改进自动微分方法及其在飞行器气动外形优化中的应用

Fast Automatic Differentiation and Its Application to Flight Vehicle Parameter Optimization

在飞行器设计优化过程中存在大量的梯度计算,简单高效的梯度计算方法可以很大地提高飞行器的优化效率。自动微分法是一种无需人工干预的高效梯度算法,为了进一步提高自动微分方法的计算效率,在函数首次执行后,形成单独的梯度计算过程,并采用矩阵的方式对该过程进行存储和调用。应用改进后的自动微分程序对某飞行器的弹翼外形进行基于梯度的优化,计算结果表明,改进后的程序计算精度与传统方法相同,计算速度可提高2倍以上,对于工程中常见的大规模稀疏问题计算效率可高达传统算法的3倍左右。

Aim. Traditional automatic differentiation （AD） method is widely used in the optimization of flight vehicle parameters but, in our opinion, it is deficient in speed. We now present a fast AD, called by us improved automatic differentiation （lAD）. In the full paper, we explain our IAD in detail. In this abstract, we just add some pertinent remarks to listing the two topics of explanation. The first topic is： traditional AD. The second topic is： our IAD. In the second topic, the most important thing is eq. （4） in the full paper, which is expressed in matrix form and which marks clearly the difference between IAD and traditional AD; the proper utilization of eq. （4） is mainly responsible for making IAD fast through the reduction of time consumed in making very frequent calculations of gradients. Finally we apply our IAD method to the optimization of the parameters of a missile wing. The numerical results are summarized in one table and three figures in the full paper. These numerical results do show preliminarily that our IAD method, as compared with traditional AD method, can reduce the time of calculations of gradients by about 50-65% while retaining the same accuracy.