Article In: scopus

Multi-step online prediction of 4 degrees of freedom motion under various wind scales based on pre-training strategy and ensemble learning framework

Ocean Engineering

Meng, Y.; Zhang, XK. ; Guedes Soares, C. — 2025 — Elvesier

Key information

Authors:

Meng, Y.; Zhang, XK.; Zhang, XF.; Duan, YT.; Xu, H.T. (Haitong Xu); Guedes Soares, C. (Carlos Guedes Soares)

Published in

11/15/2025

Abstract

Accurate multi-step prediction enhances navigational safety and optimises the performance of autonomous control systems. Given the limitations of single data-driven models and single-step prediction schemes, this paper proposes a multi-step online motion prediction scheme based on the weighted multi-kernel relevance vector machine, pre-training strategy, and ensemble learning framework. To evaluate the effectiveness and generalisation of the proposed scheme, four degrees of freedom motion data are collected under various wind conditions. A subset of motion data is used as training samples to pre-train three sub-models, whose parameters are tuned using an improved grey wolf optimiser algorithm. To integrate the prediction results of the sub-models, this paper develops an ensemble learning framework and proposes an adaptive weight updating rule. Then, this paper conducts single-step, 5-step, and 10-step time series predictions of ship motion. The comparison results with long short-term memory method confirm the adaptability and generalisation of the proposed scheme. The final experimental results show that the proposed scheme maintains good generalisation and time efficiency while ensuring low model complexity. The mean squared errors of the single-step and multi-step prediction results are below 8 × 10− 3 and 0.28. This method can provide a reliable nonparametric identification modelling scheme for USVs.

Publication details

Authors in the community:

Publisher

Elvesier

Link to the publisher's version

https://www.sciencedirect.com/science/article/pii/S0029801825017809?via%3Dihub

Title of the publication container

Ocean Engineering

First page or article number

122096

Volume

339

Issue

Part 1

DOI

10.1016/j.oceaneng.2025.122096

Fields of Science and Technology (FOS)

other-engineering-and-technologies - Other engineering and technologies

Keywords

  • Multi-step time series prediction
  • Weighted multi-kernel relevance vector machine
  • Pre-training strategy ensemble learning
  • Improved grey wolf optimiser

Publication language (ISO code)

eng - English

Rights type:

Open access

Financing entity

Centro de Engenharia e Tecnologia Naval e Oceânica, Instituto Superior Técnico

Identifier for the funding entity: 2022YFB4301402