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

以内蒙古金泉工业园区水源地为研究区,在已有地下水流数值模拟模型基础上,采用拉丁超立方抽样方法,获取输入(抽水量)数据集和输出(地下水位降深)数据集,运用双响应面方法,建立了地下水流数值模拟模型的替代模型——双响应面模型。经验证,双响应面模型计算出的地下水水位降深均值与地下水流数值模拟模型计算出的地下水水位降深均值的平均相对拟合误差为0.22%,地下水水位降深剩余标准差的平均相对拟合误差为0.03%,相对拟合误差都比较小,说明所建立的双响应面模型可以有效地替代地下水流数值模拟模型,这为地下水资源优化管理中替代模型的建立提供了有效的科学论证。

Jinquan Industrial Park groundwater sources in Neimenggu was selected as the study area ,based upon numerical simulation model of groundwater in this study ,Latin Hypercube Sampling was used to obtain input (pumping) and output(water level draw-down) data sets ,and multiple regression analytic method was proposed to establish an surrogate model of the groundwater numerical model ,namely dual response surface model .The fitting mean relative error of mean groundwater level drawdown obtained by dual response surface model and numerical simulation model of groundwater was 0 .22% ,and the fitting mean relative error of the remai-ning average relative standard deviation of groundwater level drawdown was 0 .03% .So the fitting error was small ,which indicated that the dual response surface model can effectively replace groundwater numerical model .This provides an effective scientific basis for establishing management surrogate model of resource optimization of groundwater .

轮齿表面剥落的动态响应特征是诊断齿轮早期故障的重要信息。但是,由于轮齿表面剥落部位啮合变形的复杂性和响应信号强耦合,导致诊断齿轮早期故障困难。为了解明轮齿表面剥落部位啮合引起的响应特征机理,建立了基于边缘接触时变刚度的轮齿表面剥落动力学模型,提出了轮齿表面剥落缺陷的时变刚度算法,分析了边缘接触对时变刚度激励及齿轮系统动态响应,研究了齿面剥落齿在啮出剥落边界时的边缘接触力突变及齿轮系统动态响应特性,获得了齿面剥落的时域和频域响应信号。同时,开展了齿面剥落缺陷动态响应特征的实验研究,验证了提出的理论模型的正确性。仿真与台架实验结果表明,新的模型能够准确计算齿面剥落对啮合刚度、动态响应特性的影响,可为齿轮系统状态检测提供重要参考价值。

Dynamic response characteristic of gears with tooth surface spalling is an important message to their fault diagnosis.However,the complexity of mesh deformation in tooth surface spalling area and its strong coupling with response signals result in a difficulty to diagnose gear early faults.Here,a dynamic model of gears with tooth surface spalling based on a time-varying stiffness for edge contact was built to explore the response characteristic mechanism in tooth spalling area and the new time-varying meshing stiffness algorithm was also established.The time-varying stiffness excitation and the gear system dynamic response with edge contact were analyzed.The study on the mutation characteristic of edge contact force at tooth surface spalling boundary and the dynamic response characteristic of the gear system was performed with time domain and frequency domain methods.In addition,the experimental investigation on the dynamic response features of the gear system with tooth surface spalli

选择水温、水米质量比和时间作为试验因素，在单因素的试验的基础上，采用响应面法的Box-Behnken试验设计，通过响应面分析得到米饭复水性回归模型，并利用模型求得方便米饭复水的最适工艺条件：水温75℃、水：大米为2.8∶1（质量比）、时间25 min。

With water temperature, amount of water and time as experiment factors,Box-Behnken experimental design of response surface method is used on the base of the single factor test.The regression model of rewater steamed rice is obtained through the analysis of response surface. The optimum technological conditions are obtained by the model.They are that the temperature is 75℃,the amount of water is 2.8∶1and the time is 25 min.

为提高自动炮武器系统发射动力学模型精度,基于实弹射击试验建立支持向量机响应面,对仿真模型进行了修正。应用有限元分析方法建立了双炮身管结构和炮塔结构有限元模型,基于武器系统各部件间的约束关系建立了步兵战车刚柔耦合发射动力学模型;基于相同边界条件,选取自动炮连发射击中典型结构的振动特性搭建了测试系统并进行了实弹射击试验;针对仿真数据与试验数据误差,引入支持向量机响应面方法对步兵战车刚柔耦合发射动力学模型进行了修正。修正结果表明,基于支持向量机响应面的模型修正方法大幅提高了自动炮武器系统发射动力学模型的精度,更准确地反映了自动炮射击过程中的机构动态特性。

The automatic gun firing dynamics model was built up and the simulation model was updated by use of the support vector machine response surface method based on the actual firing experiment so as to analyze the influence factor of firing precision.The finite element models of the gun barrel structure and turret structure were established by means of finite element analysis method,and the rigid-flexible cou-pled firing dynamics models of the infantry combat vehicle were set up based on the restricted relationship between components and joints of the weapon system.The test system was established and the actual fir-ing experiment was carried out by use of picking up the typical structure vibration characteristics in the burst firing of automatic gun based on the same boundary conditions.Aimed at the errors between the simula-tion data and the test data,the automatic gun firing dynamics model was updated.The updating results showed that the model updating method can increase the precision o