基于自适应代理模型的气动优化方法

气动优化设计中,为了减少优化系统的计算周期,提高搜索效率,引入结构简单、计算量较小的代理模型,而运用有效的插值和选样方法(自适应选样)可以大大减少建立代理模型的时间。因此本文提出了一种基于自适应代理模型的气动优化方法。首先对自适应代理模型进行研究,建立了 Kriging 自适应代理模型和支持向量回归自适应代理模型,这两种自适应代理模型在相同样本点情况下比一般代理模型拥有更高的预测能力,然后将这其应用到翼型优化设计中,取得了良好的优化效果,从而表明这两种自适应代理模型不仅简单实用,而且明显提高了气动分析的计算效率。     

Research on multi-fidelity aerodynamic optimization methods

 Constructing high approximation accuracy surrogate model with lower computational cost has great engineering significance. In this paper, using co-Kriging method, an efficient multifidelity surrogate model is constructed based on two independent high and low fidelity samples. Co-Kriging method can use a greater quantity of low-fidelity information to enhance the accuracy of a surrogate of the high-fidelity model by modeling the correlation between high and low fidelity model, thus computational cost of building surrogate model can be greatly reduced. A wing-body problem is taken as an example to compare characteristics of co-Kriging multi-fidelity (CKMF) model with traditional Kriging based multi-fidelity (KMF) model. A sampling convergence of the CKMF model and the KMF model is conducted, and an appropriate sampling design is selected through the sampling convergence analysis. The results indicate that CKMF model has higher approximation accuracy with the same high-fidelity samples, and converges at less high-fidelity samples. A wing-body drag reduction optimization design using genetic algorithm is implemented. Satisfying design results are obtained, which validate the feasibility of CKMF model in engineering design.     

一种基于Kriging和Monte Carlo的主动学习可靠度算法

机械结构可靠性分析时,常常会采用代理模型拟合隐式功能函数来解决计算量大的问题,但由于试验设计方案需要同时考虑代理模型的拟合精度和可靠度计算精度的问题。因此,为了能够充分使用较少的样本信息,最大化可靠度计算精度,本文充分发挥Kriging预测的随机特性,提出一种主动学习可靠度计算方法。首先,类似于优化问题中改善函数的选点方式,提出一种基于Kriging预测的学习函数,基于Monte Carlo法生成大量的候选样本点,找出学习函数最小值对应的样本点作为最佳取样点。其次,推导和提出了一种学习停止的条件,保证了Monte Carlo样本点预测符号的正确性且学习次数明显减小。最后,通过2个数值算例分析结果表明,该算法相比其他方法需要更少的样本数量,得到的可靠度计算精度更高,验证了本文算法的正确性和高效性。     

1 种基于Kriging 近似模型的叶片罩量优化设计方法

在航空发动机叶片设计过程中,需要进行叶片罩量优化来减小多种载荷引起的弯曲应力,改善其应力状况。为了提高叶片罩量优化设计效率,根据Kri gi ng近似模型和试验采样技术,提出了1种叶片罩量优化设计方法。利用序列采样方法逐步改善近似模型预测精度,然后在近似模型上进行全局寻优。结果表明:该方法简单易用,通过构造近似模型代替真实的物理模型,降低了计算成本,提高了优化效率。优化后的叶片最大等效应力减小了12.43%,有效地减小叶片的峰值应力。     

Efficient multi-response adaptive sampling algorithm for construction of variable-fidelity aerodynamic tables

Adaptive sampling is an iterative process for the construction of a global approximation model. Most of engineering analysis tools computes multiple parameters in a single run. This research proposes a novel multi-response adaptive sampling algorithm for simultaneous construction of multiple surrogate models in a time-efficient and accurate manner. The new algorithm uses the Jackknife cross-validation variance and a minimum distance metric to construct a sampling criterion function. A weighted sum of the function is used to consider the characteristics of multiple surrogate models. The proposed algorithm demonstrates good performance on total 22 numerical problems in comparison with three existing adaptive sampling algorithms. The numerical problems include several two-dimensional and six-dimensional functions which are combined into singleresponse and multi-response systems. Application of the proposed algorithm for construction of aerodynamic tables for 2 D airfoil is demonstrated. Scaling-based variable-fidelity modeling is implemented to enhance the accuracy of surrogate modeling. The algorithm succeeds in constructing a system of three highly nonlinear aerodynamic response surfaces within a reasonable amount of time while preserving high accuracy of approximation.     

代理模型选样准则研究

致力于针对确定问题,利用其在已知空间中的样本信息指导该问题其他空间中的样本选择.基于Kriging模型和拉丁超立方设计选样方法,以某数学函数为例,首先研究了设计空间大小对样本选择的影响,然后具体分析了样本分布特性对代理模型预测误差的影响.引入了样本平均疏密度、样本稀疏度、样本紧凑度等概念衡量样本特性,依据不同空间中各参数与代理模型预测精度的关系提出了样本稀疏度准则,并以不同维数的数学函数和翼型气动力分析模型验证了准则的准确性和实用性.     

Kriging模型及代理优化算法研究进展

代理模型方法由于能显著提高工程优化设计问题的效率,在航空航天及其他领域得到了广泛重视,并逐渐发展成为一类优化算法,本文称其为代理优化（SBO）算法。在现有的代理模型方法中,如多项式响应面、径向基函数、神经网络、支持向量回归、多变量插值/回归、多项式混沌展开等,源于地质统计学的Kriging模型具有代表性,是一种非常具有应用潜力的代理模型方法。以飞行器设计领域的优化问题为背景,介绍了Kriging代理模型及应用于优化设计的理论和算法的最新研究进展。首先,概述了Kriging模型的基本理论和算法,并讨论了影响Kriging模型鲁棒性和效率的几个关键性问题。其次,回顾了Kriging模型理论和算法研究的3个最新研究进展,包括梯度增强型Kriging、CoKriging和分层Kriging模型。而后,分析提炼了基于Kriging模型的代理优化算法的优化机制和优化框架,给出了“优化加点准则”和“子优化”的概念,并介绍了目前常用的几种优化加点准则及其相应子优化问题的求解与约束处理;同时,还介绍了最新提出的局部EI加点准则以及代理优化的终止条件。最后,介绍了代理优化在标准测试函数算例验证、飞行器气动与多学科优化设计典型算例确认方面的研究进展,并对当前存在的一些关键科学问题以及未来研究方向进行了讨论。     

An adaptive sequential experiment design method for model validation

Efficient experiment design is of great significance for the validation of simulation model with high nonlinearity and large input space. Excessive validation experiment raises the cost while insufficient test increases the risks of accepting an invalid model. In this paper, an adaptive sequential experiment design method combining global exploration criterion and local exploitation criterion is proposed. The exploration criterion utilizes discrepancy metric to improve the space-filling property of the design points while the exploitation criterion employs the leave one out error to discover informative points. To avoid the clustering of samples in the local region, an adaptive weight updating approach is provided to maintain the balance between exploration and exploitation. Besides, the credibility distribution function characterizing the relationship between the input and result credibility is introduced to support the model validation experiment design. Finally, six benchmark problems and an engineering case are applied to examine the performance of the proposed method. The experiments indicate that the proposed method achieves satisfactory performance for function approximation in accuracy and convergence.     

考虑飞行条件变化和制造误差的气动优化方法

提出一种渐近全局代理模型方法以提高稳健优化中的代理模型的精度.基本思路是连续成批地在样本空间的全局和局部均加入新样本点,不断提高代理模型的全局拟合精度.将基于渐近全局代理模型稳健优化方法应用于高亚声速翼型设计,结果表明不仅目标值阻力系数具有稳健性,对飞行条件的小幅度变化和制造误差不敏感,而且力矩系数的约束也具有稳健性.     

Modified Sequential Kriging Optimization for Multidisciplinary Complex Product Simulation

Directing to the high cost of computer simulation optimization problem, Kriging surrogate model is widely used to decrease the computation time. Since the sequential Kriging optimization is time consuming, this article extends the expected improvement and put forwards a modified sequential Kriging optimization (MSKO). This method changes the twice optimization problem into once by adding more than one point at the same time. Before re-fitting the Kriging model, the new sample points are verified to ensure that they do not overlap the previous one and the distance between two sample points is not too small. This article presents the double stopping criterion to keep the root mean square error (RMSE) of the final surrogate model at an acceptable level. The example shows that MSKO can approach the global optimization quickly and accurately. MSKO can ensure global optimization no matter where the initial point is. Application of active suspension indicates that the proposed method is effective.