Learning functionals via LSTM neural networks for predicting vessel dynamics in extreme sea states

Abstract

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 offline , but upon training, the prediction of the vessel dynamics online can be obtained at a fraction of a second. This work is motivated by the universal approximation theorem for functionals (Chen & Chen, 1993. IEEE Trans. Neural Netw. 4 , 910–918 ( doi:10.1109/72.286886 )), and it is the first implementation of such theory to realistic engineering problems.

An Improved Ship Trajectory Prediction Based on AIS Data Using MHA-BiGRU

“…The LSTM and GRU, excellent variants of RNN, have a gate structure that not only preserves long-term sequence information but also filters and modifies ship track historical data for enhanced time series prediction. Additionally, in comparison with LSTM, the prediction task with GRU can be accomplished with fewer model parameters, but it can perform similarly to LSTM [17][18][19]. This experiment finds that GRU can outperform LSTM in this comparison scenario, both in terms of efficiency and accuracy, regardless of whether the model is combined with a two-way structure, the MHA mechanism, or neither.…”

“…Thus, due to their effectiveness in time series prediction, RNN and its variant models have been applied to the field of ship trajectory prediction in recent years. Ferrandis et al established the LSTM method to predict the ship trajectory and solve the problem of the gradient vanishing and gradient explosion of RNN owing to rising data length [19]. Agarap utilized the GRU method for time series prediction and proved this method has a good performance and is suitable for time series forecasting [20].…”

Operator learning for predicting multiscale bubble growth dynamics

“…The input gate takes a new input point from outside and processes newly coming data; the input modulation gate takes input from the output of the LSTM cell in the last iteration; the forget gate decides when to forget the output results and thus selects the optimal time lag for the input sequence; and the output gate takes all results calculated and generates output for the LSTM cell. LSTM has been utilized for traffic flow prediction 35 , vessel dynamics prediction 36 , human trajectory prediction 37 , stock price prediction 38 , etc.…”

An attempt to predict planing hull motions using machine learning methods

“…Yet, after training both models neural network is faster in making prediction than the support vector machine. del Águila Ferrandis et al [17] developed a model for heave, pitch and roll motions for catamaran vessel and DTMB battleship for 5 th order regular waves and stochastic waves that represent real life sea-states. To summarize the workflow conducted in this research, one of the contributions of this work was trying two types of RNN (Gating recurrent unit (GRU) and LSTM.…”