A numerical method for coupled deformation between sheet metal and flexible-die was proposed. Based on the updated Lagrangian （UL） formulation, the elastoplastic deformation of sheet metal was analyzed with finite e...A numerical method for coupled deformation between sheet metal and flexible-die was proposed. Based on the updated Lagrangian （UL） formulation, the elastoplastic deformation of sheet metal was analyzed with finite element method （FEM） and the bulk deformation of flexible-die was analyzed with element-free Galerkin method （EFGM）. The frictional contact between sheet metal and flexible-die was treated by the penalty function method. The sheet elastic flexible-die bulging process was analyzed with the FEM-EFGM program for coupled deformation between sheet metal and bulk flexible-die, called CDSB-FEM-EFGM for short. Compared with finite element code DEFORM-2D and experiment results, the CDSB-FEM-EFGM program is feasible. This method provides a suitable numerical method to analyze sheet flexible-die forming.展开更多
A combined method for the fast 3-D finite element modeling of defect responses in nondestructive testing of electromagnetics is presented. The method consists of three numerical techniques: zoom-in technique, differen...A combined method for the fast 3-D finite element modeling of defect responses in nondestructive testing of electromagnetics is presented. The method consists of three numerical techniques: zoom-in technique, difference field technique and iterative solution technique. Utilizing the zoom-in technique, the computational zone focuses on a relatively small domain around the defect. Employing the difference field technique, the axisymmetrical field solution corresponding to the case with no defect can be used to simplify the mesh generation and obtain the modeling results quickly. Using the iterative solution technique, the matrix equation system in the 3-D finite element modeling of nondestructive probe signals can easily be solved. The sample calculation shows that the presented method is highly effective and can consequently save significant computer resources.展开更多
Hollow-structured Cu_(0.3)Co_(2.7)O_(4) microspheres have been synthesized by a simple one-pot template-free hydrothermal method with copper sulfate,cobalt acetate and ammonia as raw materials.The products were charac...Hollow-structured Cu_(0.3)Co_(2.7)O_(4) microspheres have been synthesized by a simple one-pot template-free hydrothermal method with copper sulfate,cobalt acetate and ammonia as raw materials.The products were characterized by powder X-ray diffraction,energy dispersive X-ray analysis,selected area electron diffraction,high-resolution transmission electron microscopy,scanning electron microscopy and BET measurements.The research results show that the hollow Cu_(0.3)Co_(2.7)O_(4) microspheres consist of single-crystalline nanocubes with the diameter of about 20 nm.The formation mechanism of hollow Cu_(0.3)Co_(2.7)O_(4) microspheres is suggested as Ostwald ripening in a solid-solution-solid process,and Cu_(0.3)Co_(2.7)O_(4) microspheres are mesoporous containing two pore sizes of 3.3 and 5.9 nm.The as-prepared Cu_(0.3)Co_(2.7)O_(4) sensors have optimal gas responses to 50×10^(−6) mg/m^(3) C_(2)H_(5)OH at 190℃.展开更多
A novel radio-map establishment based on fuzzy clustering for hybrid K-Nearest Neighbor (KNN) and Artifi cial Neural Network (ANN) position algorithm in WLAN indoor environment is proposed. First of all, the Principal...A novel radio-map establishment based on fuzzy clustering for hybrid K-Nearest Neighbor (KNN) and Artifi cial Neural Network (ANN) position algorithm in WLAN indoor environment is proposed. First of all, the Principal Component Analysis (PCA) is utilized for the purpose of simplifying input dimensions of position estimation algorithm and saving storage cost for the establishment of radio-map. Then, reference points (RPs) calibrated in the off-line phase are divided into separate clusters by Fuzzy C-means clustering (FCM), and membership degrees (MDs) for different clusters are also allocated to each RPs. However, the singular RPs cased by the multi-path effect signifi cantly decreases the clustering performance. Therefore, a novel radio-map establishment method is presented based on the modifi cation of signal samples recorded at singular RPs by surface fitting. In the on-line phase, the region which the mobile terminal (MT) belongs to is estimated according to the MDs firstly. Then, in estimated small dimensional regions, MT's coordinates are calculated byKNN positioning method for efficiency purpose. However, for the regions including singular RPs, ANN method is utilized because ofits great pattern matching ability. Furthermore, compared with other typical indoor positioning methods, feasibility and effectiveness of this hybrid KNN/ANN method are also verified by the experimental results in static and tracking situations.展开更多
In this paper a hybrid algorithm which combines the pattern search method and the genetic algorithm for unconstrained optimization is presented. The algorithm is a deterministic pattern search algorithm,but in the sea...In this paper a hybrid algorithm which combines the pattern search method and the genetic algorithm for unconstrained optimization is presented. The algorithm is a deterministic pattern search algorithm,but in the search step of pattern search algorithm,the trial points are produced by a way like the genetic algorithm. At each iterate, by reduplication,crossover and mutation, a finite set of points can be used. In theory,the algorithm is globally convergent. The most stir is the numerical results showing that it can find the global minimizer for some problems ,which other pattern search algorithms don＇t bear.展开更多
The mechanism of stress generation and propagation by detonation loading in five separate independent advance of ore breaking patterns is discussed in the paper. An elastic numerical model was developed using AN- SYS/...The mechanism of stress generation and propagation by detonation loading in five separate independent advance of ore breaking patterns is discussed in the paper. An elastic numerical model was developed using AN- SYS/LS-DYNA 3D Nonlinear Dynamic Finite Element Software. In this package ANSYS is the preprocessor and LS-DYNA is the postprocessor. Numerical models in the paper to actual were l：10 and the element mesh was dissected in scanning mode utilizing the symmetry characteristics of the numerical model. Five different advance rates were studied. Parameters, such as the time required to maximum stress, the action time of the available stress, the maximum velocity of the nodes, the stress penetration time, the magnitude of the stress peak and the time duration for high stress were numerically simulated. The 2.2 m advance appeared optimum from an analysis of the simulation results. The results from numerical simulation have been validated by tests with physical models.展开更多
For the first time, we introduce a fully quantum mechanical Hamiltonian for a semi-infinite chain model of atoms. We then derive the vibration modes of this model by virtue of the ＂invariant eigen-operator＂ method i...For the first time, we introduce a fully quantum mechanical Hamiltonian for a semi-infinite chain model of atoms. We then derive the vibration modes of this model by virtue of the ＂invariant eigen-operator＂ method in two different cases, which is concise and revealing.展开更多
For real-time and distributed features of multi-robot system,the strategy of combining the improved artificial potential field method and the rules based on priority is proposed to study the collision avoidance planni...For real-time and distributed features of multi-robot system,the strategy of combining the improved artificial potential field method and the rules based on priority is proposed to study the collision avoidance planning in multi-robot systems. The improved artificial potential field based on simulated annealing algorithm satisfactorily overcomes the drawbacks of traditional artificial potential field method,so that robots can find a local collision-free path in the complex environment. According to the movement vector trail of robots,collisions between robots can be detected,thereby the collision avoidance rules can be obtained. Coordination between robots by the priority based rules improves the real-time property of multi-robot system. The combination of these two methods can help a robot to find a collision-free path from a starting point to the goal quickly in an environment with many obstacles. The feasibility of the proposed method is validated in the VC-based simulated environment.展开更多
In this paper exact solutions of a new modified nonlinearly dispersive equation （simply called inK（m, n, a, b） Ua Ub equation）, u^m-1 ut ＋ α（ u^n）x ＋β（u^a（u^b）xx）x = 0, is investigated by using some dir...In this paper exact solutions of a new modified nonlinearly dispersive equation （simply called inK（m, n, a, b） Ua Ub equation）, u^m-1 ut ＋ α（ u^n）x ＋β（u^a（u^b）xx）x = 0, is investigated by using some direct algorithms. As a result, abundant new compacton solutions （solitons with the absence of infinite wings） and solitary pattern solutions （having infinite slopes or cusps） are obtained.展开更多
When modeling wave propagation in infinite space, it is necessary to have stable absorbing boundaries to effectively eliminate spurious reflections from the truncation boundaries. The SH wave equations for Perfectly M...When modeling wave propagation in infinite space, it is necessary to have stable absorbing boundaries to effectively eliminate spurious reflections from the truncation boundaries. The SH wave equations for Perfectly Matched Layers （PML） are deduced and their Crank-Nicolson scheme are presented in this paper. We use the second-, sixth-, and tenth-order finite difference and pseudo-spectral algorithms to compute the spatial derivatives. Two numerical models, a homogeneous isotropic medium and a multi-layer model with a cave, are designed to investigate how the absorbing boundary width and the algorithms determine PML effects. Numerical results show that, for PML, the low-order finite difference algorithms have fairly good absorbing effects when the absorbing boundary is thin, whereas, high-order algorithms always have good absorption when the boundary is thick. Finally, we discuss the reflection coefficient and point out its shortcomings, which is why we use the SNR to quantitatively scale the PML effects,展开更多
An element-free Galerkin method(EFGM) is used to solve the two-dimensional(2D) ground penetrating radar(GPR)modelling problems, due to its simple pre-processing, the absence of elements and high accuracy. Different fr...An element-free Galerkin method(EFGM) is used to solve the two-dimensional(2D) ground penetrating radar(GPR)modelling problems, due to its simple pre-processing, the absence of elements and high accuracy. Different from element-based numerical methods, this approach makes nodes free from the elemental restraint and avoids the explicit mesh discretization. First, we derived the boundary value problem for the 2D GPR simulation problems. Second, a penalty function approach and a boundary condition truncated method were used to enforce the essential and the absorbing boundary conditions, respectively. A three-layered GPR model was used to verify our element-free approach. The numerical solutions show that our solutions have an excellent agreement with solutions of a finite element method(FEM). Then, we used the EFGM to simulate one more complex model to show its capability and limitations. Simulation results show that one obvious advantage of EFGM is the absence of element mesh, which makes the method very flexible. Due to the use of MLS fitting, a key feature of EFM, is that both the dependent variable and its gradient are continuous and have high precision.展开更多
Using cluster Monte Carlo method, we numerically investigate the coupling on the simple cubic lattice. We determine critical lines belong to the criticality in the XY model with nematic three-dimensional XY universali...Using cluster Monte Carlo method, we numerically investigate the coupling on the simple cubic lattice. We determine critical lines belong to the criticality in the XY model with nematic three-dimensional XY universality class in variable of θ （2θ） between the XY-ferromagnetic （nematic） and disordered states. Fhrthermore, the phase transition between the XY-ferromagnetic and the nematie states is found to be in the three-dimensional Ising universality class. The critical points are determined from the intersections of Binder ratios for various system sizes. With two sets of critical points obtained, we finally construct the phase diagram on the A-J plane.展开更多
Wireless technology provides accurate positioning in indoor environments using time of arrival(TOA) based ranging techniques. However, the positioning accuracy is degraded due to the ranging errors caused by multipath...Wireless technology provides accurate positioning in indoor environments using time of arrival(TOA) based ranging techniques. However, the positioning accuracy is degraded due to the ranging errors caused by multipath and non-line-of-sight(NLOS) propagation. In this paper, a ranging error correction method is proposed to improve positioning performance. A TOA ranging error model(TREM) is built to provide the prior information for ranging error correction first. The mean value of TREM within a certain interval is used as the ranging error correction value(RECV). As the RECV may be unreasonable sometimes, we adjust it according to the actual positioning situation and then exploit the final RECV to correct ranging data. The experimental results show that the proposed method could well reduce ranging errors and the positioning performance is obviously improved when using corrected ranging data.展开更多
Combined with a digital bored photography system and in-situ statistics concerning the joints and fissures of both ore-body and surrounding rock,a 2D discrete model was constructed using UDEC.The stress field and disp...Combined with a digital bored photography system and in-situ statistics concerning the joints and fissures of both ore-body and surrounding rock,a 2D discrete model was constructed using UDEC.The stress field and displacement field changes of different sublevel stoping systems were also studied.Changes in the overlying rock strata settlement pattern has been analyzed and validated by in-situ monitoring data.The results show that:in the caving process,there exists an obvious delay and jump for the overlying rock strata displacement over time,and a stable arch can be formed in the process of caving,which leads to hidden goafs.Disturbed by the mining activity,a stress increase occurred in both the hanging wall and the foot wall,demonstrating a hump-shaped distribution pattern.From the comparison between simulation results and in-situ monitoring results,land subsidence shows a slow-development,suddenfailure,slow-development cycle pattern,which leads eventually to a stable state.This pattern validates the existence of balanced arch and hidden goafs.展开更多
We investigate the influence of blurred ways on pattern recognition of a Barabasi-Albert scale-free Hopfield neural network （SFHN） with a small amount of errors. Pattern recognition is an important function of infor...We investigate the influence of blurred ways on pattern recognition of a Barabasi-Albert scale-free Hopfield neural network （SFHN） with a small amount of errors. Pattern recognition is an important function of information processing in brain. Due to heterogeneous degree of scale-free network, different blurred ways have different influences on pattern recognition with same errors. Simulation shows that among partial recognition, the larger loading ratio （the number of patterns to average degree P/ （k） ） is, the smaller the overlap of SFHN is. The influence of directed （large） way is largest and the directed （small） way is smallest while random way is intermediate between them. Under the ratio of the numbers of stored patterns to the size of the network PIN is less than O. 1 conditions, there are three families curves of the overlap corresponding to directed （small）, random and directed （large） blurred ways of patterns and these curves are not associated with the size of network and the number of patterns. This phenomenon only occurs in the SFHN. These conclusions are benefit for understanding the relation between neural network structure and brain function.展开更多
基金Project(51275130)supported by the National Natural Science Foundation of China
文摘A numerical method for coupled deformation between sheet metal and flexible-die was proposed. Based on the updated Lagrangian （UL） formulation, the elastoplastic deformation of sheet metal was analyzed with finite element method （FEM） and the bulk deformation of flexible-die was analyzed with element-free Galerkin method （EFGM）. The frictional contact between sheet metal and flexible-die was treated by the penalty function method. The sheet elastic flexible-die bulging process was analyzed with the FEM-EFGM program for coupled deformation between sheet metal and bulk flexible-die, called CDSB-FEM-EFGM for short. Compared with finite element code DEFORM-2D and experiment results, the CDSB-FEM-EFGM program is feasible. This method provides a suitable numerical method to analyze sheet flexible-die forming.
文摘A combined method for the fast 3-D finite element modeling of defect responses in nondestructive testing of electromagnetics is presented. The method consists of three numerical techniques: zoom-in technique, difference field technique and iterative solution technique. Utilizing the zoom-in technique, the computational zone focuses on a relatively small domain around the defect. Employing the difference field technique, the axisymmetrical field solution corresponding to the case with no defect can be used to simplify the mesh generation and obtain the modeling results quickly. Using the iterative solution technique, the matrix equation system in the 3-D finite element modeling of nondestructive probe signals can easily be solved. The sample calculation shows that the presented method is highly effective and can consequently save significant computer resources.
基金Project(51202066)supported by the National Natural Science Foundation of ChinaProject(NCET-13-0784)supported by the Program for New Century Excellent Talents in University of China。
文摘Hollow-structured Cu_(0.3)Co_(2.7)O_(4) microspheres have been synthesized by a simple one-pot template-free hydrothermal method with copper sulfate,cobalt acetate and ammonia as raw materials.The products were characterized by powder X-ray diffraction,energy dispersive X-ray analysis,selected area electron diffraction,high-resolution transmission electron microscopy,scanning electron microscopy and BET measurements.The research results show that the hollow Cu_(0.3)Co_(2.7)O_(4) microspheres consist of single-crystalline nanocubes with the diameter of about 20 nm.The formation mechanism of hollow Cu_(0.3)Co_(2.7)O_(4) microspheres is suggested as Ostwald ripening in a solid-solution-solid process,and Cu_(0.3)Co_(2.7)O_(4) microspheres are mesoporous containing two pore sizes of 3.3 and 5.9 nm.The as-prepared Cu_(0.3)Co_(2.7)O_(4) sensors have optimal gas responses to 50×10^(−6) mg/m^(3) C_(2)H_(5)OH at 190℃.
基金supported by National High-Tech Research & Development Program of China (Grant No. 2008AA12Z305)
文摘A novel radio-map establishment based on fuzzy clustering for hybrid K-Nearest Neighbor (KNN) and Artifi cial Neural Network (ANN) position algorithm in WLAN indoor environment is proposed. First of all, the Principal Component Analysis (PCA) is utilized for the purpose of simplifying input dimensions of position estimation algorithm and saving storage cost for the establishment of radio-map. Then, reference points (RPs) calibrated in the off-line phase are divided into separate clusters by Fuzzy C-means clustering (FCM), and membership degrees (MDs) for different clusters are also allocated to each RPs. However, the singular RPs cased by the multi-path effect signifi cantly decreases the clustering performance. Therefore, a novel radio-map establishment method is presented based on the modifi cation of signal samples recorded at singular RPs by surface fitting. In the on-line phase, the region which the mobile terminal (MT) belongs to is estimated according to the MDs firstly. Then, in estimated small dimensional regions, MT's coordinates are calculated byKNN positioning method for efficiency purpose. However, for the regions including singular RPs, ANN method is utilized because ofits great pattern matching ability. Furthermore, compared with other typical indoor positioning methods, feasibility and effectiveness of this hybrid KNN/ANN method are also verified by the experimental results in static and tracking situations.
文摘In this paper a hybrid algorithm which combines the pattern search method and the genetic algorithm for unconstrained optimization is presented. The algorithm is a deterministic pattern search algorithm,but in the search step of pattern search algorithm,the trial points are produced by a way like the genetic algorithm. At each iterate, by reduplication,crossover and mutation, a finite set of points can be used. In theory,the algorithm is globally convergent. The most stir is the numerical results showing that it can find the global minimizer for some problems ,which other pattern search algorithms don＇t bear.
文摘The mechanism of stress generation and propagation by detonation loading in five separate independent advance of ore breaking patterns is discussed in the paper. An elastic numerical model was developed using AN- SYS/LS-DYNA 3D Nonlinear Dynamic Finite Element Software. In this package ANSYS is the preprocessor and LS-DYNA is the postprocessor. Numerical models in the paper to actual were l：10 and the element mesh was dissected in scanning mode utilizing the symmetry characteristics of the numerical model. Five different advance rates were studied. Parameters, such as the time required to maximum stress, the action time of the available stress, the maximum velocity of the nodes, the stress penetration time, the magnitude of the stress peak and the time duration for high stress were numerically simulated. The 2.2 m advance appeared optimum from an analysis of the simulation results. The results from numerical simulation have been validated by tests with physical models.
基金The project supported by the President Foundation of the Chinese Academy of Sciences
文摘For the first time, we introduce a fully quantum mechanical Hamiltonian for a semi-infinite chain model of atoms. We then derive the vibration modes of this model by virtue of the ＂invariant eigen-operator＂ method in two different cases, which is concise and revealing.
基金Sponsored by the Science Foundation for Youths of Heilongjiang province (Grant No.QC08C05)
文摘For real-time and distributed features of multi-robot system,the strategy of combining the improved artificial potential field method and the rules based on priority is proposed to study the collision avoidance planning in multi-robot systems. The improved artificial potential field based on simulated annealing algorithm satisfactorily overcomes the drawbacks of traditional artificial potential field method,so that robots can find a local collision-free path in the complex environment. According to the movement vector trail of robots,collisions between robots can be detected,thereby the collision avoidance rules can be obtained. Coordination between robots by the priority based rules improves the real-time property of multi-robot system. The combination of these two methods can help a robot to find a collision-free path from a starting point to the goal quickly in an environment with many obstacles. The feasibility of the proposed method is validated in the VC-based simulated environment.
基金Sponsored by K.C.Wong Magna Fund in Ningbo University and Ningbo Natural Science Foundation under Grant Nos.2008A610017 and 2007A610049
文摘In this paper exact solutions of a new modified nonlinearly dispersive equation （simply called inK（m, n, a, b） Ua Ub equation）, u^m-1 ut ＋ α（ u^n）x ＋β（u^a（u^b）xx）x = 0, is investigated by using some direct algorithms. As a result, abundant new compacton solutions （solitons with the absence of infinite wings） and solitary pattern solutions （having infinite slopes or cusps） are obtained.
基金supported jointly by the 973 Program (Grant No.2007CB209505)the National Natural Science Fund (Grant No.40704019,40674061)+1 种基金the School Basic Research Fund of Tsinghua University (JC2007030)PetroChina Innovation Fund (Grant No.060511-1-1)
文摘When modeling wave propagation in infinite space, it is necessary to have stable absorbing boundaries to effectively eliminate spurious reflections from the truncation boundaries. The SH wave equations for Perfectly Matched Layers （PML） are deduced and their Crank-Nicolson scheme are presented in this paper. We use the second-, sixth-, and tenth-order finite difference and pseudo-spectral algorithms to compute the spatial derivatives. Two numerical models, a homogeneous isotropic medium and a multi-layer model with a cave, are designed to investigate how the absorbing boundary width and the algorithms determine PML effects. Numerical results show that, for PML, the low-order finite difference algorithms have fairly good absorbing effects when the absorbing boundary is thin, whereas, high-order algorithms always have good absorption when the boundary is thick. Finally, we discuss the reflection coefficient and point out its shortcomings, which is why we use the SNR to quantitatively scale the PML effects,
基金Project(41074085)supported by the National Natural Science Foundation of ChinaProject(NCET-12-0551)supported by the Funds for New Century Excellent Talents in University,ChinaProject supported by Shenghua Yuying Program of Central South University,China
文摘An element-free Galerkin method(EFGM) is used to solve the two-dimensional(2D) ground penetrating radar(GPR)modelling problems, due to its simple pre-processing, the absence of elements and high accuracy. Different from element-based numerical methods, this approach makes nodes free from the elemental restraint and avoids the explicit mesh discretization. First, we derived the boundary value problem for the 2D GPR simulation problems. Second, a penalty function approach and a boundary condition truncated method were used to enforce the essential and the absorbing boundary conditions, respectively. A three-layered GPR model was used to verify our element-free approach. The numerical solutions show that our solutions have an excellent agreement with solutions of a finite element method(FEM). Then, we used the EFGM to simulate one more complex model to show its capability and limitations. Simulation results show that one obvious advantage of EFGM is the absence of element mesh, which makes the method very flexible. Due to the use of MLS fitting, a key feature of EFM, is that both the dependent variable and its gradient are continuous and have high precision.
基金Supported by National Natural Science Foundation of China under Grant No. 10974180
文摘Using cluster Monte Carlo method, we numerically investigate the coupling on the simple cubic lattice. We determine critical lines belong to the criticality in the XY model with nematic three-dimensional XY universality class in variable of θ （2θ） between the XY-ferromagnetic （nematic） and disordered states. Fhrthermore, the phase transition between the XY-ferromagnetic and the nematie states is found to be in the three-dimensional Ising universality class. The critical points are determined from the intersections of Binder ratios for various system sizes. With two sets of critical points obtained, we finally construct the phase diagram on the A-J plane.
基金supported in part by Huawei Innovation Research Program(Grant No.YB2013020011)
文摘Wireless technology provides accurate positioning in indoor environments using time of arrival(TOA) based ranging techniques. However, the positioning accuracy is degraded due to the ranging errors caused by multipath and non-line-of-sight(NLOS) propagation. In this paper, a ranging error correction method is proposed to improve positioning performance. A TOA ranging error model(TREM) is built to provide the prior information for ranging error correction first. The mean value of TREM within a certain interval is used as the ranging error correction value(RECV). As the RECV may be unreasonable sometimes, we adjust it according to the actual positioning situation and then exploit the final RECV to correct ranging data. The experimental results show that the proposed method could well reduce ranging errors and the positioning performance is obviously improved when using corrected ranging data.
基金financially supported by the National Natural Science Foundation of China(No.51374033)the Doctoral Program of Higher Education Research Fund(No.20120006110022)the Chenchao Iron Mine and the technical support of Itasca
文摘Combined with a digital bored photography system and in-situ statistics concerning the joints and fissures of both ore-body and surrounding rock,a 2D discrete model was constructed using UDEC.The stress field and displacement field changes of different sublevel stoping systems were also studied.Changes in the overlying rock strata settlement pattern has been analyzed and validated by in-situ monitoring data.The results show that:in the caving process,there exists an obvious delay and jump for the overlying rock strata displacement over time,and a stable arch can be formed in the process of caving,which leads to hidden goafs.Disturbed by the mining activity,a stress increase occurred in both the hanging wall and the foot wall,demonstrating a hump-shaped distribution pattern.From the comparison between simulation results and in-situ monitoring results,land subsidence shows a slow-development,suddenfailure,slow-development cycle pattern,which leads eventually to a stable state.This pattern validates the existence of balanced arch and hidden goafs.
基金Supported by "Qing Lan" Talent Engineering Funds by Lanzhou Jiaotong University under Grant No. QL-08-18A
文摘We investigate the influence of blurred ways on pattern recognition of a Barabasi-Albert scale-free Hopfield neural network （SFHN） with a small amount of errors. Pattern recognition is an important function of information processing in brain. Due to heterogeneous degree of scale-free network, different blurred ways have different influences on pattern recognition with same errors. Simulation shows that among partial recognition, the larger loading ratio （the number of patterns to average degree P/ （k） ） is, the smaller the overlap of SFHN is. The influence of directed （large） way is largest and the directed （small） way is smallest while random way is intermediate between them. Under the ratio of the numbers of stored patterns to the size of the network PIN is less than O. 1 conditions, there are three families curves of the overlap corresponding to directed （small）, random and directed （large） blurred ways of patterns and these curves are not associated with the size of network and the number of patterns. This phenomenon only occurs in the SFHN. These conclusions are benefit for understanding the relation between neural network structure and brain function.
