基于增广SVM的结构动力学模型修正方法研究

研究了基于代理模型的有限元模型修正方法,针对支持向量机(Support Vector Machine,SVM)在处理非线性程度不高函数时容易出现过拟合,提出了一种采用混合基函数形式的增广SVM方法。该方法首先是在结构动力学试验结果和结构有限元模型计算分析结果的基础上,根据设计要求、灵敏度计算或工程经验选择适合的待修正参数、修正范围来确定修正样本空间,并给出样本点,其次采用增广SVM方法构造每组样本点和与之对应的目标函数之间的代理模型,采用基于Pareto最优解的多目标优化方法,以代理模型输出为目标,样本空间为变量,寻找待修正参数在修正区间内的全局最优解。用代理模型代替原有的有限元模型进行相关的计算分析,避免在模型修正过程中反复调用原有限元模型进行计算带来的高昂计算成本。通过算例一表明,增广SVM的预测结果较传统SVM方法精度更高,而算例二、三则说明所提出的基于增广SVM方法的结构动力学模型修正方法具有实际应用价值,同时计算结果具有很高的精度。     

基于网格变形技术的机枪三脚架多目标响应面优化

针对使用过程中枪架弹性变形过大影响射击精度问题,提出网格变形、Plackett-Burman试验设计、多目标优化相结合提高枪架刚度的解决方案。利用网格变形技术定义形状变量,据Plackett-Burman试验设计筛选对目标函数显著度高的形状变量;采用优化拉丁方试验设计对整个设计空间均匀采样,据样本点拟合高精度Kriging响应面模型;以三脚架质量为约束,轴向、横向弯曲刚度为目标函数,用多目标遗传优化算法(MOGA)对响应面模型进行寻优。研究表明,该方法能同时提高三脚架轴向、横向刚度,可据Pareto最优解集合权衡各目标进行决策。     

基于Kriging代理模型的拉压不同模量平面问题的近似求解

该文建议采用Kriging代理模型数值求解拉压不同模量平面问题。通过本构方程光滑化、有限元法及拉丁超立方采样技术,对拉压不同模量桁架与二维平面问题,给出了基于Kriging模型的近似数值解,以代理基于有限元的数值解,并探讨了样本点数目和问题规模对所建Kriging近似模型求解精度/效率的影响。数值算例表明:所提方法可为求解拉压不同模量平面问题提供精度合理的近似数值解。当问题规模较大且正问题需要多次求解时,该方法有望显著减少计算时间,这对于降低拉压不同模量反问题与优化问题的计算开销十分重要。     

汽车乘员舱多层吸声材料的多目标优化

建立了汽车的统计能量分析模型,进行仿真与实验的误差分析,验证了所建模型的有效性,然后选取四层吸声材料布置于乘员舱顶棚,采用优化拉丁方法,以其厚度为设计变量,为降低驾驶员耳旁噪声和满足汽车结构轻量化和低成本的要求,以驾驶员头部声腔A声级降低幅度、吸声材料重量、降噪效率、材料价格和性价比为优化目标,选取30个样本点进行试验设计并通过计算得到全部响应值,之后建立了Kriging近似模型,为验证该近似模型模拟精度,任选三个新的样本点分析近似模型和仿真结果间的误差,最后以近似模型为基础执行多目标优化,与吸声材料初始组合相比,A声级降低幅度反而减小了0.289dB,但重量降低了54.8%,降噪效率提高了85.6%,材料价格降低了21.1%,性价比提高了6.0%。     

基于Kriging代理模型的多点加点序列优化方法

基于Kriging 代理模型提出了一种同时考虑预测响应值及其不确定性的多点加点准则,并基于该准则发展了一套序列近似优化方法。多点加点准则基于初始样本信息和所预测的对象函数特征增加新样本集,以在寻优迭代过程中自适应地提高代理模型的精度。该文方法依据多点加点准则在一次迭代中增加多个空间无关的新样本点,适用于多机同时计算或并行计算,从而提高计算效率。以两个经典的数学函数为例,将该优化方法与期望提高准则方法进行了比较,结果表明该文提出的优化方法能够有效地提高最优解的全局性。将方法用于一盒式注塑件的成型工艺优化设计,优化结果也表明了该方法的有效性。     

基于Kriging代理模型的二维分数阶粘弹性问题的数值求解

为提高求解分数阶粘弹性正问题的计算效率,提出了一种基于Kriging代理模型的数值求解方法。利用拉丁超立方采样技术选取样本点,借助有限元和有限差分技术计算样本点的位移响应,从而建立Kriging代理模型。通过均质和区域非均质两个粘弹性算例,对所提方法的计算精度和计算效率进行了测试。测试分析表明:代理模型可提供合用的计算精度,当问题规模较大且正问题需要多次求解时,有望显著降低计算时间。     

基于Kriging模型的钢管混凝土连续梁拱桥有限元模型修正

提出基于Kriging模型的有限元模型修正方法。Kriging模型为据区域内若干信息样品某种特征数据对该区域同类特征未知数作线性无偏、最小方差估计方法,其只用少量样本即可获得较高精度预测结果。用Kriging模型对平面桁架进行有限元模型修正,验证该方法的可行性与准确性;对一连续梁拱桥进行模型修正,并与GA算法、BP神经网络方法模型修正结果比较分析。Kriging模型仅需一定量测量频率信息即可完成模型修正,能避免修正过程中进行有限元模型迭代计算。结果表明,该方法能准确预测有效频率范围(active frequency range)外模态信息,计算效率、精度较高,可用于工程实践。     

基于近似模型的空调配管阻尼层优化设计

空调配管系统的减振降噪是空调结构开发中的一个设计难点,是制约空调整体品质的一个关键参数。针对空调仿真优化设计中计算成本和计算精度之间的矛盾,本文将统计学中的近似模型技术应用到空调配管系统的阻尼优化。采用正交试验设计与均匀试验设计相结合的试验设计方法,建立了多项式响应面、Kriging最优内插、BP神经网络近似模型,研究了阻尼层位置、宽度等参数与结构响应频率、阻尼比之间的近似映射关系。最后采用多目标遗传算法分析了结构阻尼比与结构质量之间的Pareto曲线,并选择最优结果进行了试验验证。研究表明,采用近似模型的阻尼层优化方法可以有效地提高设计效率,降低成本,为空调系统的仿真提供了一种可行的方法。     

结构有限元模型修正的自适应响应面方法

针对结构有限元模型修正可能陷入局部最优点的问题,提出了基于具有全局收敛特性的自适应响应面的结构有限元模型修正方法,模型修正过程中在全局最优解附近不断收缩参数设计空间,重构更为精确的响应面模型,同时,由于采用了拉丁超立方设计选择样本点,具有一定的遗传性,在使用过程中可以有效减少样本点总数。通过实例计算表明,传统的有限元模型修正方法很可能陷于局部最优,而利用该方法进行有限元模型修正时,可以有效避免陷入局部最优点,只需较少样本点便可收敛于全局最优解,有效的进行有限元模型修正。     

基于目标应变分布的TC17合金双性能盘预成形形状优化设计

目的 研究TC17合金双性能盘目标应变分布下的预成形形状优化设计方法.方法 采用拉丁超立方试验设计方法对预成形形状设计变量抽样选取样本点,并通过Deform有限元数值模拟获得样本设计变量下的局部应变分布.以局部应变分布与目标应变分布之间的方差最小为目标函数,采用Kriging方程建立近似替代模型预测响应应变误差,并结合遗传算法,以锻件的充填率及材料利用率为约束条件,优化设计预成形形状.结果 近似替代模型预测的应变误差与基于有限元数值模拟计算获得的应变误差之间的最大相对误差和最小相对误差分别为10.8％和0.01％.结论 这表明Kriging近似替代模型在预测响应应变误差时的精度较高,具有较好的可靠性,采用优化后的预成形形状经多道次等温锻造后的等效应变分布满足目标应变分布的设计要求.     

Construction of nested maximin designs based on successive local enumeration and modified novel global harmony search algorithm

Engineering design often involves different types of simulation, which results in expensive computational costs. Variable fidelity approximation-based design optimization approaches can realize effective simulation and efficiency optimization of the design space using approximation models with different levels of fidelity and have been widely used in different fields. As the foundations of variable fidelity approximation models, the selection of sample points of variable-fidelity approximation, called nested designs, is essential. In this article a novel nested maximin Latin hypercube design is constructed based on successive local enumeration and a modified novel global harmony search algorithm. In the proposed nested designs, successive local enumeration is employed to select sample points for a low-fidelity model, whereas the modified novel global harmony search algorithm is employed to select sample points for a high-fidelity model. A comparative study with multiple criteria and an engineering application are employed to verify the efficiency of the proposed nested designs approach.     

An Overview of First-Order Model Management for Engineering Optimization

First-order approximation/model management optimization (AMMO) is a rigorous methodology for solving high-fidelity optimization problems with minimal expense in high-fidelity function and derivative evaluation. AMMO is a general approach that is applicable to any derivative based optimization algorithm and any combination of high-fidelity and low-fidelity models. This paper gives an overview of the principles that underlie AMMO and puts the method in perspective with other similarly motivated methods. AMMO is first illustrated by an example of a scheme for solving bound-constrained optimization problems. The principles can be easily extrapolated to other optimization algorithms. The applicability to general models is demonstrated on two recent computational studies of aerodynamic optimization with AMMO. One study considers variable-resolution models, where the high-fidelity model is provided by solutions on a fine mesh, while the corresponding low-fidelity model is computed by solving the same differential equations on a coarser mesh. The second study uses variable-fidelity physics models, with the high-fidelity model provided by the Navier-Stokes equations and the low-fidelity model—by the Euler equations. Both studies show promising savings in terms of high-fidelity function and derivative evaluations. The overview serves to introduce the reader to the general concept of AMMO and to illustrate the basic principles with current computational results.     

Improving variable-fidelity modelling by exploring global design space and radial basis function networks for aerofoil design

The global variable-fidelity modelling (GVFM) method presented in this article extends the original variable-complexity modelling (VCM) algorithm that uses a low-fidelity and scaling function to approximate a high-fidelity function for efficiently solving design-optimization problems. GVFM uses the design of experiments to sample values of high- and low-fidelity functions to explore global design space and to initialize a scaling function using the radial basis function (RBF) network. This approach makes it possible to remove high-fidelity-gradient evaluation from the process, which makes GVFM more efficient than VCM for high-dimensional design problems. The proposed algorithm converges with 65% fewer high-fidelity function calls for a one-dimensional problem than VCM and approximately 80% fewer for a two-dimensional numerical problem. The GVFM method is applied for the design optimization of transonic and subsonic aerofoils. Both aerofoil design problems show design improvement with a reasonable number of high- and low-fidelity function evaluations.     

An adaptive sampling method for variable-fidelity surrogate models using improved hierarchical kriging

Variable-fidelity (VF) modelling methods have been widely used in complex engineering system design to mitigate the computational burden. Building a VF model generally includes two parts: design of experiments and metamodel construction. In this article, an adaptive sampling method based on improved hierarchical kriging (ASM-IHK) is proposed to refine the improved VF model. First, an improved hierarchical kriging model is developed as the metamodel, in which the low-fidelity model is varied through a polynomial response surface function to capture the characteristics of a high-fidelity model. Secondly, to reduce local approximation errors, an active learning strategy based on a sequential sampling method is introduced to make full use of the already required information on the current sampling points and to guide the sampling process of the high-fidelity model. Finally, two numerical examples and the modelling of the aerodynamic coefficient for an aircraft are provided to demonstrate the approximation capability of the proposed approach, as well as three other metamodelling methods and two sequential sampling methods. The results show that ASM-IHK provides a more accurate metamodel at the same simulation cost, which is very important in metamodel-based engineering design problems.     

Hybrid surrogate-model-based multi-fidelity efficient global optimization applied to helicopter blade design

A multi-fidelity optimization technique by an efficient global optimization process using a hybrid surrogate model is investigated for solving real-world design problems. The model constructs the local deviation using the kriging method and the global model using a radial basis function. The expected improvement is computed to decide additional samples that can improve the model. The approach was first investigated by solving mathematical test problems. The results were compared with optimization results from an ordinary kriging method and a co-kriging method, and the proposed method produced the best solution. The proposed method was also applied to aerodynamic design optimization of helicopter blades to obtain the maximum blade efficiency. The optimal shape obtained by the proposed method achieved performance almost equivalent to that obtained using the high-fidelity, evaluation-based single-fidelity optimization. Comparing all three methods, the proposed method required the lowest total number of high-fidelity evaluation runs to obtain a converged solution.     

Hierarchical surrogate model with dimensionality reduction technique for high-dimensional uncertainty propagation

In this article, hierarchical surrogate model combined with dimensionality reduction technique is investigated for uncertainty propagation of high-dimensional problems. In the proposed method, a low-fidelity sparse polynomial chaos expansion model is first constructed to capture the global trend of model response and exploit a low-dimensional active subspace (AS). Then a high-fidelity (HF) stochastic Kriging model is built on the reduced space by mapping the original high-dimensional input onto the identified AS. The effective dimensionality of the AS is estimated by maximum likelihood estimation technique. Finally, an accurate HF surrogate model is obtained for uncertainty propagation of high-dimensional stochastic problems. The proposed method is validated by two challenging high-dimensional stochastic examples, and the results demonstrate that our method is effective for high-dimensional uncertainty propagation.     

Variable-fidelity optimization: Efficiency and robustness

This paper deals with variable-fidelity optimization, a technique in which the advantages of high- and low-fidelity models are used in an optimization process. The high-fidelity model provides solution accuracy while the low-fidelity model reduces the computational cost. An outline of the theory of the Approximation Management Framework (AMF) proposed by Alexandrov (1996) and Lewis (1996) is given. The AMF algorithm provides the mathematical robustness required for variable-fidelity optimization. This paper introduces a subproblem formulation adapted to a modular implementation of the AMF. Also, we propose two types of second-order corrections (additive and multiplicative) which serve to build the approximation of the high-fidelity model based on the low-fidelity one. Results for a transonic airfoil shape optimization problem are presented. Application of a variable-fidelity algorithm leads to a threefold savings in high-fidelity solver calls, compared to a direct optimization using the high-fidelity solver only. However, premature stops of the algorithm are observed in some cases. A study of the influence of the numerical noise of solvers on robustness deficiency is presented. The study shows that numerical noise artificially introduced into an analytical function causes premature stops of the AMF. Numerical noise observed with our CFD solvers is therefore strongly suspected to be the cause of the robustness problems encountered.     

Multidisciplinary design and optimization of an air launched satellite launch vehicle using a hybrid heuristic search algorithm

A multidisciplinary design and optimization strategy for a multistage air launched satellite launch vehicle comprising of a solid propulsion system to low earth orbit with the implementation of a hybrid heuristic search algorithm is proposed in this article. The proposed approach integrated the search properties of a genetic algorithm and simulated annealing, thus achieving an optimal solution while satisfying the design objectives and performance constraints. The genetic algorithm identified the feasible region of solutions and simulated annealing exploited the identified feasible region in search of optimality. The proposed methodology coupled with design space reduction allows the designer to explore promising regions of optimality. Modules for mass properties, propulsion characteristics, aerodynamics, and flight dynamics are integrated to produce a high-fidelity model of the vehicle. The objective of this article is to develop a design strategy that more efficiently and effectively facilitates multidisciplinary design analysis and optimization for an air launched satellite launch vehicle.     

Surrogate modelling and optimization using shape-preserving response prediction: A review

Computer simulation models are ubiquitous in modern engineering design. In many cases, they are the only way to evaluate a given design with sufficient fidelity. Unfortunately, an added computational expense is associated with higher fidelity models. Moreover, the systems being considered are often highly nonlinear and may feature a large number of designable parameters. Therefore, it may be impractical to solve the design problem with conventional optimization algorithms. A promising approach to alleviate these difficulties is surrogate-based optimization (SBO). Among proven SBO techniques, the methods utilizing surrogates constructed from corrected physics-based low-fidelity models are, in many cases, the most efficient. This article reviews a particular technique of this type, namely, shape-preserving response prediction (SPRP), which works on the level of the model responses to correct the underlying low-fidelity models. The formulation and limitations of SPRP are discussed. Applications to several engineering design problems are provided.     

基于卡诺模型与联合分析的老年人APP用户体验优化设计方法

目的优化老年人APP用户体验,提出基于卡诺模型与联合分析的老年人APP用户体验优化设计方法。方法首先,建立老年人APP用户体验评价的指标体系,基于卡诺模型确定老年人对用户体验各指标的偏好权重。其次,确定APP的设计模式,选择合适的正交表确定设计模式的组合方式,建立高保真实验样本,邀请实验参与者使用实验样本执行典型任务,收集相关实验数据,并基于联合分析建立用户体验与设计模式之间的关系模型。最后,根据联合分析的结果确定最优设计,使用A/B测试对优化设计的结果进行验证。结论本文所提出方法可有效获取老年人对用户体验各指标的需求偏好,并对APP用户体验进行优化设计。