|
航空航天优化造型设计的微分和准微分方法
Differentiable and Quasi-Differentiable Methods for Optimal Shape Design in Aerospace |
|
| |
| 课程网址: |
http://videolectures.net/mla09_pironneau_daqdm/
|
| 主讲教师: |
Olivier Pironneau
|
| 开课单位: |
皮埃尔和玛丽居里大学
|
| 开课时间: |
2009-07-20
|
| 课程语种: |
英语
|
| 中文简介: |
对于大多数流体动力学问题，可以将最佳形状设计作为未知边界问题，或者作为拓扑优化的结构力学中所做的未知区域问题。我们将介绍这两种方法以及航空航天领域的一些应用。问题通过有限元方法离散化;在可能的情况下使用可微分优化，并使用伪可微方法进行拓扑优化。
形状优化通常是计算机密集型的，并行计算是必需的。虽然进化方法具有边缘，但梯度方法也可以通过域分解来并行化。
但是，当使用黑盒解算器时，灵敏度评估过于计算机密集且存在问题。可以应用数据学习和代理模型来为州提供低保真模型。这些可用于无梯度，准可微分或可微分的最小化方法。然后，不完全灵敏度可用于以零成本升级数据学习，超出仅具有功能的可用性。这些额外信息还可以深入了解设计的稳健性，并允许区分帕累托点。它还使用户能够对不是设计参数的独立参数中的不确定性的影响有所了解。这种集合导致了一种设计方法，对于学术问题可能效率较低，但在具有所有参数不确定性的实际情况下更加稳健可靠。
|
| 课程简介: |
Optimal shape design can be approached either as an unknown boundary problems as done for most problems of fluid dynamics or as an unknown domain problem as done in structural mechanics for topological optimization. We shall present both methods together with some applications in aerospace. Problems are discretized by the finite element method; differentiable optimization is used when possible and pseudo differentiable methods for topological optimization.
Shape optimization is usually computer intensive and parallel computing is a necessity. While evolutionary methods have an edge, gradient methods can be parallelized by domain decomposition just as well.
But sensitivity evaluation is too computer intensive and problematic when black-box solvers are used. Data learning and surrogated models can be applied to provide low-fidelity models for the state. These can be used in gradient free, quasi-differentiable or differentiable minimization methods. Then incomplete sensitivity can be used to upgrade data learning at zero cost beyond what available with just the functional. This extra information also gives insights on robustness of the design and allows to discriminate between Pareto points. It also enables the user to have ideas on the impact of uncertainties in independent parameters which are not design parameter. This ensemble leads to a design method, may be less efficient for academic problems, but more robust and reliable in realistic situations with uncertainties on all parameters.
|
| 关 键 词: |
流体动力学; 拓扑优化; 可微分优化
|
| 课程来源: |
视频讲座网
|
| 最后编审: |
2019-06-28：cjy
|
| 阅读次数: |
81
|
|
图 书 馆