论文标题
部分可观测时空混沌系统的无模型预测
Evaluating a strategy for measuring deformations of the primary reflector of the Green Bank telescope using a terrestrial laser scanner
论文作者
论文摘要
储层计算是预测湍流的有力工具,其简单的架构具有处理大型系统的计算效率。然而,其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间,然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用,该系统模拟了湍流的若干特征。我们表明,使用径向基函数作为非线性投影器,即使只有部分观测并且不知道控制方程,也能稳健地捕捉复杂的系统非线性。最后,我们表明,当测量稀疏、不完整且带有噪声,甚至控制方程变得不准确时,我们的网络仍然可以产生相当准确的预测,从而为实际湍流系统的无模型预测铺平了道路。
Astronomical observations in the molecule rich 3 mm window using large reflector antennas provide a unique view of the Universe. To efficiently carry out these observations gravitational and thermal deformations have to be corrected. Terrestrial laser scanners have been used to measure the deformations in large reflector antennas due to gravity, but have not yet been used for measuring thermal deformations. In this work we investigate the use of a terrestrial laser scanner to measure thermal deformations on the primary reflector of the Green Bank Telescope (GBT). Our method involves the use of differential measurements to reduce the systematic effects of the terrestrial laser scanner. We use the active surface of the primary reflector of the GBT to validate our method and explore its limitations. We find that when using differential measurements it is possible to accurately measure deformations corresponding to different Zernike polynomials down to an amplitude of 60 $μ$m. The difference between the amplitudes of known deformations and those measured are $<140~μ$m when the wind speed is $\lesssim2$ m s$^{-1}$. From these differences we estimate that it should be possible to bring the surface error of the GBT down to $240\pm6~μ$m. This suggests that using a commercial off-the-shelf terrestrial laser scanner it is possible to measure deformations induced by thermal gradients on a large parabolic reflector.