In order to solve the problems of too large mass,too complex structure and poor flexibility of the 6 DOF manipulator,the topological optimization theory based on variable density method is applied to the 6-DOF manipul...In order to solve the problems of too large mass,too complex structure and poor flexibility of the 6 DOF manipulator,the topological optimization theory based on variable density method is applied to the 6-DOF manipulator,the topology optimization of the main structural components of the manipulator is carried out with the help of the finite element software ANSYS,and the optimized structure is simplified according to the density distribution of the units and the requirements of manufacturability.the results are compared and analysed by static mechanics.It shows that the whole mass of the 6-DOF manipulator is reduced by 47.23%without changing the original mechanical properties after topological optimization,and the optimized model can meet the requirements of manufacturability,the optimization effect is signifcant,which can be used as a reference for the structure optimization of the 6-DOF manipulator.展开更多
A combined shape and topology optimization algorithm based on isogeometric boundary element method for 3D acoustics is developed in this study.The key treatment involves using adjoint variable method in shape sensitiv...A combined shape and topology optimization algorithm based on isogeometric boundary element method for 3D acoustics is developed in this study.The key treatment involves using adjoint variable method in shape sensitivity analysis with respect to non-uniform rational basis splines control points,and in topology sensitivity analysis with respect to the artificial densities of sound absorption material.OpenMP tool in Fortran code is adopted to improve the efficiency of analysis.To consider the features and efficiencies of the two types of optimization methods,this study adopts a combined iteration scheme for the optimization process to investigate the simultaneous change of geometry shape and distribution of material to achieve better noise control.Numerical examples,such as sound barrier,simple tank,and BeTSSi submarine,are performed to validate the advantage of combined optimization in noise reduction,and to demonstrate the potential of the proposed method for engineering problems.展开更多
Reliability and optimization are two key elements for structural design. The reliability~ based topology optimization （RBTO） is a powerful and promising methodology for finding the optimum topologies with the uncert...Reliability and optimization are two key elements for structural design. The reliability~ based topology optimization （RBTO） is a powerful and promising methodology for finding the optimum topologies with the uncertainties being explicitly considered, typically manifested by the use of reliability constraints. Generally, a direct integration of reliability concept and topol- ogy optimization may lead to computational difficulties. In view of this fact, three methodologies have been presented in this study, including the double-loop approach （the performance measure approach, PMA） and the decoupled approaches （the so-called Hybrid method and the sequential optimization and reliability assessment, SORA）. For reliability analysis, the stochastic response surface method （SRSM） was applied, combining with the design of experiments generated by the sparse grid method, which has been proven as an effective and special discretization technique. The methodologies were investigated with three numerical examples considering the uncertainties including material properties and external loads. The optimal topologies obtained using the de- terministic, RBTOs were compared with one another; and useful conclusions regarding validity, accuracy and efficiency were drawn.展开更多
Non-dominated sorting genetic algorithm II（NSGA-II）with multiple constraints handling is employed for multi-objective optimization of the topological structure of telescope skin,in which a bit-matrix is used as the ...Non-dominated sorting genetic algorithm II（NSGA-II）with multiple constraints handling is employed for multi-objective optimization of the topological structure of telescope skin,in which a bit-matrix is used as the representation of a chromosome,and genetic algorithm（GA）operators are introduced based on the matrix.Objectives including mass,in-plane performance,and out-of-plane load-bearing ability of the individuals are obtained by fnite element analysis（FEA）using ANSYS,and the matrix-based optimization algorithm is realized in MATLAB by handling multiple constraints such as structural connectivity and in-plane strain requirements.Feasible confgurations of the support structure are achieved.The results confrm that the matrix-based NSGA-II with multiple constraints handling provides an effective method for two-dimensional multi-objective topology optimization.展开更多
In this work,an acoustic topology optimizationmethod for structural surface design covered by porous materials is proposed.The analysis of acoustic problems is performed using the isogeometric boundary elementmethod.T...In this work,an acoustic topology optimizationmethod for structural surface design covered by porous materials is proposed.The analysis of acoustic problems is performed using the isogeometric boundary elementmethod.Taking the element density of porousmaterials as the design variable,the volume of porousmaterials as the constraint,and the minimum sound pressure or maximum scattered sound power as the design goal,the topology optimization is carried out by solid isotropic material with penalization(SIMP)method.To get a limpid 0–1 distribution,a smoothing Heaviside-like function is proposed.To obtain the gradient value of the objective function,a sensitivity analysis method based on the adjoint variable method(AVM)is proposed.To find the optimal solution,the optimization problems are solved by the method of moving asymptotes(MMA)based on gradient information.Numerical examples verify the effectiveness of the proposed topology optimization method in the optimization process of two-dimensional acoustic problems.Furthermore,the optimal distribution of sound-absorbingmaterials is highly frequency-dependent and usually needs to be performed within a frequency band.展开更多
The reliability based optimization （RBO） issue of composite laminates trader fundamental frequency constraint is studied. Considering the tmcertainties of material properties, the frequency constraint reliability of...The reliability based optimization （RBO） issue of composite laminates trader fundamental frequency constraint is studied. Considering the tmcertainties of material properties, the frequency constraint reliability of the structure is evaluated by the combination of response surface method （RSM） and finite element method. An optimization algorithm is developed based on the mechanism of laminate frequency characteristics, to optimize the laminate in terms of the ply amount and orientation angles. Numerical examples of composite laminates and cylindrical shell illustrate the advantages of the present optimization algorithm on the efficiency and applicability respects. The optimal solutions of RBO are obviously different from the deterministic optimization results, and the necessity of considering material property uncertainties in the composite structural frequency constraint optimization is revealed.展开更多
Structural topology optimization subjected to stationary random base acceleration excitations is investigated in this paper. In the random response analysis, the Large Mass Method(LMM) which attributes artificial larg...Structural topology optimization subjected to stationary random base acceleration excitations is investigated in this paper. In the random response analysis, the Large Mass Method(LMM) which attributes artificial large mass values at each driven nodal Degree Of Freedom(DOF) to transforming the base acceleration excitations into force excitations is proposed. The Complete Quadratic Combination(CQC) which is commonly used to calculate the random responses in previous optimization has been proven to be computationally expensive especially for large-scale problems. In order to conquer this difficulty, the Pseudo Excitation Method(PEM) and the combined method of PEM and Mode Acceleration Method(MAM) are adopted into the dynamic topology optimization, and random responses are calculated using these two methods to ascertain a high efficiency over the CQC. A density-based topology optimization method minimizing dynamic responses is then formulated based on the integration of LMM and PEM or the combined method of PEM and MAM. Numerical examples are presented to verify the accuracy of the proposed schemes in dynamic response analysis and the quality of the optimized design in improving dynamic performance.展开更多
For the purpose of achieving high-resolution optimal solutions this paper proposes a nodal design variablebased adaptive method for topology optimization of continuum structures. The analysis mesh-independent density ...For the purpose of achieving high-resolution optimal solutions this paper proposes a nodal design variablebased adaptive method for topology optimization of continuum structures. The analysis mesh-independent density field, interpolated by the nodal design variables at a given set of density points, is adaptively refined/coarsened accord- ing to a criterion regarding the gray-scale measure of local regions. New density points are added into the gray regions and redundant ones are removed from the regions occupied by purely solid/void phases for decreasing the number of de- sign variables. A penalization factor adaptivity technique is employed-to prevent premature convergence of the optimiza- tion iterations. Such an adaptive scheme not only improves the structural boundary description quality, but also allows for sufficient further topological evolution of the structural layout in higher adaptivity levels and thus essentially enables high-resolution solutions. Moreover, compared with the case with uniformly and finely distributed density points, the proposed adaptive method can achieve a higher numerical efficiency of the optimization process.展开更多
Sensitivity analysis and topology optimization of microstructures using strain energy-based method is presented. Compared with homogenization method, the strain energy-based method has advantages of higher computing e...Sensitivity analysis and topology optimization of microstructures using strain energy-based method is presented. Compared with homogenization method, the strain energy-based method has advantages of higher computing efficiency and simplified programming. Both the dual convex programming method and perimeter constraint scheme are used to optimize the 2D and 3D microstructures. Numerical results indicate that the strain energy-based method has the same effectiveness as that of homogenization method for orthotropic materials.展开更多
This paper presents new hybrid methods for the identification of optimal topologies by combining the teaching-learning based optimization(TLBO)and the method of moving asymptotes(MMA).The topology optimization problem...This paper presents new hybrid methods for the identification of optimal topologies by combining the teaching-learning based optimization(TLBO)and the method of moving asymptotes(MMA).The topology optimization problem is parameterizing with a low dimensional explicit method called moving morphable components(MMC),to make the use of evolutionary algorithms more efficient.Gradient-based solvers have good performance in solving large-scale topology optimization problems.However,in unconventional cases same as crashworthiness design in which there is numerical noise in the gradient information,the uses of these algorithms are unsuitable.The standard evolutionary algorithms can solve such problems since they don’t need gradient information.However,they have a high computational cost.This paper is based upon the idea of combining metaheuristics with mathematical programming to handle the probable noises and have faster convergence speed.Due to the ease of computations,the compliance minimization problem is considered as the case study and the artificial noise is added in gradient information.展开更多
This paper presents a feature modeling approach to address the 3D structural topology design optimization withfeature constraints. In the proposed algorithm, various features are formed into searchable shape features ...This paper presents a feature modeling approach to address the 3D structural topology design optimization withfeature constraints. In the proposed algorithm, various features are formed into searchable shape features bythe feature modeling technology, and the models of feature elements are established. The feature elements thatmeet the design requirements are found by employing a feature matching technology, and the constraint factorscombined with the pseudo density of elements are initialized according to the optimized feature elements. Then,through controlling the constraint factors and utilizing the optimization criterion method along with the filteringtechnology of independent mesh, the structural design optimization is implemented. The present feature modelingapproach is applied to the feature-based structural topology optimization using empirical data. Meanwhile, theimproved mathematical model based on the density method with the constraint factors and the correspondingsolution processes are also presented. Compared with the traditional method which requires complicated constraintprocessing, the present approach is flexibly applied to the 3D structural design optimization with added holesby changing the constraint factors, thus it can design a structure with predetermined features more directly andeasily. Numerical examples show effectiveness of the proposed feature modeling approach, which is suitable for thepractical engineering design.展开更多
In this paper,a fast design method is developed based on a combination of analytical and finite element(FE)methods for variable flux reluctance machines(VFRMs).Firstly,the feasibility of using analytical method in opt...In this paper,a fast design method is developed based on a combination of analytical and finite element(FE)methods for variable flux reluctance machines(VFRMs).Firstly,the feasibility of using analytical method in optimization under unsaturated condition is confirmed.Then,by applying the FE method,the influence of magnetic saturation is considered.Compared with the unsaturated case,the optimal split ratio for magnetically saturated case is increased by 1~1.2 times,the optimal rotor pole arc ratio varies within 0.33~0.44,and the stator pole arc ratio remains the same.Based on this,the optimal structural parameters can be initially set by analytical method and then refined by the FE method.Due to the fast speed of analytical method,less variable counts and narrowed variation ranges,the proposed method is significantly faster than the conventional pure FE based global optimization.Finally,the proposed method is used for optimizing the 6-stator-slots VFRMs having different numbers of rotor poles.The 6-stator-slot/7-rotor-pole(6s/7r)VFRM is found to have the highest torque density.It is prototyped and tested to verify the analyses.展开更多
目的 Linear Programming的simplexmethod建模求最优解。方法应用simplexmethod.结果建立了LinearProgramming的数学模型并用simplexmethod求得了最优解.结论因为单纯形表反映了Linear Programming的所有信息,故用simplexmethod可简便...目的 Linear Programming的simplexmethod建模求最优解。方法应用simplexmethod.结果建立了LinearProgramming的数学模型并用simplexmethod求得了最优解.结论因为单纯形表反映了Linear Programming的所有信息,故用simplexmethod可简便地求得最优解.simplexmethod的基本思路是:先将Linear Programming用sim-plexmethod划为标准型,根据问题的标准型,进行初等行变换,将主元素列除主元素化为1外其余的元素均化为0,当基变量值全为非负时,问题就得到了最优解.展开更多
In this research we are going to define two new concepts: a) “The Potential of Events” (EP) and b) “The Catholic Information” (CI). The term CI derives from the ancient Greek language and declares all the Catholic...In this research we are going to define two new concepts: a) “The Potential of Events” (EP) and b) “The Catholic Information” (CI). The term CI derives from the ancient Greek language and declares all the Catholic (general) Logical Propositions (<img src="Edit_5f13a4a5-abc6-4bc5-9e4c-4ff981627b2a.png" width="33" height="21" alt="" />) which will true for every element of a set A. We will study the Riemann Hypothesis in two stages: a) By using the EP we will prove that the distribution of events e (even) and o (odd) of Square Free Numbers (SFN) on the axis Ax(N) of naturals is Heads-Tails (H-T) type. b) By using the CI we will explain the way that the distribution of prime numbers can be correlated with the non-trivial zeros of the function ζ(s) of Riemann. The Introduction and the Chapter 2 are necessary for understanding the solution. In the Chapter 3 we will present a simple method of forecasting in many very useful applications (e.g. financial, technological, medical, social, etc) developing a generalization of this new, proven here, theory which we finally apply to the solution of RH. The following Introduction as well the Results with the Discussion at the end shed light about the possibility of the proof of all the above. The article consists of 9 chapters that are numbered by 1, 2, …, 9.展开更多
基金supported in part by China intelligent robot project of firm-universities cooperative R&D under Grant No.2021JQR021the Anhui Provincial Teaching Demonstration Course Project under Grant No.2020SJJXSFK0330+9 种基金the demonstration experiment training center project of Anhui Polytechnic University under Grant No.2020sysx02the Overseas Visiting and Research Project for Outstanding Young Backbone Talents in Universities of Anhui Province under Grant No.gxgwfx2019041the Innovation Project for Returned Overseas Students in Anhui Province under Grant No.2020LCX013Key Research and Development Projects of Anhui Province under Grant No.202004b11020006Scientific Research Foundation of Anhui Polytechnic University under Grant No.2020YQQ010Anhui Polytechnic University Research Initiation Fund for Introducing Talents under Grant No.2019YQQ004Anhui Polytechnic University Research Project under Grant No.Xjky019201905Industrial Collaborative Innovation Fund of Anhui Polytechnic University and Jiujiang District under Grant No.2021cyxtb9Open Project of Anhui Provincial Engineering Laboratory on Information Fusion and Control of Intelligent Robot under Grant No.IFCIR2020001Open project of Key Laboratory of industrial equipment quality big data Ministry of industry and information technology under Grant No.2021-IEQBD-05.
文摘In order to solve the problems of too large mass,too complex structure and poor flexibility of the 6 DOF manipulator,the topological optimization theory based on variable density method is applied to the 6-DOF manipulator,the topology optimization of the main structural components of the manipulator is carried out with the help of the finite element software ANSYS,and the optimized structure is simplified according to the density distribution of the units and the requirements of manufacturability.the results are compared and analysed by static mechanics.It shows that the whole mass of the 6-DOF manipulator is reduced by 47.23%without changing the original mechanical properties after topological optimization,and the optimized model can meet the requirements of manufacturability,the optimization effect is signifcant,which can be used as a reference for the structure optimization of the 6-DOF manipulator.
基金This study was financially supported by the National Natural Science Foundation of China(NSFC)under Grant No.11772322the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No.XDB22040502.
文摘A combined shape and topology optimization algorithm based on isogeometric boundary element method for 3D acoustics is developed in this study.The key treatment involves using adjoint variable method in shape sensitivity analysis with respect to non-uniform rational basis splines control points,and in topology sensitivity analysis with respect to the artificial densities of sound absorption material.OpenMP tool in Fortran code is adopted to improve the efficiency of analysis.To consider the features and efficiencies of the two types of optimization methods,this study adopts a combined iteration scheme for the optimization process to investigate the simultaneous change of geometry shape and distribution of material to achieve better noise control.Numerical examples,such as sound barrier,simple tank,and BeTSSi submarine,are performed to validate the advantage of combined optimization in noise reduction,and to demonstrate the potential of the proposed method for engineering problems.
基金Project supported by the National Natural Science Foundation of China(Nos.51275040 and 50905017)the Programme of Introducing Talents of Discipline to Universities(No.B12022)
文摘Reliability and optimization are two key elements for structural design. The reliability~ based topology optimization （RBTO） is a powerful and promising methodology for finding the optimum topologies with the uncertainties being explicitly considered, typically manifested by the use of reliability constraints. Generally, a direct integration of reliability concept and topol- ogy optimization may lead to computational difficulties. In view of this fact, three methodologies have been presented in this study, including the double-loop approach （the performance measure approach, PMA） and the decoupled approaches （the so-called Hybrid method and the sequential optimization and reliability assessment, SORA）. For reliability analysis, the stochastic response surface method （SRSM） was applied, combining with the design of experiments generated by the sparse grid method, which has been proven as an effective and special discretization technique. The methodologies were investigated with three numerical examples considering the uncertainties including material properties and external loads. The optimal topologies obtained using the de- terministic, RBTOs were compared with one another; and useful conclusions regarding validity, accuracy and efficiency were drawn.
基金supported by the National Natural Science Foundation of China(Nos.50905085 and 91116020)the National Science Foundation for Post-doctoral Scientists of China(No.2012M511263)
文摘Non-dominated sorting genetic algorithm II（NSGA-II）with multiple constraints handling is employed for multi-objective optimization of the topological structure of telescope skin,in which a bit-matrix is used as the representation of a chromosome,and genetic algorithm（GA）operators are introduced based on the matrix.Objectives including mass,in-plane performance,and out-of-plane load-bearing ability of the individuals are obtained by fnite element analysis（FEA）using ANSYS,and the matrix-based optimization algorithm is realized in MATLAB by handling multiple constraints such as structural connectivity and in-plane strain requirements.Feasible confgurations of the support structure are achieved.The results confrm that the matrix-based NSGA-II with multiple constraints handling provides an effective method for two-dimensional multi-objective topology optimization.
基金sponsored by Natural Science Foundation of Henan under Grant No.222300420498.
文摘In this work,an acoustic topology optimizationmethod for structural surface design covered by porous materials is proposed.The analysis of acoustic problems is performed using the isogeometric boundary elementmethod.Taking the element density of porousmaterials as the design variable,the volume of porousmaterials as the constraint,and the minimum sound pressure or maximum scattered sound power as the design goal,the topology optimization is carried out by solid isotropic material with penalization(SIMP)method.To get a limpid 0–1 distribution,a smoothing Heaviside-like function is proposed.To obtain the gradient value of the objective function,a sensitivity analysis method based on the adjoint variable method(AVM)is proposed.To find the optimal solution,the optimization problems are solved by the method of moving asymptotes(MMA)based on gradient information.Numerical examples verify the effectiveness of the proposed topology optimization method in the optimization process of two-dimensional acoustic problems.Furthermore,the optimal distribution of sound-absorbingmaterials is highly frequency-dependent and usually needs to be performed within a frequency band.
基金National Natural Science Foundation of China (51412060104HK0123)
文摘The reliability based optimization （RBO） issue of composite laminates trader fundamental frequency constraint is studied. Considering the tmcertainties of material properties, the frequency constraint reliability of the structure is evaluated by the combination of response surface method （RSM） and finite element method. An optimization algorithm is developed based on the mechanism of laminate frequency characteristics, to optimize the laminate in terms of the ply amount and orientation angles. Numerical examples of composite laminates and cylindrical shell illustrate the advantages of the present optimization algorithm on the efficiency and applicability respects. The optimal solutions of RBO are obviously different from the deterministic optimization results, and the necessity of considering material property uncertainties in the composite structural frequency constraint optimization is revealed.
基金supported by the Innovation and Development Foundation of ISE, CAEP (2017 cxj18)the Presidential Foundation of CAEP (YZJJLX2018008)
文摘Structural topology optimization subjected to stationary random base acceleration excitations is investigated in this paper. In the random response analysis, the Large Mass Method(LMM) which attributes artificial large mass values at each driven nodal Degree Of Freedom(DOF) to transforming the base acceleration excitations into force excitations is proposed. The Complete Quadratic Combination(CQC) which is commonly used to calculate the random responses in previous optimization has been proven to be computationally expensive especially for large-scale problems. In order to conquer this difficulty, the Pseudo Excitation Method(PEM) and the combined method of PEM and Mode Acceleration Method(MAM) are adopted into the dynamic topology optimization, and random responses are calculated using these two methods to ascertain a high efficiency over the CQC. A density-based topology optimization method minimizing dynamic responses is then formulated based on the integration of LMM and PEM or the combined method of PEM and MAM. Numerical examples are presented to verify the accuracy of the proposed schemes in dynamic response analysis and the quality of the optimized design in improving dynamic performance.
基金supported by the Key Project of Chinese National Programs for Fundamental Research and Development(2010CB832703)the National Natural Science Foundation of China(11072047 and 91130025)
文摘For the purpose of achieving high-resolution optimal solutions this paper proposes a nodal design variablebased adaptive method for topology optimization of continuum structures. The analysis mesh-independent density field, interpolated by the nodal design variables at a given set of density points, is adaptively refined/coarsened accord- ing to a criterion regarding the gray-scale measure of local regions. New density points are added into the gray regions and redundant ones are removed from the regions occupied by purely solid/void phases for decreasing the number of de- sign variables. A penalization factor adaptivity technique is employed-to prevent premature convergence of the optimiza- tion iterations. Such an adaptive scheme not only improves the structural boundary description quality, but also allows for sufficient further topological evolution of the structural layout in higher adaptivity levels and thus essentially enables high-resolution solutions. Moreover, compared with the case with uniformly and finely distributed density points, the proposed adaptive method can achieve a higher numerical efficiency of the optimization process.
基金National Natural Science Foundation of China （90405016, 10676028） 973 Program （2006CB601205）+1 种基金 863 Project （2006AA04Z 122） Aeronautical Science Foundation （04B53080, 2006ZA 53006） and 111 Project （B07050）
文摘Sensitivity analysis and topology optimization of microstructures using strain energy-based method is presented. Compared with homogenization method, the strain energy-based method has advantages of higher computing efficiency and simplified programming. Both the dual convex programming method and perimeter constraint scheme are used to optimize the 2D and 3D microstructures. Numerical results indicate that the strain energy-based method has the same effectiveness as that of homogenization method for orthotropic materials.
文摘This paper presents new hybrid methods for the identification of optimal topologies by combining the teaching-learning based optimization(TLBO)and the method of moving asymptotes(MMA).The topology optimization problem is parameterizing with a low dimensional explicit method called moving morphable components(MMC),to make the use of evolutionary algorithms more efficient.Gradient-based solvers have good performance in solving large-scale topology optimization problems.However,in unconventional cases same as crashworthiness design in which there is numerical noise in the gradient information,the uses of these algorithms are unsuitable.The standard evolutionary algorithms can solve such problems since they don’t need gradient information.However,they have a high computational cost.This paper is based upon the idea of combining metaheuristics with mathematical programming to handle the probable noises and have faster convergence speed.Due to the ease of computations,the compliance minimization problem is considered as the case study and the artificial noise is added in gradient information.
基金This work is supported by the National Natural Science Foundation of China(12002218)the Youth Foundation of Education Department of Liaoning Province(JYT19034).These supports are gratefully acknowledged.
文摘This paper presents a feature modeling approach to address the 3D structural topology design optimization withfeature constraints. In the proposed algorithm, various features are formed into searchable shape features bythe feature modeling technology, and the models of feature elements are established. The feature elements thatmeet the design requirements are found by employing a feature matching technology, and the constraint factorscombined with the pseudo density of elements are initialized according to the optimized feature elements. Then,through controlling the constraint factors and utilizing the optimization criterion method along with the filteringtechnology of independent mesh, the structural design optimization is implemented. The present feature modelingapproach is applied to the feature-based structural topology optimization using empirical data. Meanwhile, theimproved mathematical model based on the density method with the constraint factors and the correspondingsolution processes are also presented. Compared with the traditional method which requires complicated constraintprocessing, the present approach is flexibly applied to the 3D structural design optimization with added holesby changing the constraint factors, thus it can design a structure with predetermined features more directly andeasily. Numerical examples show effectiveness of the proposed feature modeling approach, which is suitable for thepractical engineering design.
文摘In this paper,a fast design method is developed based on a combination of analytical and finite element(FE)methods for variable flux reluctance machines(VFRMs).Firstly,the feasibility of using analytical method in optimization under unsaturated condition is confirmed.Then,by applying the FE method,the influence of magnetic saturation is considered.Compared with the unsaturated case,the optimal split ratio for magnetically saturated case is increased by 1~1.2 times,the optimal rotor pole arc ratio varies within 0.33~0.44,and the stator pole arc ratio remains the same.Based on this,the optimal structural parameters can be initially set by analytical method and then refined by the FE method.Due to the fast speed of analytical method,less variable counts and narrowed variation ranges,the proposed method is significantly faster than the conventional pure FE based global optimization.Finally,the proposed method is used for optimizing the 6-stator-slots VFRMs having different numbers of rotor poles.The 6-stator-slot/7-rotor-pole(6s/7r)VFRM is found to have the highest torque density.It is prototyped and tested to verify the analyses.
文摘目的 Linear Programming的simplexmethod建模求最优解。方法应用simplexmethod.结果建立了LinearProgramming的数学模型并用simplexmethod求得了最优解.结论因为单纯形表反映了Linear Programming的所有信息,故用simplexmethod可简便地求得最优解.simplexmethod的基本思路是:先将Linear Programming用sim-plexmethod划为标准型,根据问题的标准型,进行初等行变换,将主元素列除主元素化为1外其余的元素均化为0,当基变量值全为非负时,问题就得到了最优解.
文摘In this research we are going to define two new concepts: a) “The Potential of Events” (EP) and b) “The Catholic Information” (CI). The term CI derives from the ancient Greek language and declares all the Catholic (general) Logical Propositions (<img src="Edit_5f13a4a5-abc6-4bc5-9e4c-4ff981627b2a.png" width="33" height="21" alt="" />) which will true for every element of a set A. We will study the Riemann Hypothesis in two stages: a) By using the EP we will prove that the distribution of events e (even) and o (odd) of Square Free Numbers (SFN) on the axis Ax(N) of naturals is Heads-Tails (H-T) type. b) By using the CI we will explain the way that the distribution of prime numbers can be correlated with the non-trivial zeros of the function ζ(s) of Riemann. The Introduction and the Chapter 2 are necessary for understanding the solution. In the Chapter 3 we will present a simple method of forecasting in many very useful applications (e.g. financial, technological, medical, social, etc) developing a generalization of this new, proven here, theory which we finally apply to the solution of RH. The following Introduction as well the Results with the Discussion at the end shed light about the possibility of the proof of all the above. The article consists of 9 chapters that are numbered by 1, 2, …, 9.
