Multi-objective optimization for the optimum shape design is introduced in aerodynamics using the Game theory. Based on the control theory, the employed optimizer and the negative feedback are used to implement the co...Multi-objective optimization for the optimum shape design is introduced in aerodynamics using the Game theory. Based on the control theory, the employed optimizer and the negative feedback are used to implement the constraints. All the constraints are satisfied implicitly and automatically in the design. Furthermore,the above methodology is combined with a formulation derived from the Game theory to treat multi-point airfoil optimization. Airfoil shapes are optimized according to various aerodynamics criteria. In the symmetric Nash game, each “player” is responsible for one criterion, and the Nash equilibrium provides a solution to the multipoint optimization. Design results confirm the efficiency of the method.展开更多
Structural bionic design lacks mature and scientific theories, and the excellent structural characteristics of natural organisms sometimes cannot be transferred into engineering structures effectively. Aiming at overc...Structural bionic design lacks mature and scientific theories, and the excellent structural characteristics of natural organisms sometimes cannot be transferred into engineering structures effectively. Aiming at overcoming the existing problems, this paper summarizes three related theories: similarity theory, fuzzy evaluation theory and optimization theory. Based on the related theories, a method of structural bionic design is introduced, which includes four steps: selecting the most useful structural characteristic of natural organism; analyzing the structural characteristic finally chosen for engineering problem; completing the structural bionic design for engineering structure; and verifying the structural bionic design. Similarity theory and fuzzy evaluation theory are employed to achieve Step 1. In Step 2 and Step 3, optimization theory is employed to analyze the parameters of structures. Together with the thoughts of simplification and grouping, optimization theory can reveal the relationship between organism structure and engineering structure, providing a way to structural bionic design. A general evaluation criterion is proposed in Step 4, which is feasible to evaluate the performance of different structures. Finally, based on the method, a structural bionic design of thin-walled cylindrical shell is introduced.展开更多
The main contests of mire optimization design includes: mine field size, borizon and level height, mumber, shaft form and development disposal and so on. In this paper, based on mine dynamic analysis, the index functi...The main contests of mire optimization design includes: mine field size, borizon and level height, mumber, shaft form and development disposal and so on. In this paper, based on mine dynamic analysis, the index function model of mine different development stage is built up,applying dynamic programming method to find the solution of system’s optimum value,which makes the optimized result of mine dynamic design parameter more comprehensive, sysematical and reasonable. Through theory analysis research and practical validation, the obtained design parameters are reasonable and accurate.展开更多
Based on control theory,adjoint system for the general problem of turbomachinery aerodynamic optimization was studied and developed in the present paper by using the variation technique in the grid node coordinates co...Based on control theory,adjoint system for the general problem of turbomachinery aerodynamic optimization was studied and developed in the present paper by using the variation technique in the grid node coordinates combined with Jacobian Matrics of flow fluxes.Then the adjoint system for aerodynamic design optimization of turbine cascade governed by compressible Navier-Stokes equations was derived in detail.With the purpose of saving computation resources,the mathematic method presented in this paper avoids the coordinate system transforming in the traditional derivation process of the adjoint system and makes the adjoint system much more sententious.Given the general expression of objective functions consisting of both boundary integral and field integral,the adjoint equations and their boundary conditions were derived,and the final expression of the objective function gradient including only boundary integrals was formulated to reduce the CPU cost,especially for the complex 3D configurations.The adjoint system was solved numerically by using the finite volume method with an explicit 5-step Runge-Kutta scheme and Riemann approximate solution of Roe's scheme combined with multi-grid technique and local time step to accelerate the convergence procedure.Finally,based on the aerodynamic optimization theory in the present work,2D and 3D inviscid and viscous inverse design programs of axial turbomachinery cascade for both pressure distribution and isentropic Mach number distribution on the blade wall were developed,and several design optimization cases were performed successfully to demonstrate the ability and economy of the present optimization system.展开更多
A chaotic algorithm for providing a solution to the bi-level Discrete Equilibrium Network Design Problem （NDP） is discussed following an introduction of the Discrete Network Design Problem （DNDP） model and Chaos O...A chaotic algorithm for providing a solution to the bi-level Discrete Equilibrium Network Design Problem （NDP） is discussed following an introduction of the Discrete Network Design Problem （DNDP） model and Chaos Optimization Algorithms （COA）. A description of the chaotic approach for the DNDP model is described in details. Then a numerical example for the DNDP is carried out to investigate the chaotic approach. The results have been encouraging, indicating that the chaotic approach has great potential ability in finding the optimal solution of DNDP models.展开更多
文摘Multi-objective optimization for the optimum shape design is introduced in aerodynamics using the Game theory. Based on the control theory, the employed optimizer and the negative feedback are used to implement the constraints. All the constraints are satisfied implicitly and automatically in the design. Furthermore,the above methodology is combined with a formulation derived from the Game theory to treat multi-point airfoil optimization. Airfoil shapes are optimized according to various aerodynamics criteria. In the symmetric Nash game, each “player” is responsible for one criterion, and the Nash equilibrium provides a solution to the multipoint optimization. Design results confirm the efficiency of the method.
基金Supported by National Natural Science Foundation of China (No. 50975012)Research Fund for the Doctoral Program of Higher Education of China (No. 20091102110022)
文摘Structural bionic design lacks mature and scientific theories, and the excellent structural characteristics of natural organisms sometimes cannot be transferred into engineering structures effectively. Aiming at overcoming the existing problems, this paper summarizes three related theories: similarity theory, fuzzy evaluation theory and optimization theory. Based on the related theories, a method of structural bionic design is introduced, which includes four steps: selecting the most useful structural characteristic of natural organism; analyzing the structural characteristic finally chosen for engineering problem; completing the structural bionic design for engineering structure; and verifying the structural bionic design. Similarity theory and fuzzy evaluation theory are employed to achieve Step 1. In Step 2 and Step 3, optimization theory is employed to analyze the parameters of structures. Together with the thoughts of simplification and grouping, optimization theory can reveal the relationship between organism structure and engineering structure, providing a way to structural bionic design. A general evaluation criterion is proposed in Step 4, which is feasible to evaluate the performance of different structures. Finally, based on the method, a structural bionic design of thin-walled cylindrical shell is introduced.
文摘The main contests of mire optimization design includes: mine field size, borizon and level height, mumber, shaft form and development disposal and so on. In this paper, based on mine dynamic analysis, the index function model of mine different development stage is built up,applying dynamic programming method to find the solution of system’s optimum value,which makes the optimized result of mine dynamic design parameter more comprehensive, sysematical and reasonable. Through theory analysis research and practical validation, the obtained design parameters are reasonable and accurate.
基金supported by the National Natural Science Foundation of China (Grant No. 50776065)
文摘Based on control theory,adjoint system for the general problem of turbomachinery aerodynamic optimization was studied and developed in the present paper by using the variation technique in the grid node coordinates combined with Jacobian Matrics of flow fluxes.Then the adjoint system for aerodynamic design optimization of turbine cascade governed by compressible Navier-Stokes equations was derived in detail.With the purpose of saving computation resources,the mathematic method presented in this paper avoids the coordinate system transforming in the traditional derivation process of the adjoint system and makes the adjoint system much more sententious.Given the general expression of objective functions consisting of both boundary integral and field integral,the adjoint equations and their boundary conditions were derived,and the final expression of the objective function gradient including only boundary integrals was formulated to reduce the CPU cost,especially for the complex 3D configurations.The adjoint system was solved numerically by using the finite volume method with an explicit 5-step Runge-Kutta scheme and Riemann approximate solution of Roe's scheme combined with multi-grid technique and local time step to accelerate the convergence procedure.Finally,based on the aerodynamic optimization theory in the present work,2D and 3D inviscid and viscous inverse design programs of axial turbomachinery cascade for both pressure distribution and isentropic Mach number distribution on the blade wall were developed,and several design optimization cases were performed successfully to demonstrate the ability and economy of the present optimization system.
基金This project is supported partly by National 0utstanding Young Investigation of National Natural Science Foundation of China（70225005,70471088,70501004 and 70501005）, the Special Research Found for Doctoral Programs in State Education Ministry （20050004005）, the 211 Project of Discipline Construction of Beijing Jiaotong University and Rencai Foundation of Beijing Jiaotong University （2003RC010）
文摘A chaotic algorithm for providing a solution to the bi-level Discrete Equilibrium Network Design Problem （NDP） is discussed following an introduction of the Discrete Network Design Problem （DNDP） model and Chaos Optimization Algorithms （COA）. A description of the chaotic approach for the DNDP model is described in details. Then a numerical example for the DNDP is carried out to investigate the chaotic approach. The results have been encouraging, indicating that the chaotic approach has great potential ability in finding the optimal solution of DNDP models.
