A Ship Underwater Radiated Noise Prediction Method Based on Semi-Supervised Ensemble Learning
Abstract
1. Introduction
- (1)
- A genetic algorithm-based adaptive weighted ensemble (AWE) model is proposed. By constructing an anti-perturbation regularization term using unlabeled data, this framework optimizes base learner weights to enhance pseudo-label quality while improving ensemble robustness.
- (2)
- An ensemble semi-supervised regression (ESSR) model integrating dynamic pseudo-label screening and uncertainty bias correction (UBC) is established. Pseudo-labels are dynamically filtered based on local prediction performance improvement. Ensemble prediction variance quantifies pseudo-label uncertainty, with sample weights assigned via uncertainty-aware adjustment to minimize bias in training.
- (3)
- The UBC-AWESSR method proposed in this study is validated by cabin model experiments and sea trials of the vessel. Results confirm its superior performance in static and dynamic scenarios, outperforming traditional supervised regression (SR) and semi-supervised regression (SSR) models with maximum error reductions of 65.5% and 62.1%, respectively.
2. Related Work
2.1. Consistency Regularization
2.2. Semi-Supervised Co-Training Based on Disagreement
2.3. Ensemble Semi-Supervised Learning
3. Methodology
3.1. Symbol Setting
3.2. Adaptive Weighted Ensemble (AWE) Learning Based on Genetic Algorithm
3.2.1. Objective Function Optimization
3.2.2. Adaptive Weighting
3.3. ESS Based on Pseudo-Label Dynamic Screening and Uncertainty Bias Correction
3.3.1. Dynamic Screening of Pseudo-Labels
3.3.2. Uncertainty Bias Correction
Algorithm 1. Pseudo-code of UBC-AWESSR model pseudo-label screening |
Input: Labeled dataset: 𝓛; Unlabeled dataset: 𝓤; Trained ensemble models (EMs): {f1, f2, ..., fM} Maximum number of learning iterations: T |
Output: Get pseudo-label dataset 𝓤_pseudo: {(xu, ŷu, Wu)} |
Initialize 𝓤_pseudo = [ ] Repeat for T rounds: 𝓤’ is randomly selected from 𝓤, the size of 𝓤’ is s, the remaining part of 𝓤 is 𝓤0 |
for xu ∈ 𝓤’ do |
Φ ← KNN(xu, 𝓛) h ← EMs(𝓛, 𝓤0) |
end If exist 𝓤_pseudo ← |
h ← EMs(𝓛 ∪ 𝓤_pseudo, 𝓤0)
𝓤’← 𝓤’ remove 𝓤 ← 𝓤’ Else 𝓤_pseudo ← End End the repeat |
3.4. The Overall Framework of the Ship URN Prediction Model
- (1)
- Multi-source data acquisition and preprocessing
- (2)
- EL model optimization training
- (3)
- Pseudo-label screening and application
4. Experiment
4.1. Introduction of the Dataset
4.1.1. Experiment of the Cabin Model
4.1.2. Experiment of the Scientific Research Vessel at Sea
4.2. Model Evaluation Index
4.3. Model Parameter Setting
4.4. Experiment Result
4.4.1. Experiment on the Cabin Model
- Comparison of prediction results from different models
- b.
- Ablation test results
- (1)
- The influence of AW based on the genetic algorithm on model performance
- (2)
- The influence of the pseudo-label screening method based on UBC on model performance
4.4.2. Experiment on the Research Vessel
- Comparison of prediction results from different models
- b.
- Ablation test results
- (1)
- The influence of AW based on the genetic algorithm on model performance
- (2)
- The influence of the pseudo-label screening method based on UBC on model performance
5. Conclusions
- (1)
- We designed cabin model experiment and vessel experiment to verify the effectiveness of UBC-AWESSR model, and the results showed that UBC-AWESSR can reduce MAE and RMSE by up to 65.5% and 69.4% compared with the traditional SR and SSR models.
- (2)
- The predictive performances of different models under different numbers of labeled samples were compared. The results show that the fewer the number of labeled samples, the more obvious the advantages of UBC-AWESSR model become.
- (3)
- The experimental data collected during the sea trial contained single-frequency interference signals. However, even when the data quality was poor, UBC-AWESSR model still exhibited a relatively good predictive effect.
- (4)
- The results of the ablation tests show that the AWE integrating anti-perturbation regularization has the most significant impact on the model prediction, and the model performance degrades severely after removal, which provides supporting evidence for conclusion (3) from a different perspective.
- (5)
- To obtain more useful information to assist model training and increase the interpretability of the model, the data-driven integrating physical knowledge is the future research direction and the next focus of this paper.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Model | Parameter |
---|---|
Ridge | Alpha = 0.1 |
MLP | hidden layers = 6; activation function= ReLU; learning_rate = 0.001 |
Adaboost | n_estimators = 10; learning_rate = 0.01 |
RF | n_estimators = 10; max_features = 5 |
Self-Training | n_neighbors = 3; metric = ‘Euclidean’ |
Co-Training | n_neighbors = {3, 5}; metric = {‘Euclidean’, ‘minkowski’} |
Tri-Training | n_neighbors = {3, 5, 4}; metric = {‘Euclidean’, ‘minkowski’, ‘manhattan’} |
UBC-AWESSR | n_base_models = 5; n_neighbors = {3, 5}; metric = {‘Euclidean’, ‘minkowski’} |
MAE/dB | RMSE/dB | ||||||
---|---|---|---|---|---|---|---|
Number of Labeled Data | 10 | 15 | 20 | 10 | 15 | 20 | |
SR | Ridge | 4.72 | 3.65 | 2.89 | 6.05 | 4.64 | 4.09 |
MLP | 5.25 | 4.91 | 2.86 | 6.83 | 6.33 | 4.02 | |
Adaboost | 3.13 | 2.51 | 2.92 | 3.90 | 3.09 | 3.79 | |
RF | 5.83 | 3.65 | 2.59 | 8.63 | 4.86 | 3.23 | |
SSR | ST | 3.74 | 3.14 | 1.96 | 4.99 | 4.29 | 2.66 |
CT | 4.74 | 4.04 | 2.83 | 6.07 | 5.28 | 3.65 | |
TT | 5.00 | 4.44 | 2.54 | 6.21 | 5.89 | 3.24 | |
Proposed by us | UBC-AWESSR | 2.01 | 1.68 | 1.47 | 2.64 | 2.59 | 1.93 |
MAE/dB | RMSE/dB | |||||
---|---|---|---|---|---|---|
Number of Labeled Data | 10 | 15 | 20 | 10 | 15 | 20 |
UBC-ESSR | 6.05 | 5.00 | 3.13 | 7.36 | 6.25 | 3.94 |
UBC-AWESSR | 2.01 | 1.68 | 1.47 | 2.64 | 2.59 | 1.93 |
Error decreases | 66.8% | 66.4% | 53.0% | 64.1% | 58.6% | 51.0% |
MAE/dB | RMSE/dB | |||||
---|---|---|---|---|---|---|
Number of Labeled Data | 10 | 15 | 20 | 10 | 15 | 20 |
AWESSR | 4.83 | 3.29 | 2.38 | 5.63 | 4.04 | 2.91 |
UBC-AWESSR | 2.01 | 1.68 | 1.47 | 2.64 | 2.59 | 1.93 |
Error decreases | 58.4% | 48.9% | 38.2% | 53.1% | 35.9% | 33.7% |
MAE/dB | RMSE/dB | ||||||
---|---|---|---|---|---|---|---|
Number of Labeled Data | 10 | 15 | 20 | 10 | 15 | 20 | |
SR | Ridge | 3.90 | 4.08 | 3.68 | 5.02 | 5.08 | 4.61 |
MLP | 4.68 | 4.54 | 3.40 | 6.75 | 5.98 | 4.17 | |
Adaboost | 5.23 | 3.95 | 3.49 | 6.55 | 4.79 | 4.63 | |
RF | 3.81 | 3.88 | 3.60 | 4.92 | 4.60 | 4.41 | |
SSR | ST | 4.69 | 4.77 | 4.53 | 5.64 | 6.09 | 5.22 |
CT | 4.73 | 4.54 | 3.84 | 5.63 | 5.50 | 4.42 | |
TT | 4.57 | 4.69 | 3.92 | 5.56 | 5.70 | 4.49 | |
Proposed by us | UBC-AWESSR | 3.69 | 3.63 | 3.04 | 4.69 | 4.36 | 3.66 |
MAE/dB | RMSE/dB | |||||
---|---|---|---|---|---|---|
Number of Labeled Data | 10 | 15 | 20 | 10 | 15 | 20 |
UBC-ESSR | 7.50 | 3.83 | 3.28 | 10.08 | 4.63 | 4.21 |
UBC-AWESSR | 3.69 | 3.63 | 3.04 | 4.69 | 4.36 | 3.66 |
Error decreases | 50.8% | 5.22% | 7.32% | 53.5% | 5.83% | 13.1% |
MAE/dB | RMSE/dB | |||||
---|---|---|---|---|---|---|
Number of Labeled Data | 10 | 15 | 20 | 10 | 15 | 20 |
AWESSR | 6.98 | 4.09 | 3.17 | 8.97 | 5.30 | 4.17 |
UBC-AWESSR | 3.69 | 3.63 | 3.04 | 4.69 | 4.36 | 3.66 |
Error decreases | 47.1% | 11.3% | 4.10% | 47.8% | 17.7% | 12.2% |
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Huang, X.; Xu, R.; Li, R. A Ship Underwater Radiated Noise Prediction Method Based on Semi-Supervised Ensemble Learning. J. Mar. Sci. Eng. 2025, 13, 1303. https://doi.org/10.3390/jmse13071303
Huang X, Xu R, Li R. A Ship Underwater Radiated Noise Prediction Method Based on Semi-Supervised Ensemble Learning. Journal of Marine Science and Engineering. 2025; 13(7):1303. https://doi.org/10.3390/jmse13071303
Chicago/Turabian StyleHuang, Xin, Rongwu Xu, and Ruibiao Li. 2025. "A Ship Underwater Radiated Noise Prediction Method Based on Semi-Supervised Ensemble Learning" Journal of Marine Science and Engineering 13, no. 7: 1303. https://doi.org/10.3390/jmse13071303
APA StyleHuang, X., Xu, R., & Li, R. (2025). A Ship Underwater Radiated Noise Prediction Method Based on Semi-Supervised Ensemble Learning. Journal of Marine Science and Engineering, 13(7), 1303. https://doi.org/10.3390/jmse13071303