论文标题
部分可观测时空混沌系统的无模型预测
Analytic expressions for the moving infinite line source model
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。
Groundwater flow can have a significant impact on the thermal response of ground heat exchangers. The moving infinite line source model is thus widely used in practice as it considers both conductive and advective heat transfert processes. Solution of this model involves a relatively heavy numerical quadrature. Contrarily to the infinite line source model, there is currently no known first-order approximation that could be useful for many practical applications. In this paper, known analytical expressions of the Hantush well function and generalized incomplete gamma function are first revisited. A clear link between these functions and the moving infinite line source model is then established. Then, two new exact and integral-free analytical expressions are proposed, along with two new first-order approximations. The new analytical expressions proposed take the form of convergent power series involving no recursive evaluations. It is shown that relative errors less than 1% can be obtained with only a few summands. The convergence properties of the series, their accuracy and the validity domain of the first-order approximations are also presented and discussed.
