COMPARATIVE EVALUATION OF DIFFERENT OPTIMIZATION ALGORITHMS FOR STRUCTURAL DESIGN APPLICATIONS

Non-linear programming algorithms play an important role in structural design optimization. Fortunately, several algorithms with computer codes are available. At NASA Lewis Research Centre, a project was initiated to assess the performance of eight different optimizers through the development of a computer code CometBoards. This paper summarizes the conclusions of that research. CometBoards was employed to solve sets of small, medium and large structural problems, using the eight different optimizers on a Cray-YMP8E/8128 computer. The reliability and efficiency of the optimizers were determined from the performance of these problems. For small problems, the performance of most of the optimizers could be considered adequate. For large problems, however, three optimizers (two sequential quadratic programming routines, DNCONG of IMSL and SQP of IDESIGN, along with Sequential Unconstrained Minimizations Technique SUMT) outperformed others. At optimum, most optimizers captured an identical number of active displacement and frequency constraints but the number of active stress constraints differed among the optimizers. This discrepancy can be attributed to singularity conditions in the optimization and the alleviation of this discrepancy can improve the efficiency of optimizers.     

EXPLOITING DESIGN LENGTH SCALES IN STRUCTURAL OPTIMIZATION

Many structural optimization methods use geometric length scales as well as artificially imposed lengths such as finite element dimensions. One considers functions defined over these dimensions in characterizing and solving the problem. The natural length scales involved in the proposed design change are generally overlooked. When one proposes an optimization based on change of certain panels in a sheet metal structure, for instance, it might be helpful to use the dimensions of the redesign areas as characteristic lengths. In the present study, a Rayleigh–Ritz approach is taken where the responses of a structure to pseudo-loads (acting only over specified design-change regions) are employed as basis vectors. It is found that convergence of the optimization process is improved. The method is demonstrated for moderate-sized problems, and as with other modal methods, should become even more helpful for large problems. The new complexity involved is the requirement for a type of problem-dependent linking, in parallel with the conventional design variable linking. This can be automated. © 1997 by John Wiley & Sons, Ltd.     

基于数值模拟的注塑模熔体前沿速度优化

在注塑成型的过程中,非均匀的熔体前沿充填速度将导致非一致的取向,以及非均匀收缩和翘曲变形,理想的充填模式应尽可能使熔体在充填过程中保持熔体前沿速度为常数.文中将数值模拟技术与遗传算法相结合用于注塑成型熔体前沿速度的优化,确定螺杆行程中的最佳分段控制点,以及控制点处的注射体积流率或螺杆速度的最优值以获得均匀一致的熔体前沿速度.数值分析采用广义的Hele-Shaw流动模型,耦合利用有限元/有限差分来求解控制方程,并利用控制体积概念实现熔体前沿的自动更替和推进.算例表明,优化的工艺条件设置可以使熔体前沿速度的均匀性提高50%左右.     

APPLICATION OF AI TOOLS FOR RE-ANALYSIS WITHIN STRUCTURAL OPTIMIZATION

Structural optimization can be viewed as a logical and rational base for modern CAD/CAE applications. However, problems are encountered if major finite element systems are to be optimized for which numerous optimization variables have been specified. Particularly, the implicit nature of the governing finite element equations can result in prohibitive computational effort.

Confining to linear discrete systems, a Taylor series based approximation concept is presented which may be expanded to further finite element problems (eigenvalue problems, etc.). Specific emphasis is placed on the abstract derivation of a rulebase for symbolic differentiation of the finite element matrices with respect to named optimization variables. By means of such a rulebase, in association with an expert system shell, the explicit approximation of finite element relationships can effectively be computerized.     

正向选择免疫算法在结构损伤诊断中的应用

结构状况可根据结构响应信号的异常进行判断,人工免疫系统能有效地应用于信号的异常检测。对基于免疫机制的正向选择算法进行了研究,利用具有时频局部化特性的小波包分解得到表征结构特征的小波包能量谱,通过正向选择算法检测小波包能量谱的异常来辨识结构状况。对正向选择算法进行了改进,可减少"自我"空间检测子的生成数目,加快检测速度,促进正向选择算法的实际应用。以ASCE学会提出的基准结构为对象,验证了正向选择算法在损伤诊断中的有效性,并与反向算法进行了比较。     

适用于支护拓扑优化的双向渐进优化方法

利用近年来发展的渐进结构优化方法(ESO)的概念,发展了适用于支护拓扑优化问题的双向渐进结构优化方法(BESO).本文方法能在优化过程中控制开孔数,有效地避免了棋盘格式的出现,提出了两个解决振荡问题的技巧.将加固后的岩体看成人工支护材料,可以把加固优化的问题转化为人工支护材料在原岩中的分布的拓扑优化问题.建立了防治底臌帮臌的准则及其敏感度,研究了均匀地基不同地应力条件给定加固量时使得底臌帮臌最小的洞室开挖支护的最优拓扑.最优设计的底臌量明显小于经验设计的底臌量,证明了方法的有效性.     

基于神经网络响应面的复合材料结构优化设计

用正交试验设计的方法选择样本点构建神经网络响应面,将神经网络响应面作为优化的目标函数或约束条件,加上其它常规约束条件建立优化模型,应用遗传算法 (GA) 进行优化,形成一套适用于复杂结构设计的高效优化方法。以复合材料帽型加筋板的重量优化问题为例,建立了加筋板模型的重量响应面目标函数、强度和稳定性响应面约束条件;并用PATRAN/NASTRAN进行有限元计算,获取用于响应面训练的样本点数值。算例表明:该方法能以很少的有限元分析次数,取得高精度的响应面近似模型,并且使优化效率大大提高。      

一种基于非概率可靠性的结构水平集拓扑优化

该文在研究水平集拓扑优化方法的基础上,对具有区间参数的不确定性结构的非概率可靠性约束进行了分析,经对有限元公式的推导、变换,提出了包涵非概率可靠度信息的拟安全系数形式,从而将非概率可靠性约束问题显式化处理,使得优化过程形式简单、便于计算,避免了复杂的迭代运算。通过对算例中数据及拓扑图形的对比研究,表明该文中模型的合理性和方法的有效性。     

考虑作动器联接方式的结构形状控制优化

以压电材料梁式作动器控制复合材料层合板形状的设计问题为对象,研究有限个独立控制参数条件下的形状最优控制问题。研究了作动器与信号发生器(独立控制参数)联接关系的参数化描述方式,建立了作动器联接方式与控制参数协同设计的问题提法;针对优化问题中离散变量(联接方式描述参数)和连续变量(控制参数)共存的特点,建立了遗传算法和线性最小二乘(Linear Least Square,LLS)方法相结合的求解策略和方法;在响应分析所采用的有限元模型中,采用粘结层单元描述本体结构与作动器之间的连接。复合材料层合板形状控制设计的实例,验证了该文中建立的问题提法、优化模型和求解策略的有效性。     

USE OF COUNTERPROPAGATION NEURAL NETWORKS TO ENHANCE THE CONCURRENT SUBSPACE OPTIMIZATION STRATEGY

The paper explores the use of artificial neural networks in a concurrent optimization strategy that derives from a decomposition based approach to design of large-scale engineering systems. These problems are characterized by complex couplings that render parametric design methods inappropriate as solution tools. Decomposition methods reduce the large dimensionality problem into a sequence of smaller, more tractable optimization problems, each with a smaller set of design variables and constraints. The decomposed subproblems are rarely decoupled completely, and design changes in one subproblem have a profound influence on changes in another subproblem. Essential components of decomposition based design methods are strategies to identify a topology for problem decomposition, and to develop coordination strategies which account for couplings among the decomposed problems. The paper examines the effectiveness of artificial neural networks as a tool to both account for the coupling, and to develop methods to coordinate the solution in the different subproblems to a converged optimal design     

追究根基的结构拓扑优化方法

结合作者在结构拓扑优化方面的研究工作,围绕了ICM(独立、连续、映射)方法涉及的基本概念上的突破,叙述了将本质上为0-1离散变量的拓扑优化问题转化为连续变量优化问题的具体做法,其中介绍了若干要点:以阶跃函数把离散问题化为连续问题即完成关键的等价性转换是第一步;定义磨光函数逼近阶跃函数的可操作的近似是第二步;引入作为磨光函数反函数的过滤函数实现映射性建模是第三步;采用某些光滑算法求解连续变量模型则是第四步。通过连续体结构的典型数值算例说明了将结构拓扑优化的模型转化为独立层次的拓扑优化过程。该方法对于纯数学的0-1离散变量优化的求解也适用,方法与数值都表明了这一点。     

EFFICIENT TREATMENT OF CONSTRAINTS IN LARGE-SCALE STRUCTURAL OPTIMIZATION

The paper presents a new concept for the treatment of large numbers of stress and displacement constraints in finite dimensional optimal structural design. The idea is to replace a large number of stress and displacement constraints by a small number of equivalent functional constraints. The genesis of this concept is the distributed parameter and transient response structural design formulations where it has been used quite effectively. The major advantage of this constraint formulation is that design sensitivity vectors need to be calculated for only the reduced number of equivalent stress and displacement constraints. Thus, there is substantial computational advantage with the new formulation. Implications of the formulation are studied and several example problems are presented to show its potential in practical design applications.     

AN OPTIMIZATION METHOD TO DESIGN HYDRAULIC NETWORKS

Nonlinear programming is applied to the solution of hydraulic network problems. The significant differences between the proposed optimization method and other conventional methods are that this method can solve problems with mixed unknowns (e.g. pipe sizes, discharges and pressures), it can optimize solutions involving unknowns defined by inequalities (e.g. specifled minimum discharge and pressure values), it can handle network control problems such as required valve adjustments or in-line booster pump needs, and it may solve problems of networks with continuous discharge distribution along the pipes.     

STRUCTURAL OPTIMIZATION USING A NEW LOCAL APPROXIMATION METHOD

A new method for solving structural optimization problems using a local function approximation algorithm is proposed. This new algorithm, called the Generalized Convex Approximation (GCA), uses the design sensitivity information from the current and previous design points to generate a sequence of convex, separable subproblems. The paper contains the derivation of the parameters associated with the approximation and the formulation of the approximated problem. Numerical results from standard test problems solved using this method are presented. It is observed that this algorithm generates local approximations which lead to faster convergence for structural optimization problems.     

A SELF-SCALING IMPLICIT SQP METHOD FOR LARGE SCALE STRUCTURAL OPTIMIZATION

The basic idea of an implicit sequential quadratic programming (ISQP) method for constrained problems is to use the approximate Hessian of the Lagrangian without explicitly calculating and storing it. This overcomes one of the major drawbacks of the traditional SQP method where a large matrix needs to be calculated and stored. This concept of an implicit method is explained and an algorithm based on it is presented. The proposed method extends a similar algorithm for unconstrained problems where a two-loop recursion formula is used for the inverse Hessian matrix. The present paper develops a similar algorithm for not only the constrained problem but also the direct Hessian updates. Several scaling procedures for the Hessian are also presented and evaluated. The basic method and some of its variations are evaluated using a set of mathematical programming test problems, and a set of structural design test problems—small to larger scale. The ISQP method performs much better than a method that does not use any approximate Hessian matrix. Its performance is better than the full SQP method for larger scale problems. The test results also show that an appropriate scaling of the Hessian can improve both efficiency and reliability substantially.     

A FUTURE FOR STRUCTURAL OPTIMIZATION IN AEROSPACE

Computer-based structural optimization is now a reasonably mature technology. Nevertheless, a need for further research is highlighted in the areas of dynamics, where there is dificulty in the formulation of well-posed problems, and the integration of detail-stressing within the overall design of large engineering products, where the problem is one of scale. The principal challenge to the extensive application of structural optimization in the coming years is seen to relate to its integration within an overall multi-disciplinary design process. Different approaches to the problem of multidisciplinary design are outlined. The overall context, including the influence of Concurrent Engineering and the role of digital product models and data communication standards, are discussed.     

微型客车热环境计算机模拟与优化

应用计算流体动力学方法（CFD）对微车车室几种进出风口位置的温度场、速度场进行了计算机模拟,并对这几种温度场、速度场进行了比较,得到使热环境最优的计算结果,达到车室热环境优化的目的。证明计算流体动力学方法是进行车室热环境优化的有效方法。     

基于Newmark法敏度计算的刚架结构动力优化

提出一种有效的求解结构最小质量设计,同时满足动位移和动应力约束的二阶优化设计方法。在有限元法和纽马克法基础上导出一种高效的动应力、动位移对设计变量一阶导数和二阶导数的算法。建立含时间参数,以结构质量最小化为目标,同时满足动位移、动应力和设计变量约束的优化数学模型,通过积分型内点罚函数将含时间参数的不等式约束优化问题转变为一系列不含时间参数的无约束优化问题。利用动位移、动应力对设计变量一阶导数和二阶导数的信息计算内点罚函数的梯度和海森矩阵,利用梯度和海森矩阵构造求解优化设计问题高效有效的二阶优化算法。算例结果表明该文的优化设计方法能获得刚架结构的局部最优设计,优化的效率高于增广拉格朗日乘子法。     

TREATING CONSTRAINTS AS OBJECTIVES FOR SINGLE-OBJECTIVE EVOLUTIONARY OPTIMIZATION

This paper presents a new approach to handle constraints using evolutionary algorithms. The new technique treats constraints as objectives, and uses a multiobjective optimization approach to solve the re-stated single-objective optimization problem. The new approach is compared against other numerical and evolutionary optimization techniques in several engineering optimization problems with different kinds of constraints. The results obtained show that the new approach can consistently outperform the other techniques using relatively small sub-populations, and without a significant sacrifice in terms of performance.     

HYBRID COMPUTER OPTIMIZATION OF A CATCHMENT SIMULATION MODEL

The optimization of a two-parameter river catchment simulation model is described. The parameter K1 controls the rate of infiltration into the soil, and the second parameter, K2, is used in the routing equation. The Simplex direct search method is used and is implemented on a hybrid computer. The computer programme forms an n-dimensional “simplex” (n being the number of parameters) from initial trial values of the parameters, and uses the basic operations of reflection, expansion and contraction to find the optimum value of the objective function. The operations are carried out according to the value of the objective function at each apex of the “simplex.” The peripheral devices linked to the hybrid computer are used to give a continuous display of the optimization process, and the effects of systematically varying the parameters are studied by plotting sample hydrographs for various pairs of parameter values and by plotting the surface of the objective function.