Multi-objective optimization of a plate and frame heat exchanger via genetic algorithm

In the present paper, a plate and frame heat exchanger is considered. Multi-objective optimization using genetic algorithm is developed in order to obtain a set of geometric design parameters, which lead to minimum pressure drop and the maximum overall heat transfer coefficient. Vividly, considered objective functions are conflicting and no single solution can satisfy both objectives simultaneously. Multi-objective optimization procedure yields a set of optimal solutions, called Pareto front, each of which is a trade-off between objectives and can be selected by the user, regarding the application and the project’s limits. The presented work takes care of numerous geometric parameters in the presence of logical constraints. A sensitivity analysis is also carried out to study the effects of different geometric parameters on the considered objective functions. Modeling the system and implementing the multi-objective optimization via genetic algorithm has been performed by MATLAB.     

Non-linear design and control optimization of composite laminated plates with buckling and postbuckling objectives

Multiobjective design and control optimization of composite laminated plates is presented to minimize the postbuckling dynamic response and maximize the buckling load. The control objective aims at dissipating the postbuckling elastic energy of the laminate with the minimum possible expenditure of control energy using a closed-loop distributed force. The layer thicknesses and fiber orientations are taken as design variables. The objectives of the optimization problem are formulated based on a shear deformation theory including the von-Karman non-linear effect for various cases of boundary conditions. The non-linear control problem is solved iteratively until an appropriate convergence criterion is satisfied based on Liapunov–Bellman theory. Liapunov function is taken as a sum of positive definite functions with different degrees. Comparative examples for three-layer symmetric and four-layer antisymmetric laminates are given for various cases of edges conditions. Graphical study is carried out to assess the accuracy of results obtained due to the successive iterations. The influences of the boundary conditions, orthotropy ratio, shear deformation, aspect ratio on the laminate optimal design are elucidated.     

Multi-objective optimization of a dimpled channel for heat transfer augmentation

Staggered arrays of dimples printed on opposite surfaces of a cooling channel is formulated numerically and optimized with hybrid multi-objective evolutionary algorithm and Pareto optimal front. As Pareto optimal front produces a set of optimal solutions, the trends of objective functions with design variables are predicted by hybrid multi-objective evolutionary algorithm. The problem is defined by three non-dimensional geometric design variables composed of dimpled channel height, dimple print diameter, dimple spacing, and dimple depth, to maximize heat transfer rate compromising with pressure drop. Twenty designs generated by Latin hypercube sampling were evaluated by Reynolds-averaged Navier–Stokes solver and the evaluated objectives were used to construct Pareto optimal front through hybrid multi-objective evolutionary algorithm. The optimum designs were grouped by k-means clustering technique and some of the clustered points were evaluated by flow analysis. With increase in dimple depth, heat transfer rate increases and at the same time pressure drop also increases, while opposite behavior is obtained for the dimple spacing. The heat transfer performance is related to the vertical motion of the flow and the reattachment length in the dimple.     

Thermal-economic multi-objective optimization of shell and tube heat exchanger using particle swarm optimization (PSO)

Many studies are performed by researchers about shell and tube heat exchanger (STHE) but the multi-objective particle swarm optimization (PSO) technique has never been used in such studies. This paper presents application of thermal-economic multi-objective optimization of STHE using PSO. For optimal design of a STHE, it was first thermally modeled using e-number of transfer units method while Bell–Delaware procedure was applied to estimate its shell side heat transfer coefficient and pressure drop. Multi objective PSO (MOPSO) method was applied to obtain the maximum effectiveness (heat recovery) and the minimum total cost as two objective functions. The results of optimal designs were a set of multiple optimum solutions, called ‘Pareto optimal solutions’. In order to show the accuracy of the algorithm, a comparison is made with the non-dominated sorting genetic algorithm (NSGA-II) and MOPSO which are developed for the same problem.     

Improved non-dominated sorting genetic algorithm （NSGA）-II in multi-objective optimization studies of wind turbine blades

The non-dominated sorting genetic algorithm (NSGA) is improved with the controlled elitism and dynamic crowding distance. A novel multi-objective optimization algorithm is obtained for wind turbine blades. As an example, a 5 MW wind turbine blade design is presented by taking the maximum power coefficient and the minimum blade mass as the optimization objectives. The optimal results show that this algorithm has good performance in handling the multi-objective optimization of wind turbines, and it gives a Pareto-optimal solution set rather than the optimum solutions to the conventional multiobjective optimization problems. The wind turbine blade optimization method presented in this paper provides a new and general algorithm for the multi-objective optimization of wind turbines.     

基于应变能与频率灵敏度的静动力双目标ESO

当前在运用渐进结构优化(ESO)时,大多仅设定了单一的静力或动力目标,难以满足工程结构设计的需求。为此,将单目标优化常用的应变能灵敏度和频率灵敏度进行无量纲处理,再与多目标优化理论结合,开发出静动力双目标ESO。通过多个不同边界条件的深受弯构件数值算例,证实了新方法的运行稳定性和普遍适用性,同时还得到了静力优化与动力优化间的权重系数比取值建议。有限元对比分析结果表明,该新方法相较于传统的单目标优化,能够兼顾结构的静动力性能,使结构耗材减少但静力刚度基本维持,同时材料利用率和一阶固有频率还能不断提升。     

传热结构的多目标拓扑优化设计研究

深入分析了传热结构多目标拓扑优化设计中的几个关键问题。提出了基于结构柔度最小化和结构散热弱度最小化的多目标拓扑优化设计方法,建立了传热结构的多目标拓扑优化设计模型,推导了传热结构多目标拓扑优化中用于迭代分析求解的优化准则算法和敏度分析方程。通过数值计算验证了理论和算法的有效性。     

考虑破损-安全的连续体结构拓扑优化ICM方法

本文瞄准连续体在破损-安全考虑下的结构拓扑优化问题,旨在克服传统模型求解所得最终构型存在的弊病,避免结构因缺乏合理的冗余结构而敏感于局部破坏,实现破损-安全的目标. 首先,梳理了以往虽然用到却并不明晰的4个概念:结构局部破损模式、结构局部破损区域、结构破损状况、结构破损状况的预估分布. 之后,基于独立连续映射(ICM)方法,对该问题建立了力学性能约束下结构体积极小化的模型. 建立目标函数时,利用Minimax的概念将可能出现的结构破损状况对应的所有结构体积目标转化为原结构的唯一结构体积目标,克服了多目标问题的困难. 建立近似约束函数时,将可能出现的所有结构破损状况对应的力学性能的约束皆考虑进去,既能处理载荷单工况也能处理载荷多工况. 最后,以位移约束为例,建立了优化模型并求解. 单工况及多工况位移约束拓扑优化算例验证了算法的有效性. 结果表明:本方法相比于不考虑破损-安全的拓扑优化设计,得到的最优拓扑更复杂,体积比更大即所用材料更多,亦即最优结构具有更多的冗余,此正是考虑破损-安全设计原则的结果. 本文的研究对于航空、航天、其他水、陆等领域运载工具以及其他工程结构在意外破坏、战争创伤或恐怖袭击下的结构设计,乃是非常重要的进展.      

基于混合行为博弈的多目标仿生设计方法

将多个设计目标视为不同的博弈方,通过计算设计变量对目标函数的影响因子和模糊聚类, 将设计变量集合分割为各博弈方拥有的策略空间. 对蜥蜴种群的繁衍生存机理进行仿生,将 3种蜥蜴的行为方式分别定义为利己主义、集体主义和投机主义,并赋予相应的博弈方, 各博弈方根据所仿生蜥蜴的行为特点,建立自身博弈得益函数与目标函数之间的映射关系. 各博弈方分别以自身博弈得益函数为目标,在各自的策略空间中进行单目标优化,获得本博 弈方对其余博弈方的最佳对策,所有博弈方的最佳对策形成一轮博弈的策略组合,并根据收 敛判别,通过多轮博弈,获得最终的博弈解. 以白鹤滩拱坝体型的三目标优化设计为例,设 计结果显示坝体体积方量减少了16.412万方,或2.38%; 最大主拉应力降低 了0.036MPa, 或0.31%; 整体应变能下降了0.167GJ 或4.47% 体现了基 于混合行为博弈方式的多目标仿生设计方法的有效性.     

Optimal placement of piezoelectric active bars in vibration control by topological optimization

A continuous variable optimization method and a topological optimization method are proposed for the vibration control of piezoelectric truss structures by means of the optimal placements of active bars. In this optimization model, a zero-one discrete variable is defined in order to solve the optimal placement of piezoelectric active bars. At the same time, the feedback gains are also optimized as continuous design variables. A two-phase procedure is proposed to solve the optimization problem. The sequential linear programming algorithm is used to solve optimization problem and the sensitivity analysis is carried out for objective and constraint functions to make linear approximations. On the basis of the Newmark time integration of structural transient dynamic responses, a new sensitivity analysis method is developed in this paper for the vibration control problem of piezoelectric truss structures with respect to various kinds of design variables. Numerical examples are given in the paper to demonstrate the effectiveness of the methods.     

基于概率和非概率混合模型的结构鲁棒设计方法

讨论了同时存在概率不确定性量和非概率不确定性量时可行鲁棒性和目标函数鲁棒性的实现策略,提出了基于概率和非概率混合模型的结构鲁棒设计方法。基本做法是首先视非概率型不确定性量为参变量,按照传统概率统计的方法计算约束函数和目标函数的均值和标准方差,然后再考虑非概率型不确定性量的波动变化对约束函数和目标函数统计特征量的影响,以修正常规可行鲁棒性和目标函数鲁棒性的数学模型。所提方法应用于一个10杆桁架结构的最轻质量设计和节点位移鲁棒设计,获得了对不确定性量波动变化不敏感的设计方案。     

A multi-objective optimal PID control for a nonlinear system with time delay

It is generally difficult to design feedback controls of nonlinear systems with time delay to meet time domain specifications such as rise time, overshoot, and tracking error. Furthermore, these time domain specifications tend to be conflicting to each other to make the control design even more challenging. This paper presents a cell mapping method for multi-objective optimal feedback control design in time domain for a nonlinear Duffing system with time delay. We first review the multi-objective optimization problem and its formulation for control design. We then introduce the cell mapping method and a hybrid algorithm for global optimal solutions. Numerical simulations of the PID control are presented to show the features of the multi-objective optimal design.     

多目标结构优化设计的中心法

提出一个求解多目标结构优化设计的中心法，该方法可以看作是求解单目标优化问题中 心法的直接推广. 它针对每个目标函数引进一个``移动靶'以形成各目标函数的水平截集， 然后通过计算并跟踪这些目标函数的水平集与原约束集合形成的交集中心，来达到求解多目 标优化问题的目的. 这个方法在不增加额外计算量的情况下，实现了多目标优化与单目标优 化的算法统一，因此非常容易在现有的结构优化设计的程序中实现. 给出了几个结构优化 设计问题的算例，验证了算法的有效性和可靠性.     

带有圆弧形凹槽金属薄壁圆管抗撞性优化设计

在金属薄壁圆管的基础上,引入圆弧形凹槽诱导结构并以其为研究对象,建立以凹槽数量及其半径为优化参数,以比吸能和压溃力效率为评价指标的多目标优化模型。分析研究均布设置诱导凹槽对结构吸能、最大峰值压溃力及压溃力曲线平稳性的影响。采用有限元软件LS-DYNA得到不同几何参数模型的碰撞响应,结合径向基函数法构造近似函数,并采用理想点法进行优化设计,得出使结构最优时的凹槽数量和半径,从而得到了理想的诱导凹槽优化结构。     

仿生多胞薄壁管耐撞性分析及优化

为提高薄壁管结构耐撞性，以雀尾螳螂虾螯为仿生原型，结合仿生学设计方法，设计一种含正弦胞元的多胞薄壁管结构。以初始峰值载荷、比吸能和碰撞力效率为耐撞性指标，通过有限元数值模拟分析了不同碰撞角度（0o、10o、20o和30o）条件下，仿生胞元数对薄壁管耐撞性的影响，通过多目标的复杂比例评估法获取仿生薄壁管的最优胞元数。基于不同碰撞角度权重因子组合，设置了4种单一角度工况和3种多角度工况，采用多目标粒子群优化方法获取了不同工况下薄壁管结构最优胞元高宽比和壁厚。复杂比例评估结果表明，胞元数为4的薄壁管为最优晶胞数仿生薄壁管。优化结果表明，单一角度工况下，最优结构参数高宽比的范围为0.88～1.50，壁厚的范围为0.36～0.60 mm，碰撞角度为0o和10o的最优高宽比明显小于碰撞角度为20o和30o的；多角度工况下，最优高宽比范围为1.01～1.10，壁厚范围为0.49～0.57 mm。     

基于遗传算法的抗震钢框架多目标优化设计

考虑抗震钢框架优化问题具有多目标的特点，在遗传算法的基础上对抗震钢框架多目 标优化设计进行了探讨. 在无约束Pareto排序遗传算法的基础上，提出了一个简单、实用 而又可以避免采用罚函数的全新排序方法，在此基础上形成了一种求解有约束多目标优化 问题的Pareto遗传算法(CMOPGA), 并给出了具体的算法流程图. 以钢框架重量最轻和结构 总动应变能最小为目标，基于相关的设计规范，给出了抗震钢框架多目标优化问题的一种合 理提法. 采用CMOPGA对一个两跨六层抗震钢框架实例进行了多目标优化设计，并提出了一 个在Pareto最优解集的基础上选取妥协解的相对最小距离妥协原则. 算例结果表明，采用 CMOPGA求解抗震钢框架多目标优化问题是可行和有效的.     

Multi-objective optimization of a guide vane in the turning region of a rotating U-duct to enhance heat transfer performance

An optimization has been performed for the design of a guide vane in the turning region of a rotating U-duct using the Kriging meta-model and a hybrid multi-objective evolutionary algorithm. Rotation of the U-duct is accompanied by the Coriolis force that causes a discrepancy in heat transfer between the trailing (pressure) and leading (suction) surfaces of the duct. For the optimization, three geometric variables related to the thickness, angle, and location of the guide vanes are selected as the design variables. A Kriging model is constructed to obtain a Pareto-optimal front through a multi-objective evolutionary algorithm. The values of the objective function at the design points are evaluated by Reynolds-averaged Navier–Stokes analysis. The shear stress transport model is used as the turbulence closure model in the analysis. The tradeoff between the two competing objective functions is discussed for Pareto-optimal solutions in the design space. The optimized guide vanes show an increase in heat transfer performance with a decrease in the friction loss in the turning region and downstream straight passage in comparison with the reference design.     

A modified multi-objective particle swarm optimization approach and its application to the design of a deepwater composite riser

A modified multi-objective particle swarm optimization method is proposed for obtaining Pareto-optimal solutions effectively. Different from traditional multi-objective particle swarm optimization methods, Kriging meta-models and the trapezoid index are introduced and integrated with the traditional one. Kriging meta-models are built to match expensive or black-box functions. By applying Kriging meta-models, function evaluation numbers are decreased and the boundary Pareto-optimal solutions are identified rapidly. For bi-objective optimization problems, the trapezoid index is calculated as the sum of the trapezoid’s area formed by the Pareto-optimal solutions and one objective axis. It can serve as a measure whether the Pareto-optimal solutions converge to the Pareto front. Illustrative examples indicate that to obtain Pareto-optimal solutions, the method proposed needs fewer function evaluations than the traditional multi-objective particle swarm optimization method and the non-dominated sorting genetic algorithm II method, and both the accuracy and the computational efficiency are improved. The proposed method is also applied to the design of a deepwater composite riser example in which the structural performances are calculated by numerical analysis. The design aim was to enhance the tension strength and minimize the cost. Under the buckling constraint, the optimal trade-off of tensile strength and material volume is obtained. The results demonstrated that the proposed method can effectively deal with multi-objective optimizations with black-box functions.     

A multi-objective optimization method for uncertain structures based on nonlinear interval number programming method

A multi-objective optimization method for uncertain structures is developed based on nonlinear interval number programming (NINP) method. The NINP method is employed to transform each uncertain objective function into a deterministic single-objective optimization problem. Using the constraint penalty function method, a deterministic multi-objective and non-constraint optimization problem is formulated in terms of penalty functions. Then the micro multi-objective genetic algorithm and the intergeneration projection genetic algorithm are adopted as outer layer and inner optimization operator to solve the nesting optimization problem, respectively. Finally, four numerical examples are provided to demonstrate the effectiveness of the present method.     

Nonlinear buckling optimization of composite structures considering “worst” shape imperfections

Nonlinear buckling optimization is introduced as a method for doing laminate optimization on generalized composite shell structures exhibiting nonlinear behaviour where the objective is to maximize the buckling load. The method is based on geometrically nonlinear analyses and uses gradient information of the nonlinear buckling load in combination with mathematical programming to solve the problem. Thin-walled optimal laminated structures may have risk of a relatively high sensitivity to geometric imperfections. This is investigated by the concepts of “worst” imperfections and an optimization method to determine the “worst” shape imperfections is presented where the objective is to minimize the buckling load subject to imperfection amplitude constraints. The ability of the nonlinear buckling optimization formulation to solve the laminate problem and determine the “worst” shape imperfections is illustrated by several numerical examples of composite laminated structures and the application of both formulations gives useful insight into the interaction between laminate design and geometric imperfections.