关于集值映射向量优化问题的对偶问题

在拓扑线性空间中,针对带有约束条件的集值向量优化问题,采用抽象的拉格朗日乘子法,将其转化为无条件集值向量优化问题求解;讨论了其拉格朗日型对偶问题,得到了若干结果.

Shape Optimization With Sensitivity Analysis in Local Domain

For complicated geometries, it is ineflicient to integrate over the entire domain. A new approach for optimization is presented here, based on sensitivity analysis of local do- main and deformation of full domain. Accurate results of design sensitivity analysis are ob- tained with this approach in shape optimization. This method is shown to be efficient when used in optimization programs and results in less distortion of the mesh.

Determination of processing power and optimum billet radius of modified backward extrusion by upper bound approach

A recently developed backward extrusion method entitled “modified backward extrusion” was presented using an upper bound analysis. For this purpose deformation area was divided into four distinct zones and a kinematically admissible velocity field for each of them was suggested. Total dissipated power was calculated for the deformation zones and the extrusion power wascomputed. The correlations of important geometrical parameters with extrusion force and dissipated powers were shown. Finding the initial billet size, a challenging area in the modified backward extrusion method, was discussed and the optimum billet radius was obtained, considering the minimum relative extrusion pressure. Finite element analyses were conducted and the results werecompared with the upper bound analysis. Finally, experiments were executed on commercially pure aluminium and a good agreement between upper bound and finite element analyses with experimental values was observed.

Improvement of Low-Frequency Sound Field Obtained by an Optimized Boundary

An approach based on the finite element analysis was introduced to improve low-frequency sound field. The optimized scatters on the wall redistribute the modes of the room and provide effective diffusion of sound field. The obtained through a 1：5 scaled set up. The results show that the optimized treatment has a positive effect on sound field and the improvement is obvious.

Optimization methods of cutting depth in mining Co-rich crusts

For optimizing the cutting depth of spiral drum type cutting head,the relations among collecting ratio,interfusing ratio of mullock and cutting depth of the mining cobalt-rich crusts in ocean were discussed.Furthermore,the multi-extremum problem about cutting depth was analyzed in mining at a certain interfusing ratio of mullock.Through introducing genetic algorithm(GA),the cutting depth-control problem when the collecting ratio is maximized by controlling the interfusing ratio of mullock was solved with global-optimization-search algorithms.Then optimization theory for cutting depth in mining cobalt-rich crusts by GA,and computer programming were given to realize the algorithm.The computation result of actual data proves the validity of this method.

Structural-acoustic optimization of stiffened panels based on a genetic algorithm

For the structural-acoustic radiation optimization problem under external loading,acoustic radiation power was considered to be an objective function in the optimization method. The finite element method(FEM) and boundary element method(BEM) were adopted in numerical calculations,and structural response and the acoustic response were assumed to be de-coupled in the analysis. A genetic algorithm was used as the strategy in optimization. In order to build the relational expression of the pressure objective function and the power objective function,the enveloping surface model was used to evaluate pressure in the acoustic domain. By taking the stiffened panel structural-acoustic optimization problem as an example,the acoustic power and field pressure after optimized was compared. Optimization results prove that this method is reasonable and effective.

Finite Element Analysis and OADs Optimization of the Temperature in the Plane-strain Orthogonal Metal Cutting Process

In order to analyze the influences of the different tool’s shape and surface conditions (such as different coated and material) and their interaction on the cutting temperature, a coupled thermo-mechanical finite element analysis (FEA) model of plane-strain orthogonal metal cutting process is constructed, and 16 simulation cases with 16 different types of tools, which cover 4 rake angles, -10°, 0°, 10°, 20°, and 4 friction coefficient values, 0, 0.1, 0.2, 0.3 in the same cutting condition (cutting depth and cutting speed) have been performed. Finally the simulation results are analyzed according to the variance analysis method (VAM) of orthogonal array designs (OADs), the relationships between the rake angle, tool-workpiece interface’s friction coefficient and their interact effect to the maximum temperature value and the temperature field of the chip are obtained. This result has some instructive meaning to analyze the causes of the cutting temperature and to control the maximum temperature value and the overall temperature field in the metal cutting process.

Convergence of shape optimization calculations of mechanical components using adaptive biological growth and iterative finite element methods

Shape optimization of mechanical components is one of the issues that have been considered in recent years. Different methods were presented such as adaptive biological for reducing costs and increasing accuracy. The effects of step factor, the number of control points and the definition way of control points coordinates in convergence rate were studied. A code was written using ANSYS Parametric Design Language (APDL) which receives the studied parameters as input and obtains the optimum shape for the components. The results show that for achieving successful optimization, step factor should be in a specific range. It is found that the use of any coordinate system in defining control points coordinates and selection of any direction for stimulus vector of algorithm will also result in optimum shape. Furthermore, by increasing the number of control points, some non-uniformities are created in the studied boundary. Achieving acceptable accuracy seems impossible due to the creation of saw form at the studied boundary which is called "saw position".

Optimal design of FRMSM to decrease detent force

An optimal configuration of the flux-reversal linear synchronous motor (FRLSM) with the optimal number of attachment permanent magnets (PMs) was presented. The optimal model of 2 000 N was designed to reduce the detent force by redesigning the air-gap structure and skewing. The design parameters,mover PMs and stator core,were selected for optimal design by DOE. The thrust and the detent force of the designed optimal models were compared by finite element analysis (FEA). As a result,the thrust of the optimal model is slightly decreased by 1.97% compared with the basic model,and the detent force of the optimal model is greatly decreased by 88.47% compared with the basic model.

The Single Valley Character of Level Degree Function

Strict proof has been given to single valley character of level degree function by use of convex analysis theory, which provides reliable theoretical basis for the optimization of the data processing with respect to level degree. As circle degree and cylindrical degree have the same mathematical structures, their single valley character can be proved by the same method.

Bellman Equation for Optimal Processes with Nonlinear Multi-Parametric Binary Dynamic System

A process represented by nonlinear multi-parametric binary dynamic system is investigated in this work. This process is characterized by the pseudo Boolean objective functional. Since the transfer functions on the process are Boolean functions, the optimal control problem related to the process can be solved by relating between the transfer functions and the objective functional. An analogue of Bellman function for the optimal control problem mentioned is defined and consequently suitable Bellman equation is constructed.

Multi-objective optimization of crimping of large-diameter welding pipe

Crimping is widely adopted in the production of large-diameter submerged-arc welding pipes. Traditionally, designers obtain the technical parameters for crimping from experience or by trial and error through experiments and the finite element(FE) method. However, it is difficult to achieve ideal crimping quality by these approaches. To resolve this issue, crimping parameter design was investigated by multi-objective optimization. Crimping was simulated using the FE code ABAQUS and the FE model was validated experimentally. A welding pipe made of X80 high-strength pipeline steel was considered as a target object and the optimization problem for its crimping was formulated as a mathematical model and crimping was optimized. A response surface method based on the radial basis function was used to construct a surrogate model; the genetic algorithm NSGA-II was adopted to search for Pareto solutions; grey relational analysis was used to determine the most satisfactory solution from the Pareto solutions. The obtained optimal design of parameters shows good agreement with the initial design and remarkably improves the crimping quality. Thus, the results provide an effective approach for improving crimping quality and reducing design times.

L_2-Optimal Recovery on the Riesz Potential Spaces

The problems of best reconstruction of multivariate functions of the Riesz potential spaces from their values on a given mesh are considered, and the exact results of some classes of L_2(R^n) (and L_2(Q^n)) defined by the Riesz potential are obtained.

NONCONFORMING FINITE ELEMENT METHOD FOR NONLINEAR PARABOLIC EQUATIONS

A nonconforming finite element method for the nonlinear parabolic equations is studied inthis paper.The convergence analysis is presented and the optimal error estimate in L^2(‖·‖_h)norm isobtained through Ritz projection technique,where ‖·‖_h is a norm over the finite element space.

A combined mixed finite element method and local discontinuous Galerkin method for miscible displacement problem in porous media

A combined method consisting of the mixed finite element method for flow and the local discontinuous Galerkin method for transport is introduced for the one-dimensional coupled system of incompressible miscible displacement problem. Optimal error estimates in L∞(0,T;L2) for concentration c,in L2(0,T;L2)for cxand L∞(0,T;L2) for velocity u are derived. The main technical difficulties in the analysis include the treatment of the inter-element jump terms which arise from the discontinuous nature of the numerical method,the nonlinearity,and the coupling of the models. Numerical experiments are performed to verify the theoretical results. Finally,we apply this method to the one-dimensional compressible miscible displacement problem and give the numerical experiments to confirm the efficiency of the scheme.

A novel method of dynamic characteristics analysis of machine tool based on unit structure

A novel approach,which can be used for dynamic characteristics analysis of machine tools based on unit structure(US),is reported in this paper.The concepts of unit structures for design of machine tools are defined.In order to satisfy the dynamic characteristics requirement of high natural frequency and light-weight of US,a design method of multi-disciplinary optimization of NSGA-II about unit structures driven by natural frequency and mass is developed.Through analyzing the unit structures,key factors affecting the natural frequency and mass are extracted,and the mathematical models of natural frequency and mass about unit structures are also established by using central composite design and response surface model.The goal of high natural frequency and light-weight is reached by using the multi-objective genetic algorithms.The Pareto optimal set is also obtained.The dynamic behavior of US is investigated by the experimental modal analysis.To show the efficiency of the proposed novel method,the example of YKW51250 gear shaping machine bed is used.Through optimization of NSGA-II about US of YKW51250 machine bed,the natural frequency of YKW51250 gear shaping machine bed is increased by 30.4%and its mass decreased by 5.2%comparing with the original design.By studying the dynamic characteristics of the simplified machine tools bed,useful laws are obtained,and these laws can be used in primary design of NC machine tools structures.The optimal method based on US can be also applied to the dynamic optimal design of machine tools and other similar equipments.

FINITE ELEMENT APPROXIMATION FOR A CLASS OF PARAMETER ESTIMATION PROBLEMS

This paper investigates the finite element approximation of a class of parameter estimation problems which is the form of performance as the optimal control problems governed by bilinear parabolic equations,where the state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions.The authors derive some a priori error estimates for both the control and state approximations.Finally,the numerical experiments verify the theoretical results.

L∞-ESTIMATES OF MIXED FINITE ELEMENT METHODS FOR GENERAL NONLINEAR OPTIMAL CONTROL PROBLEMS

This paper investigates L∞--estimates for the general optimal control problems governed by two-dimensional nonlinear elliptic equations with pointwise control constraints using mixed finite element methods. The state and the co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. The authors derive L∞--estimates for the mixed finite element approximation of nonlinear optimal control problems. Finally, the numerical examples are given.