基于响应面代理模型的雷达天线阵面风载分析

基于多项式响应面代理模型,提出一种准确构建雷达阵面风载响应面模型的方法。首先,采用拉丁超立方试验设计方法构造了样本设计矩阵;其次,通过对商业软件的二次开发实现了数据流和工作流的定制及自动化,并将整个流程在iSIGHT平台下集成;最后,通过留一交叉验证方法检查了代理模型的拟合精度。结果表明,提出的基于响应面代理模型的风载分析方法计算速度快、收敛性好、能够满足工程精度需求,方便多人协同工作,具有较高的工程应用价值。     

基于广义协同高斯过程模型的结构不确定性量化解析方法

结构不确定性量化是定量参数不确定性传递到结构响应的不确定性大小。传统的蒙特卡洛法需要进行大量的数值计算,耗时较高,难以应用于大型复杂结构的不确定性量化。代理模型方法是基于少量训练样本建立的近似数学模型,可代替原始物理模型进行不确定性量化以提高计算效率。针对高精度样本计算成本高而低精度样本计算精度低的问题,该文提出了整合高、低精度训练样本的广义协同高斯过程模型。基于该模型框架推导了结构响应均值和方差的解析表达式,实现了结构不确定性的量化解析。采用三个空间结构算例来验证结构不确定性量化解析方法的准确性,并与传统的蒙特卡洛法、协同高斯过程模型和高斯过程模型的计算结果对比,结果表明所提方法在计算精度和效率方面均具有优势。     

刻蚀机装备设计中的序贯试验设计方法研究

450mm晶圆刻蚀机开发中大量应用确定性仿真来模拟腔室内部物理、化学环境,并通过仿真结果指导装备结构的详细设计。为控制仿真试验的采样规模以缩短开发周期,本文详细介绍一种新型的基于采样密度和非线性度的序贯设计方法。此方法通过蒙特卡洛方法,在设计空间中获得采样密度信息,进而对低采样密度区域增加采样点。另外,通过对每个采样的领域进行发掘,以获得采样的梯度和非线性度信息,进而对高度非线性的区域增加采样点。以450mm刻蚀机约束环设计模型和Goldstein-Price模型为背景,采用拉丁超立方和新型序贯设计方法同时采样,以代理模型精度和特征捕捉能力两个角度来对比采样结果的优劣,结果证明,在达到同样精度的前提下,新型序贯设计方法能有效减小采样规模,符合刻蚀装备设计的需要。     

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。     

基于改进的信赖域模型管理技术识别风电转子系统不对中载荷

针对求解耗时的风电转子系统不对中载荷识别问题，提出基于改进的信赖域模型管理技术的识别算法。该算法将整个先验分布空间的不对中载荷识别问题转化为一系列信赖域上的近似优化问题，通过区域遗传智能采样技术采集样本，加强径向基函数构建代理模型，再采用遗传算法进行近似优化。通过每个信赖域上的最小目标函数和近似优化结果确定信赖度和下代域的中心、半径，进而不断地缩放、平移信赖域，来保证获得与真实模型一致的不对中载荷。通过四种方法对比表明该方法样本遗传策略，遗传落在下代信赖域空间上的样本，减少实验设计样本个数而提高效率；最小目标函数作为信赖中心调整提高了关键区域代理模型的精度而加快收敛，降低了对代理模型精度的依赖。     

含区间不确定性参数的机翼气动弹性优化

提出了一种具有区间不确定性的机翼颤振优化方法.采用拉丁超立方方法建立仿真试验表,基于MSC.Nastran平台进行颤振仿真分析.获得仿真数据之后,应用Kriging方法构造了包含区间不确定性参数的机翼颤振分析代理模型,并进行有效性检验.基于建立的代理模型并按照区间序数关系,将不确定性优化目标和约束条件转化为确定性表达形式,从面形成区间不确定性的结构优化设计方法.该方法将区间法优化和代理模型相结合,同时综合有限元仿真和遗传算法的优点,计算效率较高且应用范围较广.以某复杂机翼结构为例进行了含区间不确定性的颤振优化计算.分析结果表明了所提方法的正确性和可行性.     

汽车座椅骨架固有频率的不确定度研究

工程中结构参数的随机性会导致结构固有频率不确定,而固有频率是影响结构振动和噪声的重要因素之一,因此研究结构固有频率不确定度尤为重要。提出一种基于响应面代理模型的固有频率不确定度研究方法。首先建立汽车座椅骨架有限元模型,利用试验设计筛选出对固有频率影响较大的设计变量,以便构建响应面代理模型。在考虑结构随机性因素基础上,基于响应面代理模型,分析设计变量满足不同分布时其对汽车座椅骨架的前3阶固有频率的不确定度和分布的影响。最后采用实验设计和蒙特卡洛相结合方法对结果进行验证。研究结果可为确定样本不同分布对固有频率的影响提供理论指导。     

考虑不确定性的多学科设计优化方法研究综述

目的研究多学科不确定性设计优化中多学科设计优化方法、不确定性建模与传递、不确定性设计优化的相关理论。方法通过研究并分析国内外相关文献,总结归纳考虑不确定性的多学科设计优化中的耦合系统解耦方法、参数和代理模型不确定性的建模方法,以及高效的不确定性传递和设计优化方法。结论系统探讨了在面对复杂多变的外界环境时,多学科设计优化对不确定性量化与传递的需求,提出多学科设计优化不仅要考虑确定性的系统,而且需要考虑由于外界环境变化导致的系统响应的不确定性。针对现有的多学科不确定性设计优化方法的理论研究,提出提高计算效率的关键在于将传统的三层嵌套循环计算框架解耦成单层循环。研究结果表明,考虑不确定性的多学科设计优化将成为复杂多学科系统设计的有力支撑,能显著提高系统的可靠性和稳健性,提高使用寿命,同时能够加快产品的更新换代设计。     

基于全局灵敏度分析的某自动装填机构轻量化设计

针对某自动装填机构轻量化设计中出现参数多、模型计算量大等问题,提出将全局灵敏度分析与代理模型技术相结合的优化策略。通过基于Morris轨迹的全局灵敏度分析从32个系统参数中确定14个关键参数,基于拉丁超立方采样技术及径向基函数神经网络技术(Radial basis function neural networks, RBF NN)建立系统响应关于关键参数的代理模型,用多岛遗传算法对系统参数进行优化求解,致机构重量下降21.8%。数值检验结果表明仅含关键参数的代理模型预测精度较高,证明该方法在多参数复杂系统结构轻量化设计中的有效性。     

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。     

A new hybrid reliability-based design optimization method under random and interval uncertainties

This article proposes a new method for hybrid reliability-based design optimization under random and interval uncertainties (HRBDO-RI). In this method, Monte Carlo simulation (MCS) is employed to estimate the upper bound of failure probability, and stochastic sensitivity analysis (SSA) is extended to calculate the sensitivity information of failure probability in HRBDO-RI. Due to a large number of samples involved in MCS and SSA, Kriging metamodels are constructed to substitute true constraints. To avoid unnecessary computational cost on Kriging metamodel construction, a new screening criterion based on the coefficient of variation of failure probability is developed to judge active constraints in HRBDO-RI. Then a projection-outline-based active learning Kriging is achieved by sequentially select update points around the projection outlines on the limit-state surfaces of active constraints. Furthermore, the prediction uncertainty of Kriging metamodel is quantified and considered in the termination of Kriging update. Several examples, including a piezoelectric energy harvester design, are presented to test the accuracy and efficiency of the proposed method for HRBDO-RI.     

A kriging metamodel-assisted robust optimization method based on a reverse model

The goal of robust optimization methods is to obtain a solution that is both optimum and relatively insensitive to uncertainty factors. Most existing robust optimization approaches use outer–inner nested optimization structures where a large amount of computational effort is required because the robustness of each candidate solution delivered from the outer level should be evaluated in the inner level. In this article, a kriging metamodel-assisted robust optimization method based on a reverse model (K-RMRO) is first proposed, in which the nested optimization structure is reduced into a single-loop optimization structure to ease the computational burden. Ignoring the interpolation uncertainties from kriging, K-RMRO may yield non-robust optima. Hence, an improved kriging-assisted robust optimization method based on a reverse model (IK-RMRO) is presented to take the interpolation uncertainty of kriging metamodel into consideration. In IK-RMRO, an objective switching criterion is introduced to determine whether the inner level robust optimization or the kriging metamodel replacement should be used to evaluate the robustness of design alternatives. The proposed criterion is developed according to whether or not the robust status of the individual can be changed because of the interpolation uncertainties from the kriging metamodel. Numerical and engineering cases are used to demonstrate the applicability and efficiency of the proposed approach.     

Optimizing Latin hypercube design for sequential sampling of computer experiments

Space-filling and projective properties are desired features in the design of computer experiments to create global metamodels to replace expensive computer simulations in engineering design. The goal in this article is to develop an efficient and effective sequential Quasi-LHD (Latin Hypercube design) sampling method to maintain and balance the two aforementioned properties. The sequential sampling is formulated as an optimization problem, with the objective being the Maximin Distance, a space-filling criterion, and the constraints based on a set of pre-specified minimum one-dimensional distances to achieve the approximate one-dimensional projective property. Through comparative studies on sampling property and metamodel accuracy, the new approach is shown to outperform other sequential sampling methods for global metamodelling and is comparable to the one-stage sampling method while providing more flexibility in a sequential metamodelling procedure.     

Stochastic Polynomial Interpolation for Uncertainty Quantification With Computer Experiments

Multivariate polynomials are increasingly being used to construct emulators of computer models for uncertainty quantification. For deterministic computer codes, interpolating polynomial metamodels should be used instead of noninterpolating ones for logical consistency and prediction accuracy. However, available methods for constructing interpolating polynomials only provide point predictions. There is no known method that can provide probabilistic statements about the interpolation error. Furthermore, there are few alternatives to grid designs and sparse grids for constructing multivariate interpolating polynomials. A significant disadvantage of these designs is the large gaps between allowable design sizes. This article proposes a stochastic interpolating polynomial (SIP) that seeks to overcome the problems discussed above. A Bayesian approach in which interpolation uncertainty is quantified probabilistically through the posterior distribution of the output is employed. This allows assessment of the effect of interpolation uncertainty on estimation of quantities of interest based on the metamodel. A class of transformed space-filling design and a sequential design approach are proposed to efficiently construct the SIP with any desired number of runs. Simulations demonstrate that the SIP can outperform Gaussian process (GP) emulators. This article has supplementary material online.     

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.     

Sheet forming optimization based on least square support vector regression and intelligent sampling approach

In this paper, a metamodel-based optimization method by integration of support vector regression (SVR) and intelligent sampling strategy is applied to optimize sheet forming design. Compared with other popular metamodeling techniques, the SVR is based on the principle of structure risk minimization (SRM) as opposed to the principle of the empirical risk minimization in conventional regression techniques. Thus, the accuracy and robust metamodel can be obtained. The intelligent sampling strategy is a kind of design of experiment (DOE) essentially. The characteristic of this method is to generate new sample automatically by responses of objective functions. Compared with traditional DOE methods, the number of samples isn’t constant according to different cases. Furthermore, the number of samples and size of design space can be well controlled according to the intelligent strategy. To minimize both objective functions of wrinkling, crack and thickness deformation efficiently, the proposed method is employed as a fast analysis tool to surrogate the time-consuming finite-element (FE) procedure in the iterations of optimization algorithm. An example is studied to illustrate the application of the approach proposed, and it is concluded that the proposed method is feasible for sheet forming optimization.     

A Constraint‐based Maximum Entropy Sampling Method for Kriging Models in Fuel Cell Applications

A metamodel replaces the simulation model with an approximation model to make design optimization computationally achievable. The accuracy of a metamodel depends highly on the choice of sampling points. This article proposes a constraint‐based maximum entropy sampling method that locates most sampling points within a feasible constraint domain represented as a complex nonlinear function. As a robust measure of information, a maximum entropy criterion is used to select sampling points for constructing the Kriging model. The violation ratio from the feasible domain is incorporated into the covariance function in the Kriging model. The constraint‐based maximum entropy sampling method is applied to reduce the weight of a bipolar plate in a vanadium redox battery by optimizing its channel design. The proposed sampling method rapidly approximates the boundary of the feasible domain with a relatively small number of sampling points. Final optimal design results for the plate channel using the proposed method indicate a significant reduction in the plate weight compared with the existing bipolar plate design. Copyright © 2012 John Wiley & Sons, Ltd.     

Hammersley stochastic annealing: efficiency improvement for combinatorial optimization under uncertainty

This paper presents hierarchical improvements to combinatorial stochastic annealing algorithms using a new and efficient sampling technique. The Hammersley Sequence Sampling (HSS) technique is used for updating discrete combinations, reducing the Markov chain length, determining the number of samples automatically, and embedding better confidence intervals of the samples. The improved algorithm, Hammersley stochastic annealing, can significantly improve computational efficiency over traditional stochastic programming methods. This new method can be a useful tool for large-scale combinatorial stochastic programming problems. A real-world case study involving solvent selection under uncertainty illustrates the usefulness of this new algorithm.     

Fast numerical methods for robust optimal design

A fast numerical approach for robust design optimization is presented. The core of the method is based on the state-of-the-art fast numerical methods for stochastic computations with parametric uncertainty. These methods employ generalized polynomial chaos (gPC) as a high-order representation for random quantities and a stochastic Galerkin (SG) or stochastic collocation (SC) approach to transform the original stochastic governing equations to a set of deterministic equations. The gPC-based SG and SC algorithms are able to produce highly accurate stochastic solutions with (much) reduced computational cost. It is demonstrated that they can serve as efficient forward problem solvers in robust design problems. Possible alternative definitions for robustness are also discussed. Traditional robust optimization seeks to minimize the variance (or standard deviation) of the response function while optimizing its mean. It can be shown that although variance can be used as a measure of uncertainty, it is a weak measure and may not fully reflect the output variability. Subsequently a strong measure in terms of the sensitivity derivatives of the response function is proposed as an alternative robust optimization definition. Numerical examples are provided to demonstrate the efficiency of the gPC-based algorithms, in both the traditional weak measure and the newly proposed strong measure.     

Error-based stopping criterion for the combined adaptive Kriging and importance sampling method for reliability analysis

Metamodel-based method is a wise reliability analysis technique because it uses the metamodel to substitute the actual limit state function under the predefined accuracy. Adaptive Kriging (AK) is a famous metamodel in reliability analysis for its flexibility and efficiency. AK combined with the importance sampling (IS) method abbreviate as AK–IS can extremely reduce the size of candidate sampling pool in the updating process of Kriging model, which makes the AK-based reliability method more suitable for estimating the small failure probability. In this paper, an error-based stopping criterion of updating the Kriging model in the AK–IS method is constructed and two considerable maximum relative error estimation methods between the failure probability estimated by the current Kriging model and the limit state function are derived. By controlling the maximum relative error, the accuracy of the estimate can be adjusted flexibly. Results in three case studies show that the error-based stopping criterion based AK–IS method can achieve the predefined accuracy level and simultaneously enhance the efficiency of updating the Kriging model.