本文主要研究一种梯度响应面模型及其在气动优化设计中的应用。目前应用广泛的多项式响应面模型是连续可导的，采用梯度信息构造完全二阶多项式响应面模型，所需样本数与设计参数个数呈线性关系。首先通过改进实验设计方法，快速生成满足精度要求的样本并确定梯度响应面模型。随后通过函数实验验证梯度响应面模型的精度，及该模型在多极值函数最值搜索中的有效性。最后由伴随方法快速求解气动优化设计目标函数的梯度信息，并开展基于梯度响应面模型和复合形法的叶片压力反设计和效率优化设计。结果表明：基于梯度响应面模型的优化方法在全局最优及提高优化效率两方面均有出色表现，基于该优化方法的气动优化设计能够显著改善叶片的气动性能。

This paper presents a gradient-based response surface (GBRS) model and its applications to the aerodynamic design optimization. Since the widely used polynomial response surface model is continuous and differentiable, the gradients of the original response can be involved in constructing the quadratic polynomial response surface model. For the quadratic GBRS model, the number of the required samples depends linearly, instead of quadratically on the number of design parameters. Firstly, the samples are determined through the modified design of experiment with shortened sampling time to construct the GBRS model. Then function experiments are performed to evaluate the accuracy of GBRS model and its effectiveness in searching for the global minimum. Finally the gradients for constructing the GBRS model are calculated by the adjoint method and then an inverse design and an optimization design for improving the efficiency of a cascade are performed based on the GBRS model and the complex met

针对结构优化设计问题中约束条件是设计变量隐函数的问题,分析了传统多项式基响应面法的基本思想及其在拟合精度方面存在的问题;在此基础上通过对求解区域进行网格划分以及偏导数差分的推导给出了基于泰勒展开的响应面方法的具体形式,最后结合算例分析验证了改进后的算法不仅能够提高响应面方法的求解精度,而且能够有效地实现结构优化设计中隐函数的显式化.

Considering the constraint condition in the structural optimization is the implicit func-tion of the design variables ,we analyzed the basic ideas of the traditional polynomial response surface method and its problems in fitting accuracy ,and got the specific form of response surface methodology based on Taylor expansion by meshing the region to be solved and deducing partial derivative differential .Finally ,combining with a numerical example ,we verified that the im-proved algorithm could not only greatly improve the solution accuracy ,but also effectively trans-form the function from implicit to explicit in structural optimization .

为提高设计稳健性,将6σ稳健优化设计引入车身噪声传递函数优化过程。将6σ质量管理、可靠性设计稳健设计相结合,考虑设计变量、约束条件目标函数在内所有不确定性信息,不仅满足优化目标函数、提高系统可靠性要求,使系统响应均方差最小化,即提高稳健性。以某型汽车为例,在汽车声固耦合有限元模型基础上采用基于试验设计的二阶多项式响应面模型,以车身总质量一阶模态频率为约束条件驾驶员耳旁声压级响应均方根值为目标函数,在基本随机变量概率特性已知情况下对车身噪声传递函数进行6σ稳健优化设计,与传统确定性优化设计相比表明该方法的有效性。

In order to improve the design robustness of the vehicle’s NVH performance,a six sigma robust optimization method was introduced in the optimization design of noise transfer functions.In the method,the influences of various uncertain factors which result from objective functions,design variables and constraint conditions were considered by integrating the six sigma quality management approach,reliability design approach and robust design approach in the optimization design process.Not only the proper optimal solution and reliability of the system were achieved but also the robustness of production design process was improved.Based on the acoustic-structure coupled finite element model and the quadratic response surface approximate model,the proposed method was implemented to optimize the noise transfer function of a car body.In this numerical example,the probabilistic characteristics of the design variables were assumed to be known,the total mass and the first natural frequency of the

首先运用摩擦学、传热学和有限元法研究了齿轮的本体温度场,然后利用间接耦合法对齿轮进行了结构分析,以齿轮材料的线膨胀系数、油温、主动轮转速、主动轮功率及齿面许用接触应力为随机变量,基于响应面法得到了齿面接触强度的极限状态函数,并通过蒙特卡罗法得到了各随机变量对该极限状态函数的概率敏感性。结果表明,响应面-蒙特卡罗法有效简化了复杂结构的可靠性灵敏度分析。

First use of tribology,heat transfer, finite element method to study the gear tempera-ture field,and then use the indirect coupling meth-od to study the structure analysis of gear,gear ma-terial coefficient of linear expansion,oil tempera-ture,driving gear speed,driving gear power and al-lowable contact stress of tooth surfaces are taken as random variables,the limit state function of tooth contact strength is obtained by Response Surface method,then each random variable proba-bility sensitivity of the limit state function is ob-tained by Monte Carlo method.The results show that:the Response Surface Monte Carlo method effectively simplifies the complex structure of the reliability sensitivity analysis.

针对随机结构问题,根据现有方法的优缺点,将响应面法和摄动随机有限元相结合。考虑结构载荷参数、材料参数和几何参数,结构的响应面近似函数采用步进回归分析技术被确定了,其中抽样方法为中心指数法,并利用摄动法推导出结构随机响应的中心矩表达式。以燃气涡轮叶片为例,计算出叶片的随机响应变量中心矩,及响应变量相对于输入变量的灵敏度,并分别与直接响应面法、直接Monte-Carlo模拟方法的计算结果对比。结果表明,该方法适用于结构相对复杂的模型,计算结果精度较高,计算速度较快。

Aiming at problem of the stochastic structure, according to the merits and demerits of the existing methods, the response surface method and perturbation-based stochastic finite element method are combined. Considering structure load parameters, material parameters and geometrical parameters, the approximate function of response surface structure is determined by using step regression analysis techniques, the sample of which is taken by the center index design method. And the central moment expression of the structure random response is derived by using perturbation method. Taking the gas turbine blade as an example, the central moment of the random response variables and the sensitivity of response variable corresponding to the input variables for the blade are calculated. And it is contrasted with the calculation results of direct response surface method and direct Monte-Carlo simulation method respectively. The results show that the method is suitable for a relatively complex struct