Ship Motion Prediction Research Articles

Investigation into the Prediction of Ship Heave Motion in Complex Sea Conditions Utilizing Hybrid Neural Networks

While navigating at sea, ships are influenced by various factors, including wind, waves, and currents, which can result in heave motion that significantly impacts operations and potentially leads to accidents. Accurate forecasting of ship heaving is essential to guarantee the safety of maritime navigation. Consequently, this paper proposes a hybrid neural network method that combines Convolutional Neural Networks (CNNs), Bidirectional Long Short-Term Memory Networks (BiLSTMs), and an Attention Mechanism to predict the heaving motion of ships in moderate to complex sea conditions. The data feature extraction ability of CNNs, the temporal analysis capabilities of BiLSTMs, and the dynamic adjustment function of Attention on feature weights were comprehensively utilized to predict a ship’s heave motion. Simulations of a standard container ship’s motion time series under complex sea state conditions were carried out. The model training and validation results indicate that, under sea conditions 4, 5, and 6, the CNN-BiLSTM-Attention method demonstrated significant improvements in MAPE, APE, and RMSE when compared to the traditional LSTM, Attention, and LSTM-Attention methods. The CNN-BiLSTM-Attention method could enhance the accuracy of the prediction. Heave displacement, pitch displacement, pitch velocity, pitch acceleration, and incoming wave height were chosen as key input features. Sensitivity analysis was conducted to optimize the prediction performance of the CNN-BiLSTM-Attention hybrid neural network method, resulting in a significant improvement in MAPE and enhancing the accuracy of ship motion prediction. The research presented in this paper establishes a foundation for future studies on ship motion prediction.

A ship motion forecasting approach based on Fourier transform, regularized Bi-LSTM and chaotic quantum adaptive WOA

Ship motion forecasting is of great significance to assist ship navigation and ensure ship operation. However, due to the coupling influence of wind, waves, currents and other factors, the ship motion has a strong time variation, which brings great challenges to the improvement of the ship motion forecasting accuracy. This paper proposes a novel approach for ship motion forecasting. Firstly, Fourier Transform (FT) is used for data pre-processing to deal with the data noise. Secondly, the Bi-LSTM is applied to simulate the nonlinear dynamical system of ship motion, and the Dropout mechanism and l2 regularization method are used to improve the generalization performance of the network, and a novel ship motion prediction model (FRB model) is constructed. Thirdly, in view of the inherent defects of Whale Optimization Algorithm (WOA), based on chaotic mapping and quantum computing, a new Chaotic Quantum Adaptive Whale Optimization Algorithm (CQAWOA) is proposed to construct a new ship motion forecasting approach, namely FRB&CQAWOA. Finally, based on the measured pitch and roll data of ship, the feasibility and superiority of the established FRB model and the proposed CQAWOA are tested. The test results indicate that the proposed model have better prediction accuracy than other algorithms selected in this paper.

Numerical simulation and analysis of motion responses and added resistance of a KRISO container ship in regular waves

Abstract In order to explore the influence of vessel speed on seakeeping characteristics and provide valuable insights for ship performance evaluation, the accurate prediction of ship motion and resistance in wave conditions is essential. In this study, the variations in ship motion and resistance with respect to ship speed are analyzed during navigation in regular waves. The results suggest that the added resistance coefficient of the KCS demonstrates an initial rise, succeeded by a subsequent decline, with the expansion of wavelength. Moreover, the peak non-dimensional resistance coefficient, observed at different ship speeds, demonstrates an upward trend with the augmentation of ship velocity. This research methodology provides a valuable tool for numerically predicting the hydrodynamic performance of vessels in regular wave conditions.

A fully adaptive time–frequency coupling model using self-attention mechanism based on deep operator network for very short-term forecasting of ship motion

Very short-term ship motion forecasting aims to predict future movements using historical ship motion data. While ship motion features both temporal and frequency characteristics, the latter is often neglected. This paper proposes a fully adaptive time–frequency coupling forecasting model using self-attention mechanism based on the Deep Operator Network (DeepONet), abbreviated as TFD. The multi-head attention layers enable the trunk net to adaptively learn the relationships between different frequencies in the frequency domain and assign varying weights accordingly. Thus, compared to the Fourier transform and multilayer perceptron-net enhance model based on DeepONet (FMD), which relies on manually specified filter frequencies, the TFD model is capable of fully learning the motion patterns in both the time and frequency domains, establishing nonlinear mapping relationships between them. It exhibits greater interpretability and generalization. The TFD model is tested for accuracy and generalization using ship motion data from the Iowa University experimental tank. The results indicate that, compared to the DeepONet and FMD, the TFD model reduces the mean square error (MSE) by up to 64.72% and 52.45%, with an average reduction of 55.57% and 42.47%. In terms of generalization, the forecasting MSE is reduced by up to 65.04% and 46.08%. Compared to the DeepONet and FMD, the proposed TFD model demonstrates significant improvements in forecasting horizon and generalization, providing a notable advantage in very short-term ship motion prediction applications.

Influence of sample intervals in real-sea trails on the nonparametric model of 3-DoF ship motion predictions

The accuracy of ship manoeuvrability models based on real sea trail data heavily relies on data quality, as noise and measurement errors pose significant challenges in data processing and model training. This study employs a deep learning approach for the nonparametric modelling of 3-DoF ship manoeuvrability predictions, utilizing data from zigzag tests conducted at sea. It examines how the limitations of measurement equipment affect data analysis, emphasizing the impact of different sample intervals on model accuracy. Our study further explores the efficacy of deep neural networks in capturing low-frequency components more effectively than high-frequency ones, discussing the data sampling process and frequency analysis in the response domain for training set construction. Simulation results indicate that both excessively small and large sample intervals can significantly compromise predictions of motion, location, and heading angles. Moreover, to enhance the evaluation of the deep learning-based nonparametric model, incorporating a test case with a minimal rudder angle is crucial for assessing the prediction precision. Generally, a sample interval ranging from 0.4 s to 0.6 s is identified as optimal for data down sampling in real sea trails, balancing accuracy and computational efficiency.

Dynamic nonparametric modeling of sail-assisted ship maneuvering motion based on GWO-KELM

Accurately predicting the state of ship motion is crucial for ship navigation control with energy efficiency optimization studies. When modeling the motion of novel ships equipped with propulsion devices such as sails, it is essential to consider the effects of sail thrust and lateral forces on the ship's motion states. Building upon the analysis of sail force and sail-assisted ship motion modeling, this paper proposes a ship motion dynamic modeling method utilizing Kernel Extreme Learning Machine (KELM) regression. By optimizing the hyperparameters of the kernel function using the Grey Wolf Optimizer (GWO) algorithm and incorporating a sliding time window for dynamic model updating, the proposed approach combines the efficient learning mechanism of KELM with the global search capability of GWO, effectively enhancing prediction accuracy and timeliness. Utilizing KVLCC2 ship model motion data, simulation data from the sail-assisted ship “New Aden” and real ship data as case studies, comparative analysis with traditional models such as SVM and ELM. The results demonstrate that the GWO-KELM modeling approach exhibits robustness and high prediction accuracy, the MAE of the proposed model in the real ship motion prediction effect is reduced by 8.89% and the RMSE is reduced by 9.44% compared with the other models, which significantly enhance the predictive performance of sail-assisted ship maneuvering motion states.

Real-time prediction of ship motions based on the reservoir computing model

Real-time prediction of ship motions is crucial for ensuring the safety of offshore activities. In this study, we investigate the performance of the reservoir computing (RC) model in predicting the motions of a ship sailing in irregular waves, comparing it with the long short-term memory (LSTM), bidirectional LSTM (BiLSTM), and gated recurrent unit (GRU) networks. The model tests are carried out in a towing tank to generate the datasets for training and testing the machine learning models. First, we explore the performance of machine learning models trained solely on motion data. It is found that the RC model outperforms the LSTM, BiLSTM, and GRU networks in both accuracy and efficiency for predicting ship motions. Besides, we investigate the performance of the RC model trained using the historical motion and wave elevation data. It is shown that, compared with the RC model trained solely on motion data, the RC model trained on the motion and wave elevation data can significantly improve the motion prediction accuracy. This study validates the effectiveness and efficiency of the RC model in ship motion prediction during sailing and highlights the utility of wave elevation data in enhancing the RC model’s prediction accuracy.

Four-quadrant propeller hydrodynamic performance mapping for improving ship motion predictions

On the path toward fully autonomous sea vessels, forecasting a ship’s exact velocity and position during its route plays a crucial role in dynamic positioning, target tracking, and autopilot operations of the unmanned body navigating toward predetermined locations. This paper addresses the prediction of the operational performance of a free-running submarine advancing in a straight route (in surge motion). Along with the forward advancing vessel (straight-ahead motion) the study covers all possible scenarios of ship’s surge, including crash-ahead, crash-back, and astern motions. Conventional maneuvering models cannot handle motions other than forward advancement due to the absence of propeller data in all four quadrants of hydrodynamic performance map. This study proposes an approach for predicting submarine performance in all these surge conditions by utilizing four-quadrant propeller performance and resistance test data. We developed an in-house code, SMot4QP, to simulate ship speed and position in the time domain. We obtained satisfying results for the straight-ahead and crash-ahead motions, while the crash-back and astern maneuvers require further refinement due to propeller wake interaction with the hull. The proposed method is capable of predicting the motions of all types of vessels using the ship’s resistance and four-quadrant propeller test results. Thus, SMot4QP offers a fast and robust alternative to computationally expensive free-running self-propulsion simulations for operational performance prediction in broader naval applications.

Prediction of Wave-Induced Nonlinear Ship Motions Based on an IRF-LSTM Hybrid Approach

Prediction of Wave-Induced Nonlinear Ship Motions Based on an IRF-LSTM Hybrid Approach

Prediction of ship future motions at different predictable time scales for shipboard helicopter landing in regular and irregular waves

ABSTRACT Differing from the traditional helicopter landing on land, due to ship motions induced by actual waves, the landing safety of shipboard helicopter on vessels in waves deserves to be studied. To provide a judgment basis for the timing of shipboard helicopter landing, a hydrodynamic analysis method based on the Long-Short-Term Memory (LSTM) neural network is proposed to achieve the real-time prediction of ship motions in this study. Firstly, the hydrodynamic formulations based on potential flow theory for nonlinear ship motions in waves are presented. The implementation details of the LSTM neural networks are described. Secondly, the numerical verification study is carried out in regular and irregular waves, respectively. Furthermore, a destroyer model is employed to illustrate the proposed framework, and the results corresponding to the different time scales in waves are presented. Finally, the work of this paper is summarized and the certain conclusions are drawn.

A Review on Motion Prediction for Intelligent Ship Navigation

In recent years, as intelligent ship-navigation technology has advanced, the challenge of accurately modeling and predicting the dynamic environment and motion status of ships has emerged as a prominent area of research. In response to the diverse time scales required for the prediction of ship motion, various methods for modeling ship navigation environments, ship motion, and ship traffic flow have been explored and analyzed. Additionally, these motion-prediction methods are applied for motion control, collision-avoidance planning, and route optimization. Key issues are summarized regarding ship-motion prediction, including online modeling of motion models, real ship validation, and consistency in modeling, optimization, and control. Future technology trends are predicted in mechanism-data fusion modeling, large-scale model, multi-objective motion prediction, etc.

Real-time prediction of ship motion based on improved empirical mode composition and dynamic residual neural network

Ship motion attitude data have strong random and non-stationary characteristics under severe sea states. Real-time and accurate prediction of the ship's motion attitude can significantly improve the safety of navigation. Therefore, this article proposes a prediction model based on the improved empirical mode decomposition (IEMD) and the dynamic residual recurrent neural network with bidirectional structure and time pattern attention mechanism (TPA-Bi-DRRNN), and proposes a new algorithm: dynamic adaptive beetle swarm antennae search (DABSAS) algorithm to optimise the initial weight and threshold of the prediction model. The input data are adaptively composed into multiple intrinsic mode functions (IMFs) containing their frequency characteristics using IEMD, and a prediction is made for each IMF using TPA-Bi-DRRNN. The model structure can be regulated in real time according to the sliding window. The destroyer DTMB5415 is used as an example to conduct a performance test of the hybrid prediction model and DABSAS. The results show that no mode mixing occurred in the IMFs, the noise in each IMF was significantly reduced, thus dramatically reducing the difficulty of using the input data for prediction; and the optimization performance of DABSAS in applying the TPA-Bi-DRRNN is much better than that of the traditional algorithms. Compared with other models, the difference in the predictive accuracy of TPA-Bi-DRRNN under each condition is the smallest, suggestings that it has extremely high robustness and will always be able to maintain much higher accuracy than other models over a long period, thus meeting the needs for real-time accurate prediction of ship motion attitude.

Effect of Ship Motion Prediction Model on Navigational Safety

Effect of Ship Motion Prediction Model on Navigational Safety

Prediction of wave-induced ship motions based on integrated neural network system and spatiotemporal wave-field data

This study introduces an artificial neural network system for ship motion prediction in seaways. To consider the physical characteristics of wave-induced ship motions, neural networks based on a Long Short-Term Memory (LSTM) encoder and decoder, and a convolutional neural network (CNN) are integrated. The LSTM encoder computes the state vector representing the memory effects of motion-induced radiated waves based on past motion records, that is, a sequence-to-one model. In the LSTM decoder, the motion time series is predicted using the encoded initial state vector and foreseen information on the ocean wave field around a vessel, that is, a sequence-to-sequence model. In addition, a CNN is adopted to compress the wave data into a vector sequence. Particularly, the present CNN uses spatiotemporal wave-field data, not a wave signal at single location. To validate the proposed system, a database for training the integrated system was constructed using a physics-based seakeeping program for various sea states. By applying the trained model, deterministic predictions were performed for a new ocean environment, and the accuracy and reliability of the testing results are investigated according to the input data and neural network structures. From the simulation results, it was confirmed that the present encoder–decoder system can conduct ship motion forecasting by effectively considering the motion memory effects and wave excitations as in the ship hydrodynamic model. In addition, excitations and resulting motion responses by short-crested waves can be considered through CNN-based wave-field data processing. Finally, the present machine-learning model also showed the capability of extracting ship operation information (maneuvering quantities) from the given wave-field data.

A comparison of physics-informed data-driven modeling architectures for ship motion predictions

How to select the optimal formulations for building blended physics-machine learning models for ship motions is not currently clear. This work compares and contrasts two approaches to this problem: (1) A black-box deep learning approach based on a new neural network architecture that can better handle varying wave conditions, and (2) a clear-box model based on updates to linear response amplitude operators via a Gaussian process regression. Both models are trained and evaluated on a dataset consisting of more than 15,000 30-minute-long motion observation windows from two research vessels at sea in the Atlantic and Pacific oceans. Three different hindcast weather services are used, including two models from the EU’s Copernicus system and NOAA’s WAVEWATCH III. The evaluation shows that a tradeoff exists between the formulations, with the black-box formulation offering higher accuracy and the cost of less transparency. The weather hindcast used has a small impact on the results, and the ability of both models to generalize predictions between near-sister ships is also encouraging for the practical application of these techniques.

Sparse Bayesian Relevance Vector Machine Identification Modeling and Its Application to Ship Maneuvering Motion Prediction

In order to establish a sparse and accurate ship motion prediction model, a novel Bayesian probability prediction model based on relevance vector machine (RVM) was proposed for nonparametric modeling. The sparsity, effectiveness, and generalization of RVM were verified from two aspects: (1) the processed Sinc function dataset, and (2) the tank test dataset of the KRISO container ship (KCS) model. The KCS was taken as the main research plant, and the motion prediction models of KCS were obtained. The ε-support vector regression and υ-support vector regression were taken as the compared algorithms. The sparsity, effectiveness, and generalization of the three algorithms were analyzed. According to the trained prediction models of the three algorithms, the number of relevance vectors was compared with the number of support vectors. From the prediction results of the Sinc function and tank test datasets, the highest percentage of relevance vectors in the trained sample was below 17%. The final prediction results indicated that the proposed nonparametric models had good prediction performance. They could ensure good sparsity while ensuring high prediction accuracy. Compared with the SVR, the prediction accuracy can be improved by more than 14.04%, and the time consumption was also relatively lower. A training model with good sparsity can reduce prediction time. This is essential for the online prediction of ship motion.

Numerical study on motion responses and added resistance for surge-free KCS in head and oblique waves based on the functional decomposition method

A hybrid approach of potential and viscous flows is developed, based on the functional decomposition model SWENSE (Spectral Wave Explicit Navier-Stokes Equations), to investigate the seakeeping performance of the surge-free ship models accurately and efficiently. In the SWENSE method, the total physical field, including velocity, pressure and the signed distance function of the free surface, are decomposed into the incident field and the complementary field. For the incident wave field, the linear wave model is used and the physical field is extended to the flows up to the air zone using the Wheeler stretching method. With respect to the complementary field, the variables are governed by SWENSE. The adapted single-phase level-set model is used to capture the free surface. Based on this hybrid approach, an in-house code HUST-SWENSE is developed. The spring-mass-damper module, 4DOF (Degrees of Freedom) motion equations of the rigid body, three coordinate systems and the dynamic structured grid with the overset technology are applied to deal with the 4DOF ship motions. Firstly, the size of the computational domain for the simulations of the oblique waves is discussed. The numerical results can be convergent for HUST-SWNESE when the radius R/L of the cylindrical computational domain is larger than 2.0. After determining the grid system and the time step based on the verification and validation study, simulations are conducted using the HUST-SWENSE to predict the surge, heave, roll, and pitch motions of the KCS in regular oblique waves. Wave conditions are based on the benchmark cases provided by the Tokyo2015 CFD workshop. The simulated results are then compared with experimental data and other numerical results. The comparison shows that the respective differences were less than 2% for incident regular waves, 10% for heave and pitch motion responses, 5% for roll motions and 20% for added resistances. Therefore, the HUST-SWENSE model can be considered reliable for the prediction of ship motions and added resistance in head and oblique waves. Finally, the influences of different DOFs, wavelengths and wave heights on the motions and added resistance for the surge-free ship model in oblique waves are investigated in detail. It is found that the importance of surge motion in the seakeeping performance prediction of the ship in astern seas, especially for the added resistance. Moreover, the nonlinearity of wave heights is analyzed, and the results indicate that the nonlinearity of the large-amplitude roll is mainly induced by the roll restoring moments, while the nonlinear features of the incident, radiation and diffraction wave systems were responsible for the nonlinearity of added resistance and surge motions.

Math-data integrated prediction model for ship maneuvering motion

Highly accurate motion prediction is critical to facilitate safe navigation and autonomous control of a ship. In this paper, a math-data integrated prediction (MDIP) model of ship maneuvering motion is newly developed by combining with mathematical and data-driven modules. The math part is identified by employing variable-order hydrodynamic derivatives which are derived from Taylor expansion. Using extended Kalman filter, an optimal-order mathematical prediction model is obtained. The data-driven part dwells on prediction residuals which are approximated by a least square-support vector machine. Furthermore, integration mechanisms are devised to cohere mathematical and data-driven models as a whole, by deploying summation and neural network approximation, respectively. By comparisons, it is verified that not only order selection but also math-data integration can enhance ship motion prediction accuracy, for which various maneuvering tests are analyzed. The results demonstrate that the proposed MDIP model using math-data integration offers much stronger generalization, thereby paving a new path for ship maneuvering motion prediction.

A machine learning method for the prediction of ship motion trajectories in real operational conditions

This paper presents a big data analytics method for the proactive mitigation of grounding risk. The model encompasses the dynamics of ship motion trajectories while accounting for kinematic uncertainties in real operational conditions. The approach combines K-means and DB-SCAN (Density-Based Spatial Clustering of Applications with Noise) big data clustering methods with Principal Component Analysis (PCA) to group environmental factors. A Multiple-Output Gaussian Process Regression (MOGPR) method is consequently used to predict selected ship motion dynamics. Ship sway is defined as the deviation between a ship and her motion trajectory centreline. Surge accelerations are used to idealise the time-varying manoeuvring of ships in various routes. Operational conditions are simulated by Automatic Identification System (AIS), General Bathymetric Chart of the Oceans (GEBCO), and nowcast hydro-meteorological data records. A Dynamic Time Warping (DTW) method is adopted to identify ship centre-line trajectories along selected paths. The machine learning algorithm is applied for ship motion predictions of Ro-Pax ships operating between two ports in the Gulf of Finland. Ship motion dynamics are visualised along the ship's route using a Gaussian Progress Regression (GPR) flow method. Results indicate that the present methodology may assist with predicting the probabilistic distribution of ship dynamics (speed, sway distance, drift angle, and surge accelerations) and grounding risk along selected ship routes.

LQR and LQG control of the helicopter during landing on the ship deck

PurposeThe purpose of this study is to test the performance of the designed automatic control system based on the Linear Quadratic Regulator (LQR) and Linear Quadratic Gaussian (LQG) algorithms during landing of the helicopter on the ship deck. This paper is a further development of the series based on Topczewski et al. (2020).Design/methodology/approachThe system consists of two automatic control algorithms based on LQR and the LQG. It is integrated with the ship motion prediction system based on autoregressive algorithm with parameters calculated using Burg’s method. It is assumed that the source of necessary navigation data is integrated Inertial Navigation System with Global Positioning System. Landing of the helicopter on the ship deck is performed in automatic way, based on the preselected procedure. Performance of the control system is analyzed when all necessary navigation data is available for the system and in case when one of the parameters is unavailable during performing the procedure.FindingsIn this paper, description of the designed control system developed for performing the approach and landing of the helicopter using selected procedure is presented. Helicopter dynamic model is validated using the manufacturer data and by test pilots, overview is presented. Necessary information about ship motion model is also included. Tests showing mission performance while using LQR and LQG algorithms applied to the control system are presented and analyzed, taking into account both situations when full navigation data is available/unavailable for the control system.Practical implicationsResults of the system performance analyses can be used for selection of the proper control methodology for prospective helicopters autopilots. Furthermore, the system can be used to analyze the mission safety when information about one of the navigation parameters is identified by the navigation system as unavailable or incorrect and therefore unavailable during landing on the ship deck.Originality/valueIn this paper, control system dedicated for the automatic landing of the helicopter on the ship deck, based on two different control algorithms is presented. Influence of lack of information about one of the navigation parameters on the mission performance is analyzed.