Stress Relaxation and Sensitivity Weight for Bi-Directional Evolutionary Structural Optimization to Improve the Computational Efficiency and Stabilization on Stress-Based Topology Optimization

Stress-based topology optimization is one of the most concerns of structural optimization and receives much attention in a wide range of engineering designs.To solve the inherent issues of stress-based topology optimization,many schemes are added to the conventional bi-directional evolutionary structural optimization(BESO)method in the previous studies.However,these schemes degrade the generality of BESO and increase the computational cost.This study proposes an improved topology optimization method for the continuum structures considering stress minimization in the framework of the conventional BESO method.A global stress measure constructed by p-norm function is treated as the objective function.To stabilize the optimization process,both qp-relaxation and sensitivity weight scheme are introduced.Design variables are updated by the conventional BESO method.Several 2D and 3D examples are used to demonstrate the validity of the proposed method.The results show that the optimization process can be stabilized by qp-relaxation.The value of q and p are crucial to reasonable solutions.The proposed sensitivity weight scheme further stabilizes the optimization process and evenly distributes the stress field.The computational efficiency of the proposed method is higher than the previous methods because it keeps the generality of BESO and does not need additional schemes.

A Modified Bi-Directional Evolutionary Structural Optimization Procedure with Variable Evolutionary Volume Ratio Applied to Multi-Objective Topology Optimization Problem

Natural frequency and dynamic stiffness under transient loading are two key performances for structural design related to automotive,aviation and construction industries.This article aims to tackle the multi-objective topological optimization problem considering dynamic stiffness and natural frequency using modified version of bi-directional evolutionary structural optimization(BESO).The conventional BESO is provided with constant evolutionary volume ratio(EVR),whereas low EVR greatly retards the optimization process and high EVR improperly removes the efficient elements.To address the issue,the modified BESO with variable EVR is introduced.To compromise the natural frequency and the dynamic stiffness,a weighting scheme of sensitivity numbers is employed to form the Pareto solution space.Several numerical examples demonstrate that the optimal solutions obtained from the modified BESO method have good agreement with those from the classic BESO method.Most importantly,the dynamic removal strategy with the variable EVR sharply springs up the optimization process.Therefore,it is concluded that the modified BESO method with variable EVR can solve structural design problems using multi-objective optimization.

A Smooth Bidirectional Evolutionary Structural Optimization of Vibrational Structures for Natural Frequency and Dynamic Compliance

A smooth bidirectional evolutionary structural optimization(SBESO),as a bidirectional version of SESO is proposed to solve the topological optimization of vibrating continuum structures for natural frequencies and dynamic compliance under the transient load.A weighted function is introduced to regulate the mass and stiffness matrix of an element,which has the inefficient element gradually removed from the design domain as if it were undergoing damage.Aiming at maximizing the natural frequency of a structure,the frequency optimization formulation is proposed using the SBESO technique.The effects of various weight functions including constant,linear and sine functions on structural optimization are compared.With the equivalent static load(ESL)method,the dynamic stiffness optimization of a structure is formulated by the SBESO technique.Numerical examples show that compared with the classic BESO method,the SBESO method can efficiently suppress the excessive element deletion by adjusting the element deletion rate and weight function.It is also found that the proposed SBESO technique can obtain an efficient configuration and smooth boundary and demonstrate the advantages over the classic BESO technique.

Structural Topology Optimization by Combining BESO with Reinforcement Learning

In this paper,a new algorithm combining the features of bi-direction evolutionary structural optimization(BESO)and reinforcement learning(RL)is proposed for continuum structural topology optimization(STO).In contrast to conventional approaches which only generate a certain quasi-optimal solution,the goal of the combined method is to provide more quasi-optimal solutions for designers such as the idea of generative design.Two key components were adopted.First,besides sensitivity,value function updated by Monte-Carlo reinforcement learning was utilized to measure the importance of each element,which made the solving process convergent and closer to the optimum.Second,ε-greedy policy added a random perturbation to the main search direction so as to extend the search ability.Finally,the quality and diversity of solutions could be guaranteed by controlling the value of compliance as well as Intersection-over-Union(IoU).Results of several 2D and 3D compliance minimization problems,including a geometrically nonlinear case,show that the combined method is capable of generating a group of good and different solutions that satisfy various possible requirements in engineering design within acceptable computation cost.

A Multi-Objective Optimal Evolutionary Algorithm Based on Tree-Ranking

Multi-objective optimal evolutionary algorithms (MOEAs) are a kind of new effective algorithms to solve Multi-objective optimal problem (MOP). Because ranking, a method which is used by most MOEAs to solve MOP, has some shortcoming s, in this paper, we proposed a new method using tree structure to express the relationship of solutions. Experiments prove that the method can reach the Pare-to front, retain the diversity of the population, and use less time.

Effectiveness Assessment of the Search-Based Statistical Structural Testing

Search-based statistical structural testing(SBSST)is a promising technique that uses automated search to construct input distributions for statistical structural testing.It has been proved that a simple search algorithm,for example,the hill-climber is able to optimize an input distribution.However,due to the noisy fitness estimation of the minimum triggering probability among all cover elements(Tri-Low-Bound),the existing approach does not show a satisfactory efficiency.Constructing input distributions to satisfy the Tri-Low-Bound criterion requires an extensive computation time.Tri-Low-Bound is considered a strong criterion,and it is demonstrated to sustain a high fault-detecting ability.This article tries to answer the following question:if we use a relaxed constraint that significantly reduces the time consumption on search,can the optimized input distribution still be effective in faultdetecting ability?In this article,we propose a type of criterion called fairnessenhanced-sum-of-triggering-probability(p-L1-Max).The criterion utilizes the sum of triggering probabilities as the fitness value and leverages a parameter p to adjust the uniformness of test data generation.We conducted extensive experiments to compare the computation time and the fault-detecting ability between the two criteria.The result shows that the 1.0-L1-Max criterion has the highest efficiency,and it is more practical to use than the Tri-Low-Bound criterion.To measure a criterion’s fault-detecting ability,we introduce a definition of expected faults found in the effective test set size region.To measure the effective test set size region,we present a theoretical analysis of the expected faults found with respect to various test set sizes and use the uniform distribution as a baseline to derive the effective test set size region’s definition.

基于双向渐进结构优化算法的预制拼装箱梁剪力键设计研究

为研究单项和多项荷载组合作用下节段预制拼装箱梁接缝处剪力键受力状况,以郑州南四环全预制装配高架桥为背景,采用Abaqus软件和双向渐进结构优化(BESO)算法,建立典型箱梁节段分析模型,研究剪力键在单位轴力、剪力、扭矩、弯矩和不同荷载组合作用下的布置规律。结果表明:轴力作用时剪力键应布置于顶板;剪力作用时剪力键应布置于腹板和底板;扭矩作用时剪力键应布置在顶板、腹板交接处和腹板外侧;横桥向弯矩作用时剪力键应布置于顶板、腹板下侧和底板;竖向弯矩作用时,剪力键应布置于顶板翼缘。轴剪组合作用下,当剪力占比小于50%时,轴力对剪力键布置起控制作用;当剪力占比达95.24%时,剪力对剪力键布置起控制作用。弯剪组合作用下,当剪力占比超过4.76%时,剪力对剪力键布置起控制作用;当剪力占比小于0.50%时,横桥向弯矩对剪力键布置起控制作用。扭剪组合作用下,当剪力占比超过0.10%时,剪力对剪力键布置起控制作用。预制拼装箱梁剪力键布置受荷载类型及荷载组合影响显著,应考虑不同位置剪力键的实际受力状况进行设计。

COMPUTER PROGRAM FOR DIRECTED STRUCTURE TOPOLOGY OPTIMIZATION

To compensate for the imperfection of traditional bi-directional evolutionary structural optimization, material interpolation scheme and sensitivity filter functions are introduced. A suitable filter can overcome the checkerboard and mesh-dependency. And the historical information on accurate elemental sensitivity numbers are used to keep the objective function converging steadily. Apart from rational intervals of the relevant important parameters, the concept of distinguishing between active and non-active elements design is proposed, which can be widely used for improving the function and artistry of structures directly, especially for a one whose accurate size is not given. Furthermore, user-friendly software packages are developed to enhance its accessibility for practicing engineers and architects. And to reduce the time cost for large timeconsuming complex structure optimization, parallel computing is built-in in the MATLAB codes. The program is easy to use for engineers who may not be familiar with either FEA or structure optimization. And developers can make a deep research on the algorithm by changing the MATLAB codes. Several classical examples are given to show that the improved BESO method is superior for its handy and utility computer program software.

Layout optimization of steel reinforcement in concrete structure using a truss-continuum model

Owing to advancement in advanced manufacturing technology,the reinforcement design of concrete structures has become an important topic in structural engineering.Based on bi-directional evolutionary structural optimization(BESO),a new approach is developed in this study to optimize the reinforcement layout in steel-reinforced concrete(SRC)structures.This approach combines a minimum compliance objective function with a hybrid trusscontinuum model.Furthermore,a modified bi-directional evolutionary structural optimization(M-BESO)method is proposed to control the level of tensile stress in concrete.To fully utilize the tensile strength of steel and the compressive strength of concrete,the optimization sensitivity of steel in a concrete–steel composite is integrated with the average normal stress of a neighboring concrete.To demonstrate the effectiveness of the proposed procedures,reinforcement layout optimizations of a simply supported beam,a corbel,and a wall with a window are conducted.Clear steel trajectories of SRC structures can be obtained using both methods.The area of critical tensile stress in concrete yielded by the M-BESO is more than 40%lower than that yielded by the uniform design and BESO.Hence,the M-BESO facilitates a fully digital workflow that can be extremely effective for improving the design of steel reinforcements in concrete structures.

基于柔性机构的机翼前缘变形多目标优化

全柔性机构用于自适应机翼具有实现其形状的连续平滑变形和轻量化等优点。文章根据机翼前缘在不同飞行状态下气动外形要求,以离散体结构拓扑优化为出发点,以目标形状与实际形状的边界曲线之差最小为优化目标,并考虑机构变形要求和刚性要求等问题,建立了多目标优化函数;采用遗传算法(GA)和双向渐进结构优化法(BESO)相结合,应用于Matlab与Ansys,通过二次优化,获得了稳定的最优解,不仅实现编程模块化,而且提高了优化效率。最后,对结果进行Ansys仿真分析和模型实验验证。结果表明:仿真结果和模型实验结果一致,该方法是可行的。

基于遗传算法的柔性机构形状变化综合优化研究

实现机翼在不同的飞行状态下的最优气动外形是变弯度自适应机翼的一项关键技术。针对传统铰链机构会使机翼表面产生不连续变化而导致气流提早分离的问题,从全柔性机构实现连续平滑的形状变化的技术出发,以目标形状与实际形状的边界曲线之差最小为优化目标,采用遗传算法(GA)对柔性机构的拓扑、尺寸、形状进行了综合优化。在优化方法上,以二进制编码技术和实数编码技术为基础建立初始离散柔性机构的混合变量遗传算法模型,将其映射为有限元模型并进行了结构分析。在优化过程中引入了渐进结构优化(ESO)算法的思想,消除GA优化过程中产生的自由单元,改善了优化效率和分析结果。结合机翼前缘形状变化实例,基于MATLAB进行优化设计,并用ANSYS10.0对优化结果进行了机构的仿真分析。分析结果表明,所提出的方法合理、有效。

加窗渐进结构优化算法

渐进结构优化算法通常用于寻找结构最优的拓扑形状,指导结构的设计。但其删除准则的缺陷易引起计算效率低等一系列问题。本文对删除准则进行了改进,提出了加窗渐进结构优化算法。该算法引入结构整体平均应变能密度作为单元删除准则,同时将单元删除率设定为窗口可调的自适应状态。该算法一定程度上解决了传统渐进结构优化算法中计算效率较低和优化过程易发生畸变的问题,且推广至高阶有限元单元应用后扩大了其应用范围。通过与Michell理论解对比,其构造的拓扑的可靠性也得到了证明。

大型产品结构优化问题的病毒进化遗传算法

针对一种大型产品结构的质量一成本优化问题,设计了一种病毒进化遗传算法,提出了相应的编码解码方案和适应度的计算。病毒进化遗传算法是一种协同进化算法,既实现了遗传操作在父子代群体间纵向继承进化信息进行全局搜索的功能,也实现了病毒感染操作在同一代群体中横向传播进化信息进行局部搜索的功能,从而可以比遗传算法较快获得问题的满意解。最后给出了病毒进化遗传算法的试验仿真结果。

计算机试验的分步优化设计研究

针对传统的计算机试验优化设计计算费时的不足,一方面改进了原始的随机进化寻优算法,以兼顾深度搜索与广度搜索;另一方面提出了分步试验优化设计的思路,逐步分批地布置试验样本点,化整为零地减小搜索空间;最后采用径向基神经网络替代模型,以均匀试验设计为例,检验分步试验优化设计方法的有效性.计算实践表明,改进算法可平均节省50%左右的机时,寻找到与原始算法结果相差约1%的最优值;分步试验设计较一步试验设计可减少40%-60%左右的机时,数值实验表明,随着试验样本点数量的递增,由不同试验设计所产生的替代模型的误差将趋于一致,分步试验设计尤其适合基于大规模试验样本点的替代模型。

金融结构优化方法与理论

金融结构不存在一个放之四海而皆准的最优标准,一国的最优金融结构由特定时期的国情所决定。金融结构优化是实现最优金融结构,进而促进经济健康发展的重要手段。系统梳理了金融结构理论的演变历程,分析了金融结构的优化目标,总结了金融结构的优化方法。在文献研究基础上,明确后续研究的突破口在于如何针对金融结构与经济发展多目标的复杂交互关系,实现金融结构的多目标优化。为此,提出基于进化算法的金融结构多目标优化研究新视角,明确其中的关键问题,并对后续研究做出展望。

基于生态算法的城市建设用地结构优化

借鉴自然生态系统解决优化问题的思想和机制,提出了"城市土地生态系统"概念.首先定义城市土地生态系统的结构及其自主进化机理,然后创建城市土地生态系统自主进化过程的算法模型——城市土地生态系统进化算法(简称城市生态算法).最后,构建城市建设用地结构优化数学模型,并使用城市生态算法进行求解.选取上海市作为算法应用实例,结果表明城市生态算法能够很好地解决城市建设用地结构优化问题.

桁架结构尺寸和形状、拓扑的渐进优化方法

提出了一种求解桁架结构尺寸 ,形状和拓扑组合优化的渐进优化方法。将优化问题分解为拓扑优化和尺寸、形状优化两个子问题分层求解。通过连续化的拓扑变量和近似方法构造了拓扑变量灵敏度系数计算式 ,由拓扑变量灵敏度系数识别和删除杆件单元。结构尺寸、形状优化采用准则法和渐进移点法的组合方法。分层优化时 ,在桁架中加上所有可能的杆件 ,先进行尺寸、形状优化 ,再进行拓扑优化 ,随后二者交替进行迭代 ,迭代过程的结构重量最小值即为最优解。算例表明了文中方法的有效性 。

复合材料后掠机翼的气动弹性剪裁方法研究

提出了一种混合多级结构优化算法,以大展弦比复合材料后掠机翼为研究对象进行了气动弹性剪裁设计。在满足强度、变形约束等前提下,以梁、肋、蒙皮厚度,对结构重量进行最小化设计;继续以减重为目标,满足颤振速度的约束,优化蒙皮各铺层的比例,并分析了优化中铺层比例对颤振速度的影响;采用遗传算法优化蒙皮的铺层顺序,以增大机翼的颤振速度。研究表明:混合多级结构优化不仅可以减轻机翼的结构重量,还能大大提高机翼的颤振速度;铺层比例优化结果表明较高的±45°铺层比例能使刚度分布更加合理高效。

基于遗传算法的液压机上梁交互式结构优化

很多结构优化问题的数学模型并不存在或难以求解,传统优化方法难以对这类问题进行准确寻优,需要使用交互式结构优化方法。针对基本遗传算法的缺陷,提出了一种改进型遗传算法。以700T铸造式液压机上梁(简称上梁)为例,建立结构优化模型和遗传算法模型。以上梁的最大变形和最大等效应力为约束条件,以重量为目标函数,基于有限元法和改进遗传算法对上梁进行了交互式结构优化设计。优化结果使上梁变形基本保持不变,最大等效应力降低5.87%,同时使上梁减重12.09%。

遗传演化建模方法研究

根据观测数据建模 ,首先需要确定模型的结构 ,其后才是估计模型参数 ,而模型结构的确定是建模过程中最困难的阶段。遗传演化建模根据生物遗传机制 ,随机构造一组模型表达式 ,应用简单的基因复制、杂交和变异算子进行模型结构调整 ,同时进行非线性优化估计模型参数 ,从而得到一组优化的模型。遗传演化建模能够获得简单的显式表达式 。