-dimensional data are prone to,such as local optimality,long detection time,and reduced accuracy.First,the initial population’s diversity is increased using the Gaussian Mutation mechanism.Then,Non-linear Shrinking Factor balances global exploration and local development,avoiding premature convergence.Lastly,Variable-step Levy Flight operator and Dynamic Differential Evolution strategy are introduced to improve the algorithm’s search efficiency and convergence accuracy in highdimensional feature space.Experiments on the NSL-KDD and WUSTL-IIoT-2021 datasets demonstrate that the feature subset selected by GSLDWOA significantly improves detection performance.Compared to the traditional WOA algorithm,the detection rate and F1-score increased by 3.68%and 4.12%.On the WUSTL-IIoT-2021 dataset,accuracy,recall,and F1-score all exceed 99.9%.展开更多
Concrete-filled steel tubes(CFST)are widely utilized in civil engineering due to their superior load-bearing capacity,ductility,and seismic resistance.However,existing design codes,such as AISC and Eurocode 4,tend to ...Concrete-filled steel tubes(CFST)are widely utilized in civil engineering due to their superior load-bearing capacity,ductility,and seismic resistance.However,existing design codes,such as AISC and Eurocode 4,tend to be excessively conservative as they fail to account for the composite action between the steel tube and the concrete core.To address this limitation,this study proposes a hybrid model that integrates XGBoost with the Pied Kingfisher Optimizer(PKO),a nature-inspired algorithm,to enhance the accuracy of shear strength prediction for CFST columns.Additionally,quantile regression is employed to construct prediction intervals for the ultimate shear force,while the Asymmetric Squared Error Loss(ASEL)function is incorporated to mitigate overestimation errors.The computational results demonstrate that the PKO-XGBoost model delivers superior predictive accuracy,achieving a Mean Absolute Percentage Error(MAPE)of 4.431%and R2 of 0.9925 on the test set.Furthermore,the ASEL-PKO-XGBoost model substantially reduces overestimation errors to 28.26%,with negligible impact on predictive performance.Additionally,based on the Genetic Algorithm(GA)and existing equation models,a strength equation model is developed,achieving markedly higher accuracy than existing models(R^(2)=0.934).Lastly,web-based Graphical User Interfaces(GUIs)were developed to enable real-time prediction.展开更多
Optimization problems are prevalent in various fields of science and engineering,with several real-world applications characterized by high dimensionality and complex search landscapes.Starfish optimization algorithm(...Optimization problems are prevalent in various fields of science and engineering,with several real-world applications characterized by high dimensionality and complex search landscapes.Starfish optimization algorithm(SFOA)is a recently optimizer inspired by swarm intelligence,which is effective for numerical optimization,but it may encounter premature and local convergence for complex optimization problems.To address these challenges,this paper proposes the multi-strategy enhanced crested porcupine-starfish optimization algorithm(MCPSFOA).The core innovation of MCPSFOA lies in employing a hybrid strategy to improve SFOA,which integrates the exploratory mechanisms of SFOA with the diverse search capacity of the Crested Porcupine Optimizer(CPO).This synergy enhances MCPSFOA’s ability to navigate complex and multimodal search spaces.To further prevent premature convergence,MCPSFOA incorporates Lévy flight,leveraging its characteristic long and short jump patterns to enable large-scale exploration and escape from local optima.Subsequently,Gaussian mutation is applied for precise solution tuning,introducing controlled perturbations that enhance accuracy and mitigate the risk of insufficient exploitation.Notably,the population diversity enhancement mechanism periodically identifies and resets stagnant individuals,thereby consistently revitalizing population variety throughout the optimization process.MCPSFOA is rigorously evaluated on 24 classical benchmark functions(including high-dimensional cases),the CEC2017 suite,and the CEC2022 suite.MCPSFOA achieves superior overall performance with Friedman mean ranks of 2.208,2.310 and 2.417 on these benchmark functions,outperforming 11 state-of-the-art algorithms.Furthermore,the practical applicability of MCPSFOA is confirmed through its successful application to five engineering optimization cases,where it also yields excellent results.In conclusion,MCPSFOA is not only a highly effective and reliable optimizer for benchmark functions,but also a practical tool for solving real-world optimization problems.展开更多
Early and accurate detection of bone cancer and marrow cell abnormalities is critical for timely intervention and improved patient outcomes.This paper proposes a novel hybrid deep learning framework that integrates a ...Early and accurate detection of bone cancer and marrow cell abnormalities is critical for timely intervention and improved patient outcomes.This paper proposes a novel hybrid deep learning framework that integrates a Convolutional Neural Network(CNN)with a Bidirectional Long Short-Term Memory(BiLSTM)architecture,optimized using the Firefly Optimization algorithm(FO).The proposed CNN-BiLSTM-FO model is tailored for structured biomedical data,capturing both local patterns and sequential dependencies in diagnostic features,while the Firefly Algorithm fine-tunes key hyperparameters to maximize predictive performance.The approach is evaluated on two benchmark biomedical datasets:one comprising diagnostic data for bone cancer detection and another for identifying marrow cell abnormalities.Experimental results demonstrate that the proposed method outperforms standard deep learning models,including CNN,LSTM,BiLSTM,and CNN-LSTM hybrids,significantly.The CNNBiLSTM-FO model achieves an accuracy of 98.55%for bone cancer detection and 96.04%for marrow abnormality classification.The paper also presents a detailed complexity analysis of the proposed algorithm and compares its performance across multiple evaluation metrics such as precision,recall,F1-score,and AUC.The results confirm the effectiveness of the firefly-based optimization strategy in improving classification accuracy and model robustness.This work introduces a scalable and accurate diagnostic solution that holds strong potential for integration into intelligent clinical decision-support systems.展开更多
In this paper,we propose a new full-Newton step feasible interior-point algorithm for the special weighted linear complementarity problems.The proposed algorithm employs the technique of algebraic equivalent transform...In this paper,we propose a new full-Newton step feasible interior-point algorithm for the special weighted linear complementarity problems.The proposed algorithm employs the technique of algebraic equivalent transformation to derive the search direction.It is shown that the proximity measure reduces quadratically at each iteration.Moreover,the iteration bound of the algorithm is as good as the best-known polynomial complexity for these types of problems.Furthermore,numerical results are presented to show the efficiency of the proposed algorithm.展开更多
Optimizing convolutional neural networks(CNNs)for IoT attack detection remains a critical yet challenging task due to the need to balance multiple performance metrics beyond mere accuracy.This study proposes a unified...Optimizing convolutional neural networks(CNNs)for IoT attack detection remains a critical yet challenging task due to the need to balance multiple performance metrics beyond mere accuracy.This study proposes a unified and flexible optimization framework that leverages metaheuristic algorithms to automatically optimize CNN configurations for IoT attack detection.Unlike conventional single-objective approaches,the proposed method formulates a global multi-objective fitness function that integrates accuracy,precision,recall,and model size(speed/model complexity penalty)with adjustable weights.This design enables both single-objective and weightedsum multi-objective optimization,allowing adaptive selection of optimal CNN configurations for diverse deployment requirements.Two representativemetaheuristic algorithms,GeneticAlgorithm(GA)and Particle Swarm Optimization(PSO),are employed to optimize CNNhyperparameters and structure.At each generation/iteration,the best configuration is selected as themost balanced solution across optimization objectives,i.e.,the one achieving themaximum value of the global objective function.Experimental validation on two benchmark datasets,Edge-IIoT and CIC-IoT2023,demonstrates that the proposed GA-and PSO-based models significantly enhance detection accuracy(94.8%–98.3%)and generalization compared with manually tuned CNN configurations,while maintaining compact architectures.The results confirm that the multi-objective framework effectively balances predictive performance and computational efficiency.This work establishes a generalizable and adaptive optimization strategy for deep learning-based IoT attack detection and provides a foundation for future hybrid metaheuristic extensions in broader IoT security applications.展开更多
Precisely estimating the state of health(SOH)of lithium-ion batteries is essential for battery management systems(BMS),as it plays a key role in ensuring the safe and reliable operation of battery systems.However,curr...Precisely estimating the state of health(SOH)of lithium-ion batteries is essential for battery management systems(BMS),as it plays a key role in ensuring the safe and reliable operation of battery systems.However,current SOH estimation methods often overlook the valuable temperature information that can effectively characterize battery aging during capacity degradation.Additionally,the Elman neural network,which is commonly employed for SOH estimation,exhibits several drawbacks,including slow training speed,a tendency to become trapped in local minima,and the initialization of weights and thresholds using pseudo-random numbers,leading to unstable model performance.To address these issues,this study addresses the challenge of precise and effective SOH detection by proposing a method for estimating the SOH of lithium-ion batteries based on differential thermal voltammetry(DTV)and an SSA-Elman neural network.Firstly,two health features(HFs)considering temperature factors and battery voltage are extracted fromthe differential thermal voltammetry curves and incremental capacity curves.Next,the Sparrow Search Algorithm(SSA)is employed to optimize the initial weights and thresholds of the Elman neural network,forming the SSA-Elman neural network model.To validate the performance,various neural networks,including the proposed SSA-Elman network,are tested using the Oxford battery aging dataset.The experimental results demonstrate that the method developed in this study achieves superior accuracy and robustness,with a mean absolute error(MAE)of less than 0.9%and a rootmean square error(RMSE)below 1.4%.展开更多
Complex network models are frequently employed for simulating and studyingdiverse real-world complex systems.Among these models,scale-free networks typically exhibit greater fragility to malicious attacks.Consequently...Complex network models are frequently employed for simulating and studyingdiverse real-world complex systems.Among these models,scale-free networks typically exhibit greater fragility to malicious attacks.Consequently,enhancing the robustness of scale-free networks has become a pressing issue.To address this problem,this paper proposes a Multi-Granularity Integration Algorithm(MGIA),which aims to improve the robustness of scale-free networks while keeping the initial degree of each node unchanged,ensuring network connectivity and avoiding the generation of multiple edges.The algorithm generates a multi-granularity structure from the initial network to be optimized,then uses different optimization strategies to optimize the networks at various granular layers in this structure,and finally realizes the information exchange between different granular layers,thereby further enhancing the optimization effect.We propose new network refresh,crossover,and mutation operators to ensure that the optimized network satisfies the given constraints.Meanwhile,we propose new network similarity and network dissimilarity evaluation metrics to improve the effectiveness of the optimization operators in the algorithm.In the experiments,the MGIA enhances the robustness of the scale-free network by 67.6%.This improvement is approximately 17.2%higher than the optimization effects achieved by eight currently existing complex network robustness optimization algorithms.展开更多
Accurate short-term wind power forecast technique plays a crucial role in maintaining the safety and economic efficiency of smart grids.Although numerous studies have employed various methods to forecast wind power,th...Accurate short-term wind power forecast technique plays a crucial role in maintaining the safety and economic efficiency of smart grids.Although numerous studies have employed various methods to forecast wind power,there remains a research gap in leveraging swarm intelligence algorithms to optimize the hyperparameters of the Transformer model for wind power prediction.To improve the accuracy of short-term wind power forecast,this paper proposes a hybrid short-term wind power forecast approach named STL-IAOA-iTransformer,which is based on seasonal and trend decomposition using LOESS(STL)and iTransformer model optimized by improved arithmetic optimization algorithm(IAOA).First,to fully extract the power data features,STL is used to decompose the original data into components with less redundant information.The extracted components as well as the weather data are then input into iTransformer for short-term wind power forecast.The final predicted short-term wind power curve is obtained by combining the predicted components.To improve the model accuracy,IAOA is employed to optimize the hyperparameters of iTransformer.The proposed approach is validated using real-generation data from different seasons and different power stations inNorthwest China,and ablation experiments have been conducted.Furthermore,to validate the superiority of the proposed approach under different wind characteristics,real power generation data fromsouthwestChina are utilized for experiments.Thecomparative results with the other six state-of-the-art prediction models in experiments show that the proposed model well fits the true value of generation series and achieves high prediction accuracy.展开更多
In disaster relief operations,multiple UAVs can be used to search for trapped people.In recent years,many researchers have proposed machine le arning-based algorithms,sampling-based algorithms,and heuristic algorithms...In disaster relief operations,multiple UAVs can be used to search for trapped people.In recent years,many researchers have proposed machine le arning-based algorithms,sampling-based algorithms,and heuristic algorithms to solve the problem of multi-UAV path planning.The Dung Beetle Optimization(DBO)algorithm has been widely applied due to its diverse search patterns in the above algorithms.However,the update strategies for the rolling and thieving dung beetles of the DBO algorithm are overly simplistic,potentially leading to an inability to fully explore the search space and a tendency to converge to local optima,thereby not guaranteeing the discovery of the optimal path.To address these issues,we propose an improved DBO algorithm guided by the Landmark Operator(LODBO).Specifically,we first use tent mapping to update the population strategy,which enables the algorithm to generate initial solutions with enhanced diversity within the search space.Second,we expand the search range of the rolling ball dung beetle by using the landmark factor.Finally,by using the adaptive factor that changes with the number of iterations.,we improve the global search ability of the stealing dung beetle,making it more likely to escape from local optima.To verify the effectiveness of the proposed method,extensive simulation experiments are conducted,and the result shows that the LODBO algorithm can obtain the optimal path using the shortest time compared with the Genetic Algorithm(GA),the Gray Wolf Optimizer(GWO),the Whale Optimization Algorithm(WOA)and the original DBO algorithm in the disaster search and rescue task set.展开更多
The development of algebraic and numerical algorithms is a kind of complicated creative work and it is difficult to guarantee the correctness of the algorithms. This paper introduces a systematic and unified formal de...The development of algebraic and numerical algorithms is a kind of complicated creative work and it is difficult to guarantee the correctness of the algorithms. This paper introduces a systematic and unified formal development method of algebraic and numerical algorithms. The method implements the complete refinement process from abstract specifications to a concrete executable program. It uses the core idea of partition and recursion for formal derivation and combines the mathematical induction based on strict mathematical logic with Hoare axiom for correctness verification. This development method converts creative work into non-creative work as much as possible while ensuring the correctness of the algorithm, which can not only verify the correctness of the existing algebraic and numerical algorithms but also guide the development of efficient unknown algorithms for such problems. This paper takes the non-recursive implementation of the Extended Euclidean Algorithm and Horner's method as examples. Therefore, the effectiveness and feasibility of this method are further verified.展开更多
基金supported by the P.G.Senapathy Center for Computing Resources at IIT Madrasfunding provided by the Ministry of Education,Government of Indiasupported by the National Natural Science Foundation of China(Grant Nos.12388101,12472224 and 92252104).
文摘This paper presents an Eulerian-Lagrangian algorithm for direct numerical simulation(DNS)of particle-laden flows.The algorithm is applicable to perform simulations of dilute suspensions of small inertial particles in turbulent carrier flow.The Eulerian framework numerically resolves turbulent carrier flow using a parallelized,finite-volume DNS solver on a staggered Cartesian grid.Particles are tracked using a point-particle method utilizing a Lagrangian particle tracking(LPT)algorithm.The proposed Eulerian-Lagrangian algorithm is validated using an inertial particle-laden turbulent channel flow for different Stokes number cases.The particle concentration profiles and higher-order statistics of the carrier and dispersed phases agree well with the benchmark results.We investigated the effect of fluid velocity interpolation and numerical integration schemes of particle tracking algorithms on particle dispersion statistics.The suitability of fluid velocity interpolation schemes for predicting the particle dispersion statistics is discussed in the framework of the particle tracking algorithm coupled to the finite-volume solver.In addition,we present parallelization strategies implemented in the algorithm and evaluate their parallel performance.
基金Supported by the Science and Technology Program of Guizhou Province(Grant No.QKHJC QN[2025]362)the National Natural Science Foundation of China(Grant No.12361005).
文摘Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algebras and tri-associative algebras.We introduce the notion of a quad-dendriform algebra,which is a splitting of a di-associative algebra.We show that a relative averaging operator on dendriform algebras gives rise to a quad-dendriform algebra.Furthermore,we introduce the notion of six-dendriform algebras,which are splittings of the tri-associative algebras,and demonstrate that homomorphic relative averaging operators induce six-dendriform algebras.
基金CHINA POSTDOCTORAL SCIENCE FOUNDATION(Grant No.2025M771925)Young Scientists Fund(C Class)(Grant No.32501636)Special Fund of Fundamental Scientific Research Business Expense for Higher School of Central Government(Grant No.2572025JT04).
文摘This paper introduces a novel nature-inspired metaheuristic algorithm called the Gekko japonicus algorithm.The algo-rithm draws inspiration mainly from the predation strategies and survival behaviors of the Gekko japonicus.The math-ematical model is developed by simulating various biological behaviors of the Gekko japonicus,such as hybrid loco-motion patterns,directional olfactory guidance,implicit group advantage tendencies,and the tail autotomy mechanism.By integrating multi-stage mutual constraints and dynamically adjusting parameters,GJA maintains an optimal balance between global exploration and local exploitation,thereby effectively solving complex optimization problems.To assess the performance of GJA,comparative analyses were performed against fourteen state-of-the-art metaheuristic algorithms using the CEC2017 and CEC2022 benchmark test sets.Additionally,a Friedman test was performed on the experimen-tal results to assess the statistical significance of differences between various algorithms.And GJA was evaluated using multiple qualitative indicators,further confirming its superiority in exploration and exploitation.Finally,GJA was utilized to solve four engineering optimization problems and further implemented in robotic path planning to verify its practical applicability.Experimental results indicate that,compared to other high-performance algorithms,GJA demonstrates excep-tional performance as a powerful optimization algorithm in complex optimization problems.We make the code publicly available at:https://github.com/zhy1109/Gekko-japonicusalgorithm.
基金supported by the NSFC(Grant Nos.62176273,62271070,62441212)The Open Foundation of State Key Laboratory of Networking and Switching Technology(Beijing University of Posts and Telecommunications)under Grant SKLNST-2024-1-062025Major Project of the Natural Science Foundation of Inner Mongolia(2025ZD008).
文摘The Intrusion Detection System(IDS)is a security mechanism developed to observe network traffic and recognize suspicious or malicious activities.Clustering algorithms are often incorporated into IDS;however,conventional clustering-based methods face notable drawbacks,including poor scalability in handling high-dimensional datasets and a strong dependence of outcomes on initial conditions.To overcome the performance limitations of existing methods,this study proposes a novel quantum-inspired clustering algorithm that relies on a similarity coefficient-based quantum genetic algorithm(SC-QGA)and an improved quantum artificial bee colony algorithm hybrid K-means(IQABC-K).First,the SC-QGA algorithmis constructed based on quantum computing and integrates similarity coefficient theory to strengthen genetic diversity and feature extraction capabilities.For the subsequent clustering phase,the process based on the IQABC-K algorithm is enhanced with the core improvement of adaptive rotation gate and movement exploitation strategies to balance the exploration capabilities of global search and the exploitation capabilities of local search.Simultaneously,the acceleration of convergence toward the global optimum and a reduction in computational complexity are facilitated by means of the global optimum bootstrap strategy and a linear population reduction strategy.Through experimental evaluation with multiple algorithms and diverse performance metrics,the proposed algorithm confirms reliable accuracy on three datasets:KDD CUP99,NSL_KDD,and UNSW_NB15,achieving accuracy of 98.57%,98.81%,and 98.32%,respectively.These results affirm its potential as an effective solution for practical clustering applications.
基金funding from the European Commission by the Ruralities project(grant agreement no.101060876).
文摘In this paper,we propose a new privacy-aware transmission scheduling algorithm for 6G ad hoc networks.This system enables end nodes to select the optimum time and scheme to transmit private data safely.In 6G dynamic heterogeneous infrastructures,unstable links and non-uniform hardware capabilities create critical issues regarding security and privacy.Traditional protocols are often too computationally heavy to allow 6G services to achieve their expected Quality-of-Service(QoS).As the transport network is built of ad hoc nodes,there is no guarantee about their trustworthiness or behavior,and transversal functionalities are delegated to the extreme nodes.However,while security can be guaranteed in extreme-to-extreme solutions,privacy cannot,as all intermediate nodes still have to handle the data packets they are transporting.Besides,traditional schemes for private anonymous ad hoc communications are vulnerable against modern intelligent attacks based on learning models.The proposed scheme fulfills this gap.Findings show the probability of a successful intelligent attack reduces by up to 65%compared to ad hoc networks with no privacy protection strategy when used the proposed technology.While congestion probability can remain below 0.001%,as required in 6G services.
基金supported by the Research Project of China Southern Power Grid(No.056200KK52222031).
文摘This paper proposes an equivalent modeling method for photovoltaic(PV)power stations via a particle swarm optimization(PSO)K-means clustering(KMC)algorithm with passive filter parameter clustering to address the complexities,simulation time cost and convergence problems of detailed PV power station models.First,the amplitude–frequency curves of different filter parameters are analyzed.Based on the results,a grouping parameter set for characterizing the external filter characteristics is established.These parameters are further defined as clustering parameters.A single PV inverter model is then established as a prerequisite foundation.The proposed equivalent method combines the global search capability of PSO with the rapid convergence of KMC,effectively overcoming the tendency of KMC to become trapped in local optima.This approach enhances both clustering accuracy and numerical stability when determining equivalence for PV inverter units.Using the proposed clustering method,both a detailed PV power station model and an equivalent model are developed and compared.Simulation and hardwarein-loop(HIL)results based on the equivalent model verify that the equivalent method accurately represents the dynamic characteristics of PVpower stations and adapts well to different operating conditions.The proposed equivalent modeling method provides an effective analysis tool for future renewable energy integration research.
基金supported in part by the Ministry of Higher Education Malaysia(MOHE)through Fundamental Research Grant Scheme(FRGS)Ref:FRGS/1/2024/ICT02/UTM/02/10,Vot.No:R.J130000.7828.5F748the Scientific Research Project of Education Department of Hunan Province(Nos.22B1046 and 24A0771).
文摘Engineering optimization problems are often characterized by high dimensionality,constraints,and complex,multimodal landscapes.Traditional deterministic methods frequently struggle under such conditions,prompting increased interest in swarm intelligence algorithms.Among these,the Cuckoo Search(CS)algorithm stands out for its promising global search capabilities.However,it often suffers from premature convergence when tackling complex problems.To address this limitation,this paper proposes a Grouped Dynamic Adaptive CS(GDACS)algorithm.Theenhancements incorporated intoGDACS can be summarized into two key aspects.Firstly,a chaotic map is employed to generate initial solutions,leveraging the inherent randomness of chaotic sequences to ensure a more uniform distribution across the search space and enhance population diversity from the outset.Secondly,Cauchy and Levy strategies replace the standard CS population update.This strategy involves evaluating the fitness of candidate solutions to dynamically group the population based on performance.Different step-size adaptation strategies are then applied to distinct groups,enabling an adaptive search mechanism that balances exploration and exploitation.Experiments were conducted on six benchmark functions and four constrained engineering design problems,and the results indicate that the proposed GDACS achieves good search efficiency and produces more accurate optimization results compared with other state-of-the-art algorithms.
文摘With the rapid development of intelligent navigation technology,efficient and safe path planning for mobile robots has become a core requirement.To address the challenges of complex dynamic environments,this paper proposes an intelligent path planning framework based on grid map modeling.First,an improved Safe and Smooth A*(SSA*)algorithm is employed for global path planning.By incorporating obstacle expansion and cornerpoint optimization,the proposed SSA*enhances the safety and smoothness of the planned path.Then,a Partitioned Dynamic Window Approach(PDWA)is integrated for local planning,which is triggered when dynamic or sudden static obstacles appear,enabling real-time obstacle avoidance and path adjustment.A unified objective function is constructed,considering path length,safety,and smoothness comprehensively.Multiple simulation experiments are conducted on typical port grid maps.The results demonstrate that the improved SSA*significantly reduces the number of expanded nodes and computation time in static environmentswhile generating smoother and safer paths.Meanwhile,the PDWA exhibits strong real-time performance and robustness in dynamic scenarios,achieving shorter paths and lower planning times compared to other graph search algorithms.The proposedmethodmaintains stable performance across maps of different scales and various port scenarios,verifying its practicality and potential for wider application.
基金supported by the Major Science and Technology Programs in Henan Province(No.241100210100)Henan Provincial Science and Technology Research Project(No.252102211085,No.252102211105)+3 种基金Endogenous Security Cloud Network Convergence R&D Center(No.602431011PQ1)The Special Project for Research and Development in Key Areas of Guangdong Province(No.2021ZDZX1098)The Stabilization Support Program of Science,Technology and Innovation Commission of Shenzhen Municipality(No.20231128083944001)The Key scientific research projects of Henan higher education institutions(No.24A520042).
文摘Existing feature selection methods for intrusion detection systems in the Industrial Internet of Things often suffer from local optimality and high computational complexity.These challenges hinder traditional IDS from effectively extracting features while maintaining detection accuracy.This paper proposes an industrial Internet ofThings intrusion detection feature selection algorithm based on an improved whale optimization algorithm(GSLDWOA).The aim is to address the problems that feature selection algorithms under high-dimensional data are prone to,such as local optimality,long detection time,and reduced accuracy.First,the initial population’s diversity is increased using the Gaussian Mutation mechanism.Then,Non-linear Shrinking Factor balances global exploration and local development,avoiding premature convergence.Lastly,Variable-step Levy Flight operator and Dynamic Differential Evolution strategy are introduced to improve the algorithm’s search efficiency and convergence accuracy in highdimensional feature space.Experiments on the NSL-KDD and WUSTL-IIoT-2021 datasets demonstrate that the feature subset selected by GSLDWOA significantly improves detection performance.Compared to the traditional WOA algorithm,the detection rate and F1-score increased by 3.68%and 4.12%.On the WUSTL-IIoT-2021 dataset,accuracy,recall,and F1-score all exceed 99.9%.
基金funded by United Arab Emirates University(UAEU)under the UAEU-AUA grant number G00004577(12N145)with the corresponding grant at Universiti Malaya(UM)under grant number IF019-2024.
文摘Concrete-filled steel tubes(CFST)are widely utilized in civil engineering due to their superior load-bearing capacity,ductility,and seismic resistance.However,existing design codes,such as AISC and Eurocode 4,tend to be excessively conservative as they fail to account for the composite action between the steel tube and the concrete core.To address this limitation,this study proposes a hybrid model that integrates XGBoost with the Pied Kingfisher Optimizer(PKO),a nature-inspired algorithm,to enhance the accuracy of shear strength prediction for CFST columns.Additionally,quantile regression is employed to construct prediction intervals for the ultimate shear force,while the Asymmetric Squared Error Loss(ASEL)function is incorporated to mitigate overestimation errors.The computational results demonstrate that the PKO-XGBoost model delivers superior predictive accuracy,achieving a Mean Absolute Percentage Error(MAPE)of 4.431%and R2 of 0.9925 on the test set.Furthermore,the ASEL-PKO-XGBoost model substantially reduces overestimation errors to 28.26%,with negligible impact on predictive performance.Additionally,based on the Genetic Algorithm(GA)and existing equation models,a strength equation model is developed,achieving markedly higher accuracy than existing models(R^(2)=0.934).Lastly,web-based Graphical User Interfaces(GUIs)were developed to enable real-time prediction.
基金supported by the National Natural Science Foundation of China(Grant No.12402139,No.52368070)supported by Hainan Provincial Natural Science Foundation of China(Grant No.524QN223)+3 种基金Scientific Research Startup Foundation of Hainan University(Grant No.RZ2300002710)State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment,Dalian University of Technology(Grant No.GZ24107)the Horizontal Research Project(Grant No.HD-KYH-2024022)Innovative Research Projects for Postgraduate Students in Hainan Province(Grant No.Hys2025-217).
文摘Optimization problems are prevalent in various fields of science and engineering,with several real-world applications characterized by high dimensionality and complex search landscapes.Starfish optimization algorithm(SFOA)is a recently optimizer inspired by swarm intelligence,which is effective for numerical optimization,but it may encounter premature and local convergence for complex optimization problems.To address these challenges,this paper proposes the multi-strategy enhanced crested porcupine-starfish optimization algorithm(MCPSFOA).The core innovation of MCPSFOA lies in employing a hybrid strategy to improve SFOA,which integrates the exploratory mechanisms of SFOA with the diverse search capacity of the Crested Porcupine Optimizer(CPO).This synergy enhances MCPSFOA’s ability to navigate complex and multimodal search spaces.To further prevent premature convergence,MCPSFOA incorporates Lévy flight,leveraging its characteristic long and short jump patterns to enable large-scale exploration and escape from local optima.Subsequently,Gaussian mutation is applied for precise solution tuning,introducing controlled perturbations that enhance accuracy and mitigate the risk of insufficient exploitation.Notably,the population diversity enhancement mechanism periodically identifies and resets stagnant individuals,thereby consistently revitalizing population variety throughout the optimization process.MCPSFOA is rigorously evaluated on 24 classical benchmark functions(including high-dimensional cases),the CEC2017 suite,and the CEC2022 suite.MCPSFOA achieves superior overall performance with Friedman mean ranks of 2.208,2.310 and 2.417 on these benchmark functions,outperforming 11 state-of-the-art algorithms.Furthermore,the practical applicability of MCPSFOA is confirmed through its successful application to five engineering optimization cases,where it also yields excellent results.In conclusion,MCPSFOA is not only a highly effective and reliable optimizer for benchmark functions,but also a practical tool for solving real-world optimization problems.
文摘Early and accurate detection of bone cancer and marrow cell abnormalities is critical for timely intervention and improved patient outcomes.This paper proposes a novel hybrid deep learning framework that integrates a Convolutional Neural Network(CNN)with a Bidirectional Long Short-Term Memory(BiLSTM)architecture,optimized using the Firefly Optimization algorithm(FO).The proposed CNN-BiLSTM-FO model is tailored for structured biomedical data,capturing both local patterns and sequential dependencies in diagnostic features,while the Firefly Algorithm fine-tunes key hyperparameters to maximize predictive performance.The approach is evaluated on two benchmark biomedical datasets:one comprising diagnostic data for bone cancer detection and another for identifying marrow cell abnormalities.Experimental results demonstrate that the proposed method outperforms standard deep learning models,including CNN,LSTM,BiLSTM,and CNN-LSTM hybrids,significantly.The CNNBiLSTM-FO model achieves an accuracy of 98.55%for bone cancer detection and 96.04%for marrow abnormality classification.The paper also presents a detailed complexity analysis of the proposed algorithm and compares its performance across multiple evaluation metrics such as precision,recall,F1-score,and AUC.The results confirm the effectiveness of the firefly-based optimization strategy in improving classification accuracy and model robustness.This work introduces a scalable and accurate diagnostic solution that holds strong potential for integration into intelligent clinical decision-support systems.
基金Supported by the Optimisation Theory and Algorithm Research Team(Grant No.23kytdzd004)University Science Research Project of Anhui Province(Grant No.2024AH050631)the General Programs for Young Teacher Cultivation of Educational Commission of Anhui Province(Grant No.YQYB2023090).
文摘In this paper,we propose a new full-Newton step feasible interior-point algorithm for the special weighted linear complementarity problems.The proposed algorithm employs the technique of algebraic equivalent transformation to derive the search direction.It is shown that the proximity measure reduces quadratically at each iteration.Moreover,the iteration bound of the algorithm is as good as the best-known polynomial complexity for these types of problems.Furthermore,numerical results are presented to show the efficiency of the proposed algorithm.
文摘Optimizing convolutional neural networks(CNNs)for IoT attack detection remains a critical yet challenging task due to the need to balance multiple performance metrics beyond mere accuracy.This study proposes a unified and flexible optimization framework that leverages metaheuristic algorithms to automatically optimize CNN configurations for IoT attack detection.Unlike conventional single-objective approaches,the proposed method formulates a global multi-objective fitness function that integrates accuracy,precision,recall,and model size(speed/model complexity penalty)with adjustable weights.This design enables both single-objective and weightedsum multi-objective optimization,allowing adaptive selection of optimal CNN configurations for diverse deployment requirements.Two representativemetaheuristic algorithms,GeneticAlgorithm(GA)and Particle Swarm Optimization(PSO),are employed to optimize CNNhyperparameters and structure.At each generation/iteration,the best configuration is selected as themost balanced solution across optimization objectives,i.e.,the one achieving themaximum value of the global objective function.Experimental validation on two benchmark datasets,Edge-IIoT and CIC-IoT2023,demonstrates that the proposed GA-and PSO-based models significantly enhance detection accuracy(94.8%–98.3%)and generalization compared with manually tuned CNN configurations,while maintaining compact architectures.The results confirm that the multi-objective framework effectively balances predictive performance and computational efficiency.This work establishes a generalizable and adaptive optimization strategy for deep learning-based IoT attack detection and provides a foundation for future hybrid metaheuristic extensions in broader IoT security applications.
基金supported by the National Natural Science Foundation of China(NSFC)under Grant(No.51677058).
文摘Precisely estimating the state of health(SOH)of lithium-ion batteries is essential for battery management systems(BMS),as it plays a key role in ensuring the safe and reliable operation of battery systems.However,current SOH estimation methods often overlook the valuable temperature information that can effectively characterize battery aging during capacity degradation.Additionally,the Elman neural network,which is commonly employed for SOH estimation,exhibits several drawbacks,including slow training speed,a tendency to become trapped in local minima,and the initialization of weights and thresholds using pseudo-random numbers,leading to unstable model performance.To address these issues,this study addresses the challenge of precise and effective SOH detection by proposing a method for estimating the SOH of lithium-ion batteries based on differential thermal voltammetry(DTV)and an SSA-Elman neural network.Firstly,two health features(HFs)considering temperature factors and battery voltage are extracted fromthe differential thermal voltammetry curves and incremental capacity curves.Next,the Sparrow Search Algorithm(SSA)is employed to optimize the initial weights and thresholds of the Elman neural network,forming the SSA-Elman neural network model.To validate the performance,various neural networks,including the proposed SSA-Elman network,are tested using the Oxford battery aging dataset.The experimental results demonstrate that the method developed in this study achieves superior accuracy and robustness,with a mean absolute error(MAE)of less than 0.9%and a rootmean square error(RMSE)below 1.4%.
基金National Natural Science Foundation of China(11971211,12171388).
文摘Complex network models are frequently employed for simulating and studyingdiverse real-world complex systems.Among these models,scale-free networks typically exhibit greater fragility to malicious attacks.Consequently,enhancing the robustness of scale-free networks has become a pressing issue.To address this problem,this paper proposes a Multi-Granularity Integration Algorithm(MGIA),which aims to improve the robustness of scale-free networks while keeping the initial degree of each node unchanged,ensuring network connectivity and avoiding the generation of multiple edges.The algorithm generates a multi-granularity structure from the initial network to be optimized,then uses different optimization strategies to optimize the networks at various granular layers in this structure,and finally realizes the information exchange between different granular layers,thereby further enhancing the optimization effect.We propose new network refresh,crossover,and mutation operators to ensure that the optimized network satisfies the given constraints.Meanwhile,we propose new network similarity and network dissimilarity evaluation metrics to improve the effectiveness of the optimization operators in the algorithm.In the experiments,the MGIA enhances the robustness of the scale-free network by 67.6%.This improvement is approximately 17.2%higher than the optimization effects achieved by eight currently existing complex network robustness optimization algorithms.
基金supported by Yunnan Provincial Basic Research Project(202401AT070344,202301AT070443)National Natural Science Foundation of China(62263014,52207105)+1 种基金Yunnan Lancang-Mekong International Electric Power Technology Joint Laboratory(202203AP140001)Major Science and Technology Projects in Yunnan Province(202402AG050006).
文摘Accurate short-term wind power forecast technique plays a crucial role in maintaining the safety and economic efficiency of smart grids.Although numerous studies have employed various methods to forecast wind power,there remains a research gap in leveraging swarm intelligence algorithms to optimize the hyperparameters of the Transformer model for wind power prediction.To improve the accuracy of short-term wind power forecast,this paper proposes a hybrid short-term wind power forecast approach named STL-IAOA-iTransformer,which is based on seasonal and trend decomposition using LOESS(STL)and iTransformer model optimized by improved arithmetic optimization algorithm(IAOA).First,to fully extract the power data features,STL is used to decompose the original data into components with less redundant information.The extracted components as well as the weather data are then input into iTransformer for short-term wind power forecast.The final predicted short-term wind power curve is obtained by combining the predicted components.To improve the model accuracy,IAOA is employed to optimize the hyperparameters of iTransformer.The proposed approach is validated using real-generation data from different seasons and different power stations inNorthwest China,and ablation experiments have been conducted.Furthermore,to validate the superiority of the proposed approach under different wind characteristics,real power generation data fromsouthwestChina are utilized for experiments.Thecomparative results with the other six state-of-the-art prediction models in experiments show that the proposed model well fits the true value of generation series and achieves high prediction accuracy.
基金supported by the National Natural Science Foundation of China(No.62373027).
文摘In disaster relief operations,multiple UAVs can be used to search for trapped people.In recent years,many researchers have proposed machine le arning-based algorithms,sampling-based algorithms,and heuristic algorithms to solve the problem of multi-UAV path planning.The Dung Beetle Optimization(DBO)algorithm has been widely applied due to its diverse search patterns in the above algorithms.However,the update strategies for the rolling and thieving dung beetles of the DBO algorithm are overly simplistic,potentially leading to an inability to fully explore the search space and a tendency to converge to local optima,thereby not guaranteeing the discovery of the optimal path.To address these issues,we propose an improved DBO algorithm guided by the Landmark Operator(LODBO).Specifically,we first use tent mapping to update the population strategy,which enables the algorithm to generate initial solutions with enhanced diversity within the search space.Second,we expand the search range of the rolling ball dung beetle by using the landmark factor.Finally,by using the adaptive factor that changes with the number of iterations.,we improve the global search ability of the stealing dung beetle,making it more likely to escape from local optima.To verify the effectiveness of the proposed method,extensive simulation experiments are conducted,and the result shows that the LODBO algorithm can obtain the optimal path using the shortest time compared with the Genetic Algorithm(GA),the Gray Wolf Optimizer(GWO),the Whale Optimization Algorithm(WOA)and the original DBO algorithm in the disaster search and rescue task set.
基金Supported by the National Natural Science Foundation of China (61862033, 61762049, 61902162)Jiangxi Provincial Natural Science Foundation (20202BABL202026, 20202BABL202025, 20202BAB202015)。
文摘The development of algebraic and numerical algorithms is a kind of complicated creative work and it is difficult to guarantee the correctness of the algorithms. This paper introduces a systematic and unified formal development method of algebraic and numerical algorithms. The method implements the complete refinement process from abstract specifications to a concrete executable program. It uses the core idea of partition and recursion for formal derivation and combines the mathematical induction based on strict mathematical logic with Hoare axiom for correctness verification. This development method converts creative work into non-creative work as much as possible while ensuring the correctness of the algorithm, which can not only verify the correctness of the existing algebraic and numerical algorithms but also guide the development of efficient unknown algorithms for such problems. This paper takes the non-recursive implementation of the Extended Euclidean Algorithm and Horner's method as examples. Therefore, the effectiveness and feasibility of this method are further verified.
