Application of the optimal Latin hypercube design and radial basis function network to collaborative optimization

Improving the efficiency of ship optimization is crucial for modem ship design. Compared with traditional methods, multidisciplinary design optimization （MDO） is a more promising approach. For this reason, Collaborative Optimization （CO） is discussed and analyzed in this paper. As one of the most frequently applied MDO methods, CO promotes autonomy of disciplines while providing a coordinating mechanism guaranteeing progress toward an optimum and maintaining interdisciplinary compatibility. However, there are some difficulties in applying the conventional CO method, such as difficulties in choosing an initial point and tremendous computational requirements. For the purpose of overcoming these problems, optimal Latin hypercube design and Radial basis function network were applied to CO. Optimal Latin hypercube design is a modified Latin Hypercube design. Radial basis function network approximates the optimization model, and is updated during the optimization process to improve accuracy. It is shown by examples that the computing efficiency and robustness of this CO method are higher than with the conventional CO method.

Multidisciplinary Design and Optimization of Satellite Launch Vehicle Using Latin Hypercube Design of Experiments

The design of new Satellite Launch Vehicle （SLV） is of interest, especially when a combination of Solid and Liquid Propulsion is included. Proposed is a conceptual design and optimization technique for multistage Low Earth Orbit （LEO） bound SLV comprising of solid and liquid stages with the use of Genetic Algorithm （GA） as global optimizer. Convergence of GA is improved by introducing initial population based on the Design of Experiments （DOE） Technique. Latin Hypercube Sampling （LHS）-DOE is used for its good space filling properties. LHS is a stratified random procedure that provides an efficient way of sampling variables from their multivariate distributions. In SLV design minimum Gross Lift offWeight （GLOW） concept is traditionally being sought. Since the development costs tend to vary as a function of GLOW, this minimum GLOW is considered as a minimum development cost concept. The design approach is meaningful to initial design sizing purpose for its computational efficiency gives a quick insight into the vehicle performance prior to detailed design.

Robust design and optimization for autonomous PV-wind hybrid power systems

This study presents a robust design method for autonomous photovoltaic (PV)-wind hybrid power systems to obtain an optimum system configuration insensitive to design variable variations. This issue has been formulated as a constraint multi-objective optimization problem, which is solved by a multi-objective genetic algorithm, NSGA-II. Monte Carlo Simulation (MCS) method, combined with Latin Hypercube Sampling (LHS), is applied to evaluate the stochastic system performance. The potential of the proposed method has been demonstrated by a conceptual system design. A comparative study between the proposed robust method and the deterministic method presented in literature has been conducted. The results indicate that the proposed method can find a large mount of Pareto optimal system configurations with better compromising performance than the deterministic method. The trade-off information may be derived by a systematical comparison of these configurations. The proposed robust design method should be useful for hybrid power systems that require both optimality and robustness.

基于响应面法的60MN压剪试验机上横梁优化设计

针对压剪试验机大承载、小变形与轻量化的要求,结合有限元分析运用响应面法对60MN压剪试验机上横梁进行优化设计。首先运用拉丁超立方抽样法生成试验设计样本点,并根据设计结果采用多种拟合方法拟合并对精度校验,发现克里金(Kriging)法能够精确地与拉丁超立法实验设计法生成的实验点匹配,而且拟合的响应面模型高效且精准;然后以上横梁应力、质量、变形为优化目标,运用多目标遗传算法进行优化设计得出最优解,并通过灵敏度分析对优化后的结果进行修正,使其更具有工程应用价值。经校验优化后的结构比原始结构减重11.8%,优化效果显著,节省了生产成本,对压剪试验机的结构优化设计有重要的实际意义,同时也为其它类似结构件的优化分析提供参考。

基于Kriging模型的船舶主机隔离系统抗冲击优化

为了提高系统的抗冲击性能和优化效率,本文以限位隔离系统的刚度阻尼等7个参数为设计变量,以系统冲击响应中的相对位移响应和绝对加速度响最大峰值为响应值建立Kriging代理模型。通过NSGA-II多目标优化算法对构建的代理模型进行多目标优化,优化目标为相对位移响应和绝对加速度响最大峰值两者和的最小值。与初始方案相比,优化后系统相对位移响应降低了27.139%,绝对加速度响应降低了37.846%。结果表明:建立的代理模型对隔离系统的冲击响应有较精确的预报作用,优化后船舶主机隔离系统的抗冲击得到明显提高。

基于最优拉丁超立方设计的糖尿病足鞋垫优化设计

目的提出一种鞋材弹性模量与厚度联合优化设计糖尿病足鞋垫的方法,以降低足底压力和软组织内部应力。方法通过逆向工程方法建立足部有限元模型,基于足底压力分布特征划分鞋垫压力区域,采用有限元法对接触力学进行研究,为优化过程中调整不同区域内材料的弹性模量和鞋垫前后足厚度奠定基础,使用最优拉丁超立方设计得到最优参数组合。结果设计的鞋垫增加约37.55%的足底接触面积,跖骨区和足跟区的压力峰值分别降低15.07%、36.96%,足跟处软组织内部应力降低20.83%,足底筋膜张力降低约60%。结论所提出的方法可用于设计定制鞋垫,设计的个性化鞋垫具有更大的接触面积和降低糖尿病足底溃疡的良好潜力。

基于组合优化算法的致动器安装位置与间隙优化设计

针对小口径火炮连续发射时的射击精度问题,基于使用以超磁致伸缩材料为核心的致动器对身管的振动抑制展开研究。基于最优拉丁超立方设计方法,开展了DOE试验设计,以身管振幅和致动器受力为目标函数,以致动器安装位置和致动器与身管的间隙为设计变量,采用多岛遗传算法与修正可行方向法形成组合优化算法,使用Isight多学科优化软件对近似模型进行了优化计算。优化后致动器受力降低了88%,同时身管振动幅值降低了52.1%。与仅使用全局优化算法相比较,使用组合优化算法得到最优解时迭代次数减少了47.6%,证明了多岛遗传算法与修正可行方向法形成组合优化算法具有较高的优化效率。

演化排列优化拉丁超立方设计方法

拉丁超立方设计是最常用的计算机试验设计方法之一,针对现有拉丁超立方设计方法采样一次性且难以兼顾设计的空间均匀性和计算效率的问题,提出了一种演化排列拉丁超立方试验设计方法。通过对小样本设计的演化、排列信息继承和扩充等操作,以较小的计算量实现了样本的扩充与优化。此外,所提方法可以兼顾现有样本和新增采样点之间的关系,实现样本的序列扩充,这在实际近似建模过程中十分方便。通过多组数值试验,验证了本文方法在空间均匀性和计算效率等方面的优越性。

Global Optimization Method Using SLE and Adaptive RBF Based on Fuzzy Clustering

High fidelity analysis models,which are beneficial to improving the design quality,have been more and more widely utilized in the modern engineering design optimization problems.However,the high fidelity analysis models are so computationally expensive that the time required in design optimization is usually unacceptable.In order to improve the efficiency of optimization involving high fidelity analysis models,the optimization efficiency can be upgraded through applying surrogates to approximate the computationally expensive models,which can greately reduce the computation time.An efficient heuristic global optimization method using adaptive radial basis function（RBF） based on fuzzy clustering（ARFC） is proposed.In this method,a novel algorithm of maximin Latin hypercube design using successive local enumeration（SLE） is employed to obtain sample points with good performance in both space-filling and projective uniformity properties,which does a great deal of good to metamodels accuracy.RBF method is adopted for constructing the metamodels,and with the increasing the number of sample points the approximation accuracy of RBF is gradually enhanced.The fuzzy c-means clustering method is applied to identify the reduced attractive regions in the original design space.The numerical benchmark examples are used for validating the performance of ARFC.The results demonstrates that for most application examples the global optima are effectively obtained and comparison with adaptive response surface method（ARSM） proves that the proposed method can intuitively capture promising design regions and can efficiently identify the global or near-global design optimum.This method improves the efficiency and global convergence of the optimization problems,and gives a new optimization strategy for engineering design optimization problems involving computationally expensive models.

Multi-objectives nonlinear structure optimization for actuator in trajectory correction fuze subject to high impact loadings

This paper presents an actuator used for the trajectory correction fuze,which is subject to high impact loadings during launch.A simulation method is carried out to obtain the peak-peak stress value of each component,from which the ball bearings are possible failures according to the results.Subsequently,three schemes against impact loadings,full-element deep groove ball bearing and integrated raceway,needle roller thrust bearing assembly,and gaskets are utilized for redesigning the actuator to effectively reduce the bearings’stress.However,multi-objectives optimization still needs to be conducted for the gaskets to decrease the stress value further to the yield stress.Four gasket’s structure parameters and three bearings’peak-peak stress are served as the four optimization variables and three objectives,respectively.Optimized Latin hypercube design is used for generating sample points,and Kriging model selected according to estimation result can establish the relationship between the variables and objectives,representing the simulation which is time-consuming.Accordingly,two optimization algorithms work out the Pareto solutions,from which the best solutions are selected,and verified by the simulation to determine the gaskets optimized structure parameters.It can be concluded that the simulation and optimization method based on these components is effective and efficient.

Reliability-Based Optimization:Small Sample Optimization Strategy

The aim of the paper is to present a newly developed approach for reliability-based design optimization. It is based on double loop framework where the outer loop of algorithm covers the optimization part of process of reliability-based optimization and reliability constrains are calculated in inner loop. Innovation of suggested approach is in application of newly developed optimization strategy based on multilevel simulation using an advanced Latin Hypercube Sampling technique. This method is called Aimed multilevel sampling and it is designated for optimization of problems where only limited number of simulations is possible to perform due to enormous com- putational demands.

基于拉丁超立方算法的永磁同步电机设计优化

为了设计出起动性能好,运行更加稳定的V形内置式永磁同步电机,通过改善空气隔磁槽结构的方法对空载反电势、气隙磁密、齿槽转矩、转矩脉动进行优化。将空气隔磁槽几何参数作为待优化变量,采用拉丁超立方抽样算法进行多目标优化,得到最优参数组合。优化后齿槽转矩下降了45%,转矩脉动下降了4.4%,电磁转矩提升了5.2%。优化结果理想,验证了该永磁同步电机优化方案的合理性。

基于LHD与GPR的机器学习超参数建模及优化

针对机器学习超参数与算法性能之间的非线性、高阶交互作用和约束的复杂作用关系,文章提出一种基于高斯过程回归和遗传算法相结合的建模及优化方法。采用超拉丁方抽样在超参数配置空间内进行取点设计,建立超参数与算法性能之间的高斯过程回归模型并对所构建的模型进行遗传算法寻优。仿真研究表明,该方法能够在超参数配置空间内较好地拟合超参数与算法性能之间的复杂作用关系,与传统响应曲面法相比,在超参数配置空间内以较少的实验次数实现了全局最优,从而有效提升了优化的效率和精度。

基于Kriging代理模型的高升力构型优化设计

本文发展了一种基于Kriging模型的高升力构型优化设计方法。采用分区对接网格技术求解N-S方程以及遗传算法,在着陆构型下使多段翼型升力系数最大。为了降低计算量和计算时间,在优化过程中采用Kriging模型代替复杂的流场计算。为了提高模型的精度,采用EI方法增加新的样本点。利用该方法完成了多段翼型缝道参数和外形优化设计。结果表明,在只优化襟翼缝道和襟翼缝道与外形同时优化两种情况下,该方法使得多段翼型最大升力系数分别提高7.55%和9.48%。

多学科设计优化在整车轻量化设计中的应用研究

采用最优拉丁方试验设计方法进行样本数据设计,同时,为了提高计算效率,采用了一种新型的响应面构建方法——逐步回归响应面方法构建了整车耐撞性与白车身自由模态多学科系统的近似模型,利用序列二次规划优化方法对此近似模型进行优化,避免了整车碰撞传统优化设计方法计算量大,在碰撞非线性系统优化中常常易导致收敛缓慢甚至不收敛的缺点,在满足了CMVDR294安全法规的同时,使得白车身的扭转模态值得到提高,汽车重量得到较大程度的减轻。

基于正交试验的深井泵优化设计

以深井泵叶片数、出口安放角、出口宽度等7个因素,每个因素取3个水平,按L18(37)正交试验方案,设计了18副叶轮。通过CFD技术对叶轮、导叶在内的两级深井泵的全流场进行了设计工况下的三维数值模拟,获得了18组设计方案的效率、扬程值。通过正交试验法探索了各几何参数对效率、扬程的影响规律,并通过极差分析找到了影响这些性能的主要因素和次要因素,根据优选结果结合内部流场测试及样机试验验证对模型泵提出了进一步优化设计方案。本试验结果对采用叶轮极大扬程设计法的深井泵水力设计具有一定的参考价值。

离心泵叶轮轴面图的全自动CFD优化

叶轮轴面图设计的好坏直接影响离心泵的效率。以轴面图上的前盖板圆弧半径R0和R1、前盖板倾角T1、后盖板圆弧半径R2、后盖板倾角T2等5个几何参数为自变量,以泵水力效率最大为目标,采用Isight集成Pro/E、Gambit和Fluent等软件,实现了对离心泵叶轮轴面图进行CFD全自动优化。优化样本数据设计采用最优拉丁方试验设计方法确定。采用该方法对一比转数为84.8的离心泵进行优化。结果表明:优化后的扬程比优化前提高了4.85%,且优化后的水力效率从83.20%增加到84.51%,提高了1.31个百分点。因此,建立的叶轮轴面图全自动CFD优化方法是可行有效的,可为离心泵的水力优化设计提供参考。

改进Kriging模型在翼型气动优化设计中的应用研究

文章将拉丁超立方抽样试验设计方法,Kriging模型与优化方法结合发展了一套基于改进Kriging模型的优化设计算法。首先对Kriging模型的拟合精度进行了研究,针对一维函数以及气动问题进行了测试,验证了文中发展的Kriging模型能够较好地对函数进行拟合以及能够运用到气动问题中。为了提高Kriging模型的拟合精度,文章对原有的Kriging模型优化设计算法进行了改进,在引入EI方法的同时将优化搜索算法得到的最优点加入到原有的样本集中,每次增加2个样本点,然后再重新生成Kriging模型进行优化设计。为了验证该方法的正确性和有效性,使用该算法进行了RAE2822翼型减阻优化设计,优化后的RAE2822翼型的阻力系数降低了33.6%,算例表明采用该方法能够逐步提高Kriging模型的拟合精度,最终实现高效的翼型气动性能优化设计。

汽车发动机悬置系统的多目标稳健优化设计

针对悬置元件的参数不确定性问题和单目标优化的局限,将稳健设计与多目标优化相结合,提出一种发动机悬置系统多目标稳健优化方法。该方法考虑了悬置刚度的不确定性,并假设其服从正态分布;通过拉丁超立方抽样得到动反力的稳健性函数,并将其作为Pareto多目标优化目标函数向量的组成部分;应用遗传算法对优化模型进行全局寻优,找到所有Pareto最优解,并通过稳健性评价得到既优化又稳健的解。最后以某型轿车的发动机悬置系统优化为例,验证了该方法的有效性。

一种快速优化拉丁超立方试验设计方法

工程设计优化中,优化试验设计方法常常用于求解大型复杂系统问题。针对传统优化试验设计方法计算耗时长、效率低的问题,提出一种快速优化拉丁超立方试验设计方法:在拉丁超立方抽样框架下,采用基于最大最小距离准则连续局部枚举方法设计生成高性能小尺寸基础样本,然后利用平移传播算法通过"平移"基础样本快速获得大尺寸试验样本。结合提出的样本尺寸调整策略,使该方法可以快速得到空间填充性能和映射性能良好的任意尺寸试验样本。测试结果表明快速优化拉丁超立方试验设计方法能够兼顾设计效率和样本性能,优于已有典型试验设计方法。