Underwater sound field prediction based on empirical orthogonal function and Bayesian neural network

Fangbing JIANG; Jinrong WU; Qiannan HOU; Zuoxiang ZHANG; Yaxiao MO

doi:10.11990/jheu.202506011

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Underwater sound field prediction based on empirical orthogonal function and Bayesian neural network

Research Article | 更新时间：2026-03-31

- Underwater sound field prediction based on empirical orthogonal function and Bayesian neural network
- Journal of Harbin Engineering University Vol. 46, Issue 8, Pages: 1508-1515(2025)
- 作者机构：
  
  1.中国科学院声学研究所, 北京 100190
  2.中国科学院水声环境特性重点实验室, 北京 100190
  3.中国科学院大学, 北京 100049
- 作者简介：
- 基金信息：
- DOI：10.11990/jheu.202506011
  CLC： O427.1
- Received：06 June 2025，
  
  Online First：24 June 2025，
  
  Published：05 August 2025
- 稿件说明：
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Fangbing JIANG, Jinrong WU, Qiannan HOU, et al. Underwater sound field prediction based on empirical orthogonal function and Bayesian neural network[J]. Journal of Harbin Engineering University, 2025, 46(8): 1508-1515.
DOI：

Fangbing JIANG, Jinrong WU, Qiannan HOU, et al. Underwater sound field prediction based on empirical orthogonal function and Bayesian neural network[J]. Journal of Harbin Engineering University, 2025, 46(8): 1508-1515. DOI： 10.11990/jheu.202506011.

摘要

在水下声场预报中，数据驱动模型的预报精度主要取决于训练样本数对样本空间的覆盖程度。针对现有方法多局限于单一水文环境、且水文样本数量不足导致精度下降的问题，本文提出一种基于经验正交函数和贝叶斯神经网络的水下声场预报方法。利用经验正交函数有效降低声速剖面输入维度，并通过其系数组合生成覆盖多样化水文环境的样本集；进而借助具有强泛化能力的贝叶斯神经网络在部分数据空间内学习有效特征，预报变化水文条件下的声传播损失，并给出置信区间。结果表明: 相较于传统神经网络，该方法在训练集范围内的预报误差更小，对未知数据的适应能力更强，且通过概率建模可实现端到端的不确定性量化

提升了数据驱动模型在复杂水文条件下的鲁棒性与可靠性。

Abstract

The accuracy of data-driven models for forecasting underwater acoustic fields primarily depends on the sample space covered by the training sample. To address the limitations of existing methods

which are often confined to single sound speed profiles (SSPs) and suffer from accuracy loss due to insufficient SSP samples

this study proposes a method employing an empirical orthogonal function and Bayesian neural network (EOF-BNN). First

the input dimension of the SSPs is effectively reduced using the EOF

generating diverse SSP samples via coefficient combinations. The method then employs a BNN with strong generalization ability to learn effective features from limited data

forecasting acoustic transmission loss under varying SSP conditions while providing confidence intervals. Compared with the traditional neural network

this method has smaller prediction error in the training set range

better adaptability to unknown data

and end-to-end uncertainty quantification through probabilistic modeling

which improves the robustness and reliability of data-driven models under complex hydrological conditions.

关键词

Keywords

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