Influence from numerical noise in the objective function for flow design optimisation
Influence from numerical noise in the objective function for flow design optimisation
复制标题
流量设计优化目标函数中数值噪声的影响
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
R. Gebart
中科院分区：
文献类型：
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作者：
J. Burman;R. Gebart
使用两种不同的网格尺寸使轴对称收缩中的总压降最小化。过渡区仅用两个设计变量进行参数化，以便能够在设计空间中创建目标函数的曲面图，这些曲面图基于每个网格的121个计算流体动力学计算。粗网格显示出在目标函数中具有显著的数值噪声，而细网格具有较小的数值噪声。优化采用两种方法进行，响应面模型（RSM）和基于梯度的方法（可行方向法），以研究数值噪声的影响。两种优化方法都能够在两种不同的网格尺寸下找到全局最优值（粗网格上基于梯度的方法的搜索路径能够避免设计空间中包含局部最小值的区域）。然而，响应面在达到最优值时需要较少的迭代。从设计空间两点的网格收敛研究来看，当有限差分计算的相对步长为10-4时，噪声水平似乎足够低，如果这种收缩几何形状的误差低于5%，则不会影响收敛。
The overall pressure drop in an axisymmetric contraction is minimised using two different grid sizes. The transition region was parameterised with only two design variables to make it possible to create surface plots of the objective function in the design space, which were based on 121 CFD calculations for each grid. The coarse grid showed to have significant numerical noise in the objective function while the finer grid had less numerical noise. The optimisation was performed with two methods, a Response Surface Model (RSM) and a gradient‐based method (the Method of Feasible Directions) to study the influence from numerical noise. Both optimisation methods were able to find the global optimum with the two different grid sizes (the search path for the gradient‐based method on the coarse grid was able to avoid the region in the design space containing local minima). However, the RSM needed fewer iterations in reaching the optimum. From a grid convergence study at two points in the design space the level of noise appeared to be sufficiently low, when the relative step size is 10–4 for the finite difference calculations, to not influence the convergence if the errors are below 5 per cent for this contraction geometry.