论文标题
部分可观测时空混沌系统的无模型预测
Model of block media taking into account internal friction
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。
The block medium is modeled by a discrete-periodic spatial lattice of masses connected by elastic springs and viscous dampers. To describe the viscoelastic behavior of the interblock layers, a rheological model of internal friction with two Maxwell elements and one Voigt element with the quality factor of the material as the determining parameter is proposed. Numerical experiments show that, within the framework of this interlayer model, it is possible to select the viscosity and stiffness of the Maxwell and Voigt elements so that the quality factor of the material differs from the given constant value by no more than 5%. In the one-dimensional case, within the framework of the proposed model, the influence of the quality factor on the dispersion properties of a block medium is studied and it is shown that the greatest effect of the quality factor on the dispersion is observed in the low-frequency part of the spectrum. In the three-dimensional case, within the framework of the proposed model, some geomechanical problems are numerically studied for a block half-space under the action of a surface concentrated vertical load. Namely, the attenuation of the velocity amplitudes of surface blocks was studied depending on the Q-factor under step action and under the action of a Gaussian pulse. In addition, we study a layer on the surface of a half-space under the action of a concentrated vertical impulse load in the case when both the layer and the half-space are block media but have different properties.
