Del Águila Ferrandis J, Triantafyllou M S, Chryssostomidis C, Karniadakis G E
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139-4307, USA.
Division of Applied Mathematics, Brown University, Providence, RI, USA.
Proc Math Phys Eng Sci. 2021 Jan;477(2245):20190897. doi: 10.1098/rspa.2019.0897. Epub 2021 Jan 27.
Predicting motions of vessels in extreme sea states represents one of the most challenging problems in naval hydrodynamics. It involves computing complex nonlinear wave-body interactions, hence taxing heavily computational resources. Here, we put forward a new simulation paradigm by training recurrent type neural networks (RNNs) that take as input the stochastic wave elevation at a certain sea state and output the main vessel motions, e.g. pitch, heave and roll. We first compare the performance of standard RNNs versus GRU and LSTM neural networks (NNs) and show that LSTM NNs lead to the best performance. We then examine the testing error of two representative vessels, a catamaran in sea state 1 and a battleship in sea state 8. We demonstrate that good accuracy is achieved for both cases in predicting the vessel motions for unseen wave elevations. We train the NNs with expensive CFD simulations , but upon training, the prediction of the vessel dynamics can be obtained at a fraction of a second. This work is motivated by the universal approximation theorem for functionals (Chen & Chen, 1993. , 910-918 (doi:10.1109/72.286886)), and it is the first implementation of such theory to realistic engineering problems.
预测极端海况下船舶的运动是海军流体力学中最具挑战性的问题之一。它涉及到计算复杂的非线性波 - 体相互作用，因此对计算资源的需求极大。在此，我们提出一种新的模拟范式，通过训练递归型神经网络（RNN）来实现，该网络将特定海况下的随机波面高程作为输入，并输出船舶的主要运动，如纵摇、垂荡和横摇。我们首先比较了标准RNN与门控循环单元（GRU）和长短期记忆神经网络（LSTM）的性能，结果表明LSTM神经网络具有最佳性能。然后，我们研究了两艘具有代表性船舶的测试误差，一艘是海况1下的双体船，另一艘是海况8下的战列舰。我们证明，在预测未见过的波面高程下的船舶运动时，这两种情况都能达到良好的精度。我们使用昂贵的计算流体动力学（CFD）模拟来训练神经网络，但训练完成后，船舶动力学的预测可以在几分之一秒内获得。这项工作的灵感来源于泛函的通用逼近定理（Chen & Chen, 1993., 910 - 918 (doi:10.1109/72.286886)），并且这是该理论在实际工程问题中的首次应用。
