Combining the advantages of a genetic algorithm and an artificial immune system, a novel genetic algorithm named immune genetic algorithm based on quasi secondary response (IGA QSR) is proposed. IGA QSR employs a da...Combining the advantages of a genetic algorithm and an artificial immune system, a novel genetic algorithm named immune genetic algorithm based on quasi secondary response (IGA QSR) is proposed. IGA QSR employs a database to simulate the standard secondary response and the quasi secondary response. Elitist strategy, automatic extinction, clonal propagation, diversity guarantee, and selection based on comprehensive fitness are also used in the process of IGA QSR. Theoretical analysis, numerical examples of three benchmark mathematical optimization problems and a trave ling salesman problem all demonstrate that IGA-QSR is more effective not only on convergence speed but also on convergence probability than a simple genetic algorithm with the elitist strategy ( SGA ES). Besides, IGA QSR allows the designers to stop and restart the optimization process freely with out losing the best results that have already been obtained. These properties make IGA QSR be a fea sible, effective and robust search algorithm for complex engineering problems.展开更多
A new method for simulating the folding pathway of RNA secondary structure using the modified ant colony algorithmis proposed.For a given RNA sequence,the set of all possible stems is obtained and the energy of each s...A new method for simulating the folding pathway of RNA secondary structure using the modified ant colony algorithmis proposed.For a given RNA sequence,the set of all possible stems is obtained and the energy of each stem iscalculated and stored at the initial stage.Furthermore,a more realistic formula is used to compute the energy ofmulti-branch loop in the following iteration.Then a folding pathway is simulated,including such processes as constructionof the heuristic information,the rule of initializing the pheromone,the mechanism of choosing the initial andnext stem and the strategy of updating the pheromone between two different stems.Finally by testing RNA sequences withknown secondary structures from the public databases,we analyze the experimental data to select appropriate values forparameters.The measure indexes show that our procedure is more consistent with phylogenetically proven structures thansoftware RNAstructure sometimes and more effective than the standard Genetic Algorithm.展开更多
The advantages and disadvantages of genetic algorithm and BP algorithm are introduced. A neural network based on GA-BP algorithm is proposed and applied in the prediction of protein secondary structure, which combines...The advantages and disadvantages of genetic algorithm and BP algorithm are introduced. A neural network based on GA-BP algorithm is proposed and applied in the prediction of protein secondary structure, which combines the advantages of BP and GA. The prediction and training on the neural network are made respectively based on 4 structure classifications of protein so as to get higher rate of predication---the highest prediction rate 75.65%,the average prediction rate 65.04%.展开更多
This paper introduces a distributed secondary control scheme for achieving current sharing and average voltage regulation objectives in a DC microgrid.The proposed scheme employs a dynamic diffusion algorithm(DDA)inst...This paper introduces a distributed secondary control scheme for achieving current sharing and average voltage regulation objectives in a DC microgrid.The proposed scheme employs a dynamic diffusion algorithm(DDA)instead of the consensus algorithm to enable distributed communication among converters.To help understand DDA,the relation of DDA and other diffusion algorithms is discussed in detail and its superiority is shown by comparison with diffusion and consensus algorithms.Furthermore,considering the discrete nature and different sampling time of the digital controller and communication network,a z-domain model of the entire DC microgrid is established.The influence of communication and secondary control parameters on the system stability is investigated.Based on the established model,the tolerable communication rates are obtained.Real-time simulations conducted on the OPAL-RT platform validate the effectiveness of the proposed scheme,showcasing its advantages in terms of convergence speed and stability.展开更多
A self-adaptive learning based immune algorithm (SALIA) is proposed to tackle diverse optimization problems, such as complex multi-modal and ill-conditioned prc,blems with the high robustness. The SALIA algorithm ad...A self-adaptive learning based immune algorithm (SALIA) is proposed to tackle diverse optimization problems, such as complex multi-modal and ill-conditioned prc,blems with the high robustness. The SALIA algorithm adopted a mutation strategy pool which consists of four effective mutation strategies to generate new antibodies. A self-adaptive learning framework is implemented to select the mutation strategies by learning from their previous performances in generating promising solutions. Twenty-six state-of-the-art optimization problems with different characteristics, such as uni-modality, multi-modality, rotation, ill-condition, mis-scale and noise, are used to verify the validity of SALIA. Experimental results show that the novel algorithm SALIA achieves a higher universality and robustness than clonal selection algorithms (CLONALG), and the mean error index of each test function in SALIA decreases by a factor of at least 1.0×10^7 in average.展开更多
The research methods of protein structure prediction mainly focus on finding effective features of protein sequences and developing suitable machine learning algorithms. But few people consider the importance of weigh...The research methods of protein structure prediction mainly focus on finding effective features of protein sequences and developing suitable machine learning algorithms. But few people consider the importance of weights of features in classification. We propose the GASVM algorithm (classification accuracy of support vector machine is regarded as the fitness value of genetic algorithm) to optimize the coefficients of these 16 features (5 features are proposed first time) in the classification, and further develop a new feature vector. Finally, based on the new feature vector, this paper uses support vector machine and 10-fold cross-validation to classify the protein structure of 3 low similarity datasets (25PDB, 1189, FC699). Experimental results show that the overall classification accuracy of the new method is better than other methods.展开更多
Based on the research of predictingβ-hairpin motifs in proteins, we apply Random Forest and Support Vector Machine algorithm to predictβ-hairpin motifs in ArchDB40 dataset. The motifs with the loop length of 2 to 8 ...Based on the research of predictingβ-hairpin motifs in proteins, we apply Random Forest and Support Vector Machine algorithm to predictβ-hairpin motifs in ArchDB40 dataset. The motifs with the loop length of 2 to 8 amino acid residues are extracted as research object and thefixed-length pattern of 12 amino acids are selected. When using the same characteristic parameters and the same test method, Random Forest algorithm is more effective than Support Vector Machine. In addition, because of Random Forest algorithm doesn’t produce overfitting phenomenon while the dimension of characteristic parameters is higher, we use Random Forest based on higher dimension characteristic parameters to predictβ-hairpin motifs. The better prediction results are obtained;the overall accuracy and Matthew’s correlation coefficient of 5-fold cross-validation achieve 83.3% and 0.59, respectively.展开更多
The structure and function of proteins are closely related, and protein structure decides its function, therefore protein structure prediction is quite important.β-turns are important components of protein secondary ...The structure and function of proteins are closely related, and protein structure decides its function, therefore protein structure prediction is quite important.β-turns are important components of protein secondary structure. So development of an accurate prediction method ofβ-turn types is very necessary. In this paper, we used the composite vector with position conservation scoring function, increment of diversity and predictive secondary structure information as the input parameter of support vector machine algorithm for predicting theβ-turn types in the database of 426 protein chains, obtained the overall prediction accuracy of 95.6%, 97.8%, 97.0%, 98.9%, 99.2%, 91.8%, 99.4% and 83.9% with the Matthews Correlation Coefficient values of 0.74, 0.68, 0.20, 0.49, 0.23, 0.47, 0.49 and 0.53 for types I, II, VIII, I’, II’, IV, VI and nonturn respectively, which is better than other prediction.展开更多
Microgrids are networked control systems with multiple distributed generators(DGs).Microgrids are associated with many problems,such as communication delays,high sampling rates,and frequent controller updates,which ma...Microgrids are networked control systems with multiple distributed generators(DGs).Microgrids are associated with many problems,such as communication delays,high sampling rates,and frequent controller updates,which make it challenging to realize coordination control among the DGs.Therefore,finite-time consensus algorithms and event-triggered control methods are combined to propose a distributed coordination control method for microgrid systems.The DG in the microgrid system serves as an agent node in the control network,and a distributed secondary controller is designed using finite-time consensus algorithm,such that the frequency and voltage restoration control has a faster convergence time and better anti-interference performance.The event-triggered function was designed based on the state information of the agents.The controller exchanges the state information at the trigger instants.System stability is analyzed using the Lyapunov stability theory,and it is verified that the controller cannot exhibit the Zeno phenomenon in the event-triggered process.A simulation platform was developed in Matlab/Simulink to verify that the proposed control method can effectively reduce the frequency of controller updates during communication delays and the burden on the communication network.展开更多
Traditional linear motor optimization methods typically use analytical models combined with intelligent optimization algorithms.However,this approach has disadvantages,e.g.,the analytical model might not be accurate e...Traditional linear motor optimization methods typically use analytical models combined with intelligent optimization algorithms.However,this approach has disadvantages,e.g.,the analytical model might not be accurate enough,and the intelligent optimization algorithm can easily fall into local optimization.A new linear motor optimization strategy combining an R-deep neural network(R-DNN)and modified cuckoo search(MCS)is proposed;additionally,the thrust lifting and thrust fluctuation reductions are regarded as optimization objectives.The R-DNN is a deep neural network modeling method using the rectified linear unit(RELU)activation function,and the MCS provides a faster convergence speed and stronger data search capability as compared with genetic algorithms,particle swarm optimization,and standard CS algorithms.Finally,the validity and accuracy of this work are proven based on prototype experiments.展开更多
Hybrid reactive power compensation(HRPC)combines step-controlled shunt reactors and series compensation,and will be employed in ultra-high-voltage(UHV)power systems.The single-phase auto-reclosure characteristics of s...Hybrid reactive power compensation(HRPC)combines step-controlled shunt reactors and series compensation,and will be employed in ultra-high-voltage(UHV)power systems.The single-phase auto-reclosure characteristics of secondary arcs in systems with HRPC require further investigation.In this paper,both the arc-recalling voltage and subsidiary variations in arc current are investigated with and without HRPC.The frequency components of the secondary arc current and variations in arcing time are analyzed for various influential factors,such as the neutral reactor,arc resistance,fault location,degrees of compensation of HRPC,and the length of the transmission line.The non-dominated sorting genetic algorithm II(NSGA-II)and support vector machine regression are combined to create a multi-variable dependent forecasting algorithm to predict the characteristics of the secondary arc in UHV systems with HRPC.This paper provides a theoretical reference for optimizing the parameters of HRPC,and for developing adaptive auto-reclosure schemes and protection equipment.展开更多
A more relaxed sufficient condition for the convergence of filtered-X LMS (FXLMS) algorithm is presented. It is pointed out that if some positive real condition for secondary path transfer function and its estimates i...A more relaxed sufficient condition for the convergence of filtered-X LMS (FXLMS) algorithm is presented. It is pointed out that if some positive real condition for secondary path transfer function and its estimates is satisfied within all the frequency bands, FXLMS algorithm converges whatever the reference signal is like. But if the above positive real condition is satisfied only within some frequency bands, the convergence of FXLMS algorithm is dependent on the distribution of power spectral density of the reference signal, and the convergence step size is determined by the distribution of some specific correlation matrix eigenvalues.Applying the conclusion above to the Delayed LMS (DLMS) algorithm, it is shown that DLMS algorithm with some error of time delay estimation converges in certain discrete frequency bands, and the width of which are determined only by the 'time-delay estimation error frequency' which is equal to one fourth of the inverse of estimated error of the time delay.展开更多
Hydrodynamic optimization design of the bend pipe from pump using theNavier-Stokes solver and evolutionary algorithms was conducted. The minimization of the totalpressure loss of the bend pipe was chosen as the design...Hydrodynamic optimization design of the bend pipe from pump using theNavier-Stokes solver and evolutionary algorithms was conducted. The minimization of the totalpressure loss of the bend pipe was chosen as the design object in order to obtain the uniform exitflows through suppressing the secondary flows. The 3-D Navier-Stokes solver was applied to evaluatethe hydrodynamic performance of the bend-pipe flows. A 7th-order Bezier curve was used toparameterize the meridional section and elliptic representation was adopted to represent thecross-section profiles of the bend pipe. Evolutionary algorithms were applied in optimization. Theobtained results show that the designed bend pipe shape has much more uniform exit flows comparedwith the initial one and much weaker secondary flows, and that the evolutionary algorithms and CFDtechnique are the powerful optimization tools for the fluid machinery desiga展开更多
Performance analysis of filtered-X LMS (FXLMS) algorithm with secondary path modeling error is carried out in both time and frequency domain. It is shown firstly that the effects of secondary path modeling error on th...Performance analysis of filtered-X LMS (FXLMS) algorithm with secondary path modeling error is carried out in both time and frequency domain. It is shown firstly that the effects of secondary path modeling error on the performance of FXLMS algorithm are determined by the distribution of the relative error of secondary path model along with frequency. In case of that the distribution of relative error is uniform the modeling error of secondary path will have no effects on the performance of the algorithm. In addition, a limitation property of FXLMS algorithm is proved, which implies that the negative effects of secondary path modeling error can be compensated by increasing the adaptive filter length. At last, some insights into the 'spillover' phenomenon of FXLMS algorithm are given.展开更多
With advantages of strong drive capability,nested-loop secondary linear machine(NLS-LM)has great potentiality in linear metro.For its secondary structure with multiple loops,it is difficult to calculate the electromag...With advantages of strong drive capability,nested-loop secondary linear machine(NLS-LM)has great potentiality in linear metro.For its secondary structure with multiple loops,it is difficult to calculate the electromagnetic thrust of NLS-LM reasonably.Hence,in this paper,one thrust calculation method is proposed considering variable loop inductance and transient loop current.Firstly,to establish the secondary winding function,the modeling domain is confined to a limited range,and the equivalent loop span is employed by analyzing the coupling relationship between primary and secondary.Then,in order to obtain the secondary flux density,the transient secondary current is solved based on the loop impedance and induced voltage.Finally,the electromagnetic thrust can be calculated reasonably by the given primary current sheet and the calculated secondary flux density.Comprehensive simulations and experiments have demonstrated the effectiveness of the proposed method.展开更多
基金Supported by the National Science Foundation for Post-doctoral Scientists of China(20090460216)the National Defense Fundamental Research Foundation of China(B222006060)
文摘Combining the advantages of a genetic algorithm and an artificial immune system, a novel genetic algorithm named immune genetic algorithm based on quasi secondary response (IGA QSR) is proposed. IGA QSR employs a database to simulate the standard secondary response and the quasi secondary response. Elitist strategy, automatic extinction, clonal propagation, diversity guarantee, and selection based on comprehensive fitness are also used in the process of IGA QSR. Theoretical analysis, numerical examples of three benchmark mathematical optimization problems and a trave ling salesman problem all demonstrate that IGA-QSR is more effective not only on convergence speed but also on convergence probability than a simple genetic algorithm with the elitist strategy ( SGA ES). Besides, IGA QSR allows the designers to stop and restart the optimization process freely with out losing the best results that have already been obtained. These properties make IGA QSR be a fea sible, effective and robust search algorithm for complex engineering problems.
基金supported by the National Natural Science Foundation of China(Grant No.60971089)the Specialized Research Foundation for the Doctoral Program of Higher Education of China(Grant No.20070183057)
文摘A new method for simulating the folding pathway of RNA secondary structure using the modified ant colony algorithmis proposed.For a given RNA sequence,the set of all possible stems is obtained and the energy of each stem iscalculated and stored at the initial stage.Furthermore,a more realistic formula is used to compute the energy ofmulti-branch loop in the following iteration.Then a folding pathway is simulated,including such processes as constructionof the heuristic information,the rule of initializing the pheromone,the mechanism of choosing the initial andnext stem and the strategy of updating the pheromone between two different stems.Finally by testing RNA sequences withknown secondary structures from the public databases,we analyze the experimental data to select appropriate values forparameters.The measure indexes show that our procedure is more consistent with phylogenetically proven structures thansoftware RNAstructure sometimes and more effective than the standard Genetic Algorithm.
文摘The advantages and disadvantages of genetic algorithm and BP algorithm are introduced. A neural network based on GA-BP algorithm is proposed and applied in the prediction of protein secondary structure, which combines the advantages of BP and GA. The prediction and training on the neural network are made respectively based on 4 structure classifications of protein so as to get higher rate of predication---the highest prediction rate 75.65%,the average prediction rate 65.04%.
基金supported by the Natural Science Foundation of Shanghai(No.22ZR1429800)China Southern Power Grid Company Limited(No.GDKJXM20222178).
文摘This paper introduces a distributed secondary control scheme for achieving current sharing and average voltage regulation objectives in a DC microgrid.The proposed scheme employs a dynamic diffusion algorithm(DDA)instead of the consensus algorithm to enable distributed communication among converters.To help understand DDA,the relation of DDA and other diffusion algorithms is discussed in detail and its superiority is shown by comparison with diffusion and consensus algorithms.Furthermore,considering the discrete nature and different sampling time of the digital controller and communication network,a z-domain model of the entire DC microgrid is established.The influence of communication and secondary control parameters on the system stability is investigated.Based on the established model,the tolerable communication rates are obtained.Real-time simulations conducted on the OPAL-RT platform validate the effectiveness of the proposed scheme,showcasing its advantages in terms of convergence speed and stability.
基金Project(2010ZC13012) supported by the Aviation Science Funds of China
文摘A self-adaptive learning based immune algorithm (SALIA) is proposed to tackle diverse optimization problems, such as complex multi-modal and ill-conditioned prc,blems with the high robustness. The SALIA algorithm adopted a mutation strategy pool which consists of four effective mutation strategies to generate new antibodies. A self-adaptive learning framework is implemented to select the mutation strategies by learning from their previous performances in generating promising solutions. Twenty-six state-of-the-art optimization problems with different characteristics, such as uni-modality, multi-modality, rotation, ill-condition, mis-scale and noise, are used to verify the validity of SALIA. Experimental results show that the novel algorithm SALIA achieves a higher universality and robustness than clonal selection algorithms (CLONALG), and the mean error index of each test function in SALIA decreases by a factor of at least 1.0×10^7 in average.
文摘The research methods of protein structure prediction mainly focus on finding effective features of protein sequences and developing suitable machine learning algorithms. But few people consider the importance of weights of features in classification. We propose the GASVM algorithm (classification accuracy of support vector machine is regarded as the fitness value of genetic algorithm) to optimize the coefficients of these 16 features (5 features are proposed first time) in the classification, and further develop a new feature vector. Finally, based on the new feature vector, this paper uses support vector machine and 10-fold cross-validation to classify the protein structure of 3 low similarity datasets (25PDB, 1189, FC699). Experimental results show that the overall classification accuracy of the new method is better than other methods.
文摘Based on the research of predictingβ-hairpin motifs in proteins, we apply Random Forest and Support Vector Machine algorithm to predictβ-hairpin motifs in ArchDB40 dataset. The motifs with the loop length of 2 to 8 amino acid residues are extracted as research object and thefixed-length pattern of 12 amino acids are selected. When using the same characteristic parameters and the same test method, Random Forest algorithm is more effective than Support Vector Machine. In addition, because of Random Forest algorithm doesn’t produce overfitting phenomenon while the dimension of characteristic parameters is higher, we use Random Forest based on higher dimension characteristic parameters to predictβ-hairpin motifs. The better prediction results are obtained;the overall accuracy and Matthew’s correlation coefficient of 5-fold cross-validation achieve 83.3% and 0.59, respectively.
文摘The structure and function of proteins are closely related, and protein structure decides its function, therefore protein structure prediction is quite important.β-turns are important components of protein secondary structure. So development of an accurate prediction method ofβ-turn types is very necessary. In this paper, we used the composite vector with position conservation scoring function, increment of diversity and predictive secondary structure information as the input parameter of support vector machine algorithm for predicting theβ-turn types in the database of 426 protein chains, obtained the overall prediction accuracy of 95.6%, 97.8%, 97.0%, 98.9%, 99.2%, 91.8%, 99.4% and 83.9% with the Matthews Correlation Coefficient values of 0.74, 0.68, 0.20, 0.49, 0.23, 0.47, 0.49 and 0.53 for types I, II, VIII, I’, II’, IV, VI and nonturn respectively, which is better than other prediction.
基金National Natural Science Foundation of China(62063016).
文摘Microgrids are networked control systems with multiple distributed generators(DGs).Microgrids are associated with many problems,such as communication delays,high sampling rates,and frequent controller updates,which make it challenging to realize coordination control among the DGs.Therefore,finite-time consensus algorithms and event-triggered control methods are combined to propose a distributed coordination control method for microgrid systems.The DG in the microgrid system serves as an agent node in the control network,and a distributed secondary controller is designed using finite-time consensus algorithm,such that the frequency and voltage restoration control has a faster convergence time and better anti-interference performance.The event-triggered function was designed based on the state information of the agents.The controller exchanges the state information at the trigger instants.System stability is analyzed using the Lyapunov stability theory,and it is verified that the controller cannot exhibit the Zeno phenomenon in the event-triggered process.A simulation platform was developed in Matlab/Simulink to verify that the proposed control method can effectively reduce the frequency of controller updates during communication delays and the burden on the communication network.
基金Supported by the National Natural Science Foundation of China(51837001,51907001,51707002).
文摘Traditional linear motor optimization methods typically use analytical models combined with intelligent optimization algorithms.However,this approach has disadvantages,e.g.,the analytical model might not be accurate enough,and the intelligent optimization algorithm can easily fall into local optimization.A new linear motor optimization strategy combining an R-deep neural network(R-DNN)and modified cuckoo search(MCS)is proposed;additionally,the thrust lifting and thrust fluctuation reductions are regarded as optimization objectives.The R-DNN is a deep neural network modeling method using the rectified linear unit(RELU)activation function,and the MCS provides a faster convergence speed and stronger data search capability as compared with genetic algorithms,particle swarm optimization,and standard CS algorithms.Finally,the validity and accuracy of this work are proven based on prototype experiments.
文摘Hybrid reactive power compensation(HRPC)combines step-controlled shunt reactors and series compensation,and will be employed in ultra-high-voltage(UHV)power systems.The single-phase auto-reclosure characteristics of secondary arcs in systems with HRPC require further investigation.In this paper,both the arc-recalling voltage and subsidiary variations in arc current are investigated with and without HRPC.The frequency components of the secondary arc current and variations in arcing time are analyzed for various influential factors,such as the neutral reactor,arc resistance,fault location,degrees of compensation of HRPC,and the length of the transmission line.The non-dominated sorting genetic algorithm II(NSGA-II)and support vector machine regression are combined to create a multi-variable dependent forecasting algorithm to predict the characteristics of the secondary arc in UHV systems with HRPC.This paper provides a theoretical reference for optimizing the parameters of HRPC,and for developing adaptive auto-reclosure schemes and protection equipment.
文摘A more relaxed sufficient condition for the convergence of filtered-X LMS (FXLMS) algorithm is presented. It is pointed out that if some positive real condition for secondary path transfer function and its estimates is satisfied within all the frequency bands, FXLMS algorithm converges whatever the reference signal is like. But if the above positive real condition is satisfied only within some frequency bands, the convergence of FXLMS algorithm is dependent on the distribution of power spectral density of the reference signal, and the convergence step size is determined by the distribution of some specific correlation matrix eigenvalues.Applying the conclusion above to the Delayed LMS (DLMS) algorithm, it is shown that DLMS algorithm with some error of time delay estimation converges in certain discrete frequency bands, and the width of which are determined only by the 'time-delay estimation error frequency' which is equal to one fourth of the inverse of estimated error of the time delay.
文摘Hydrodynamic optimization design of the bend pipe from pump using theNavier-Stokes solver and evolutionary algorithms was conducted. The minimization of the totalpressure loss of the bend pipe was chosen as the design object in order to obtain the uniform exitflows through suppressing the secondary flows. The 3-D Navier-Stokes solver was applied to evaluatethe hydrodynamic performance of the bend-pipe flows. A 7th-order Bezier curve was used toparameterize the meridional section and elliptic representation was adopted to represent thecross-section profiles of the bend pipe. Evolutionary algorithms were applied in optimization. Theobtained results show that the designed bend pipe shape has much more uniform exit flows comparedwith the initial one and much weaker secondary flows, and that the evolutionary algorithms and CFDtechnique are the powerful optimization tools for the fluid machinery desiga
文摘Performance analysis of filtered-X LMS (FXLMS) algorithm with secondary path modeling error is carried out in both time and frequency domain. It is shown firstly that the effects of secondary path modeling error on the performance of FXLMS algorithm are determined by the distribution of the relative error of secondary path model along with frequency. In case of that the distribution of relative error is uniform the modeling error of secondary path will have no effects on the performance of the algorithm. In addition, a limitation property of FXLMS algorithm is proved, which implies that the negative effects of secondary path modeling error can be compensated by increasing the adaptive filter length. At last, some insights into the 'spillover' phenomenon of FXLMS algorithm are given.
基金supported in part by the National Natural Science Foundation of China under Grants 52277050the Shenzhen International Collaboration under Grant GJHZ20210705142539007。
文摘With advantages of strong drive capability,nested-loop secondary linear machine(NLS-LM)has great potentiality in linear metro.For its secondary structure with multiple loops,it is difficult to calculate the electromagnetic thrust of NLS-LM reasonably.Hence,in this paper,one thrust calculation method is proposed considering variable loop inductance and transient loop current.Firstly,to establish the secondary winding function,the modeling domain is confined to a limited range,and the equivalent loop span is employed by analyzing the coupling relationship between primary and secondary.Then,in order to obtain the secondary flux density,the transient secondary current is solved based on the loop impedance and induced voltage.Finally,the electromagnetic thrust can be calculated reasonably by the given primary current sheet and the calculated secondary flux density.Comprehensive simulations and experiments have demonstrated the effectiveness of the proposed method.