响应面法在结构优化应用上的研究

发布时间：2018-04-29 02:16

本文选题：轻量化研究 + 不确定性误差　；参考：《上海海洋大学》2017年硕士论文

【摘要】：在产品轻量化研究中可以使用轻质材料,但是其成本往往很高,在满足一定强度和刚度下,提高设计质量从而达到轻量化设计,为前期设计减少成本。针对数学非线性回归问题,不断改进设计模型和设计参数,本文主要的目标是对比前人的算例来体现响应面优化方法的优越性:全局搜索、迭代次数少、能减少更多体积或重量。用函数关系拟合实际的仿真模型,采用筛选试验来确定优化方向,主要的工作是找到最佳领域并得到最优解,响应面法的精髓是在于减少试验的基础上获得更精确地拟合目标值,降低不确定性误差ε值,尽量平衡试验次数和效果,以达到高效率平衡点,从而使设计效果最佳。RSM是一种序贯方法,先析因分析,确定是一阶线性回归模型还是二阶曲面模型,如果方差分析中所有P值都小于0.05则为二阶模型,再调中心点和水平范围寻优。RSM的拟合方程不外乎是一阶模型或者二阶方程。一阶模型采用最小二乘法可以快速定位最优解;二阶模型先找到最佳邻域然后在最佳领域内求最优解,其中最佳邻域的判定条件是实际约束S与拟合约束均值β_0相对误差小于5%,最优解的条件是拟合约束小于实际约束且体积最小。研究的对象是桁架杆、曲柄和三角臂,利用计算机CAD和CAE技术编写ANSYS的APDL程序内嵌应力并能得到各应力和体积,利用Soildworks建模分析,采用优化软件Minitab和Design-expert进行集成优化,必须要求试验者有工程基础知识和经验,最终才能解决和优化工程实际结构问题,通过响应面法的反馈调整,在确定的全局内,人为设置中心点和搜索水平范围,从而提高寻优效率。在桁架杆实例中要做的是进行协同优化,即考虑形状变化和尺寸变化下同时进行两者的优化,难点在于形状变化和尺寸变化的相互耦合性,采用响应面法不仅无需Lagrange乘子,而且能避开形状变化和尺寸变化间的相互耦合,通过调整试验中心点和搜索水平范围,以响应面为指向进行优化。在优化过程中发现桁架杆5杆有耦合性,表现形式为应力集中,为此应提高A5截面积大小,这些都是实验者人工调控的,根据响应面法的反馈指向人工调整设计域,这也是响应面法高效的来源,只需迭代三次就能找到形状最优点,迭代两次能找到尺寸最优点,最后迭代一次能找到协同优化设计最优解。在连杆和三角臂算例中为方便计算采用Soildworks建模并用其自带算法优化,但是优化精度不高,所以用响应面法进行二次优化,在最佳领域内找最优解。
[Abstract]:Lightweight materials can be used in product lightweight research, but their costs are often very high. Under certain strength and rigidity, the design quality can be improved to achieve lightweight design, which can reduce the cost for early design. In view of the mathematical nonlinear regression problem, the design model and design parameters are continuously improved. The main goal of this paper is to show the superiority of the response surface optimization method by comparing with the previous examples: global search, fewer iterations, Can reduce more volume or weight. The function relation is used to fit the actual simulation model and the selection experiment is used to determine the optimization direction. The main work is to find the best field and get the optimal solution. The essence of response surface method is to obtain more accurate fitting target value, reduce uncertainty error 蔚 value, and balance test times and effect as far as possible, so as to achieve high efficiency balance point. RSM is a sequential method to optimize the design effect. First, factor analysis is used to determine whether it is a first-order linear regression model or a second-order surface model, and if all P values in ANOVA are less than 0.05, it is a second-order model. The fitting equation of RSM is either a first order model or a second order equation. The first order model uses the least square method to locate the optimal solution quickly, and the second order model first finds the best neighborhood and then finds the optimal solution in the best domain. The optimal neighborhood condition is that the relative error between the actual constraint S and the fitting constraint mean 尾 0 is less than 5 and the optimal solution condition is that the fitting constraint is less than the actual constraint and the volume is the smallest. The object of this study is truss bar, crank and triangle arm. The embedded stress in APDL program of ANSYS is compiled by computer CAD and CAE technology, and each stress and volume can be obtained. Soildworks modeling and analysis are used, and the optimization software Minitab and Design-expert are used for integrated optimization. The basic engineering knowledge and experience must be required in order to solve and optimize the practical structural problems of the project. Through feedback adjustment of the response surface method, the center point and the search level range should be set artificially within the determined overall situation. In order to improve the efficiency of optimization. In the example of truss, the cooperative optimization is done, that is to say, considering the change of shape and size, both of them are optimized simultaneously. The difficulty lies in the mutual coupling between shape change and size change. The response surface method does not need Lagrange multiplier. Moreover, it can avoid the coupling between shape change and dimension change, and optimize the response surface by adjusting the test center and searching horizontal range. In the process of optimization, it is found that the truss bar 5 has coupling, and the form of stress concentration is stress concentration. Therefore, the size of A5 cross section should be increased. These are all artificially regulated by the experimenter. According to the feedback of response surface method, the design domain is adjusted manually. This is also the efficient source of response surface method. The shape optimization can be found by only three iterations, the size optimization can be found by two iterations, and the optimal solution of cooperative optimization design can be found by the last iteration. In the example of connecting rod and triangular arm, Soildworks is used to model and optimize with its own algorithm, but the precision of optimization is not high, so the quadratic optimization is carried out by response surface method, and the optimal solution is found in the best field.
【学位授予单位】：上海海洋大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TH122

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