# Ship Flooding Time Prediction Based on Composite Neural Network

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Process Sketch

_{f}). In order to make this idea easy to realize, the selected flooding images have two characteristics: First, the flooding images are an ordered set that evolves over time. In practice, considering the limited working time of the recording equipment in the flooded compartments, the evolution time needs to be as short as possible. Only then the images required for prediction are obtained from the damaged compartment. This reduces the workload and makes flooding images easy to get, as well.

#### 2.2. Conversion of Flooding Time for Cruise Ship and Model Ship

_{A}, and P

_{B}are the pressures at points A and B, respectively, and take the value of atmospheric pressure, ρ is the density of water, ${\mathit{v}}_{\mathit{A}}$, ${\mathit{v}}_{\mathit{B}}$ are the velocity of water at points A and B, respectively, and $\mathit{g}$ is the acceleration of gravity. ${\mathit{h}}_{\mathit{A}}$, ${\mathit{h}}_{\mathit{B}}$ are the depths from points A and B, respectively, to the grounding of the water.

_{d}is the flow coefficient of the opening, which is a constant. For the cruise ship, ${\mathit{h}}_{\mathit{A}}-{\mathit{h}}_{\mathit{B}}$ is ${\mathit{h}}_{\mathit{C}}$ in Figure 2, and for the model, it is ${\mathit{h}}_{\mathit{M}}$. The relationship between the water speed of the cruise ship and the model at the same opening is shown in Equation (3):

**C**of the flooding time of the cruise ship and the model is obtained, as shown in Equation (4):

#### 2.3. Framework

#### 2.3.1. Depth Feature Extractor

#### 2.3.2. Temporal Feature Extract

**h**is the hidden state at the t − 1 s, and x

_{t − }_{1}**is the input of the LSTM at the current moment.**

_{t}**W**contains learnable parameters. The sigmoid function is given by Equation (8):

_{f}) p

_{1}, p

_{2}, p

_{3}, p

_{4}for four compartments. These predicted values and target values q

_{1}, q

_{2}, q

_{3}, q

_{4}are put into the cross-entropy function to obtain the loss values L

_{1}, L

_{2}, L

_{3}, L

_{4}. Then, all the loss values are summed to obtain the final loss value L

_{S}. This loss value is the final value participating in the backpropagation, shown in Equation (10):

## 3. Flooding Experiment and Dataset

#### 3.1. Parameters

#### 3.2. Flooding Scenario

#### 3.3. Dataset Production

## 4. Experience and Discussion

#### 4.1. The Input of Neural Network

#### 4.2. Time Accuracy

_{pred}of the four compartments in each flooding scenario. The target times T

_{target}are given by the flooding experiments. The timing is accurate to two decimal digits. Equation (11) is the accuracy rate T

_{ACC}calculation method:

**T**,

_{pred}**T**into Equation (11). The summarized results can be divided by the number corresponding to the categories. The average time accuracy of each compartment under different scenarios,

_{target}**T**,

_{Acc-A}**T**,

_{Acc-B}**T**,

_{Acc-C}**T**, is obtained, and the results are shown in Table 4. For example, for the opening in compartment A, by bringing 41 prediction time and 41 target time into Equation (11), we obtain 41 numbers. Then, we calculate the average of 41 numbers, which is the

_{Acc-D}**T**.

_{Acc-A}#### 4.3. Decision Making

#### 4.4. The Accuracy between the Model and the Real Ship

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Luca, B.; Germano, D.; Serena, B.; Vittorio, B.; Alberto, M. A Comparison of Different Linearized Formulations for Progressive Flooding Simulations in Full-Scale. Procedia Comput. Sci.
**2021**, 180, 219–228. [Google Scholar] - Vassalos, D.; Mujeb-Ahmed, M.P. Conception and Evolution of the Probabilistic Methods for Ship Damage Stability and Flooding Risk Assessment. J. Mar. Sci. Eng.
**2021**, 9, 667. [Google Scholar] [CrossRef] - Ruponen, P. Progressive Flooding of a Damaged Passenger Ship. Ph.D. Thesis, Helsinki University of Technology, Espoo, Finland, November 2007. [Google Scholar]
- Ruponen, P.; Basten, B.R.; Bandringa, H.; Bu, S.X.; Dankowski, H.; Lee, G.J.; Mauro, F.; Murphy, A.; Rosano, G.; Ruth, E.; et al. Benchmark study on simulation of flooding progression. In Proceedings of the 1st International Conference on the Stability and Safety of Ships and Ocean Vehicles, Online, 7–11 June 2021. [Google Scholar]
- Pekka, R.; Rinnert, B.B.; van Veer, R.; Braidotti, L.; Bu, S.; Dankowski, H.; Lee, G.J.; Mauro, F.; Ruth, E.; Tompuri, M. International benchmark study on numerical simulation of flooding and motions of a damaged cruise ship. Appl. Ocean. Res.
**2022**, 129, 103403. [Google Scholar] - Dankowski, H.; Krüger, S. A fast, direct approach for the simulation of damage scenarios in the time domain. In Proceedings of the 11th International Marine Design Conference—IMDC, Glasgow, Scotland, 11–14 June 2012. [Google Scholar]
- Pekka, R.; Markku, L.; Petri, P. Flooding Prediction Onboard a Damaged Ship. In Proceedings of the 11th International Conference on the Stability of Ships and Ocean Vehicles, Athens, Greece, 23–28 September 2012. [Google Scholar]
- Pekka, R.; Aappo, P.; Jarkko, L. A method for breach assessment onboard a damaged passenger ship. Appl. Ocean. Res.
**2017**, 64, 236–248. [Google Scholar] - Braidotti, L.; Mauro, F. A new calculation technique for onboard progressive flooding simulation. Ship Technol. Res.
**2019**, 66, 150–162. [Google Scholar] [CrossRef] - Braidotti, L.; Mauro, F. A Fast Algorithm for Onboard Progressive Flooding Simulation. J. Mar. Sci. Eng.
**2020**, 8, 369. [Google Scholar] [CrossRef] - Braidotti, L.; Jasna, P.O.; Utzeri, S.; Bucci, V.; Marino, A. Fast Estimation of the Time-to-Flood on Simple Geometries. Technol. Sci. Ships Future
**2022**, 6, 555–563. [Google Scholar] - Varela, J.M.; Rodrigues, J.M.; Soares, C.G. On-board Decision Support System for Ship Flooding Emergency Response. Procedia Comput. Sci.
**2014**, 29, 1688–1700. [Google Scholar] [CrossRef] - van Walree, F.; Papanikolaou, A. Benchmark study of numerical codes for the prediction of time to flood of ships: Phase I. In Proceedings of the 9th International Ship Stability Workshop, Hamburg, Germany, 30–31 August 2007. [Google Scholar]
- Basic, J.; Degiuli, N.; Dejhalla, R. Total resistance prediction of an intact and damaged tanker with flooded tanks in calm water. Ocean. Eng.
**2017**, 130, 83–91. [Google Scholar] [CrossRef] - FLARE, 2018–2022. FLARE Flooding Accident Response, EU Funded Research Project, Horizon 2020, Contract No.: 814753. Available online: http://www.flare-project.eu (accessed on 6 June 2019).
- Gao, Z.L.; Gao, Q.X.; Vassalos, D. Numerical simulation of flooding of a damaged ship. Ocean. Eng.
**2011**, 38, 1649–1662. [Google Scholar] [CrossRef] - Manderbacka, T.; Ruponen, P. The impact of the inflow momentum on the transient roll response of a damaged ship. Ocean Eng.
**2016**, 120, 346–352. [Google Scholar] [CrossRef] - Jasionowski, A. An Integrated Approach to Damage Ship Survivability Assessment. Ph.D. Thesis, University of Strathclyde, Glasgow, Scotland, 2001. [Google Scholar]
- Lee, G.J. Dynamic orifice flow model and compartment models for flooding simulation of a damaged ship. Ocean Eng.
**2015**, 109, 635–653. [Google Scholar] [CrossRef] - Bu, S.; Gu, M. Study on damaged ship motion coupled with damaged flow based on the unified viscous and potential model. In Proceedings of the 17th International Ship Stability Workshop, Helsinki, Finland, 10–12 June 2019; pp. 209–220. [Google Scholar]
- Bu, S.; Gu, M. Unified viscous and potential prediction method for the coupled motion of damaged ship and floodwater in calm water. Ocean. Eng.
**2020**, 210, 107441. [Google Scholar] [CrossRef] - Ruth, E.; Olufsen, O.; Rognebakke, O. CFD in damage stability. In Proceedings of the 17th International Ship Stability Workshop, Helsinki, Finland, 10–12 June 2019; pp. 259–263. [Google Scholar]
- Ruponen, P.; Valanto, P.; Acanfora, M.; Dankowski, H.; Lee, G.J.; Mauro, F.; Murphy, A.; Rosano, G.; van Veer, R. Results of an international benchmark study on numerical simulation of flooding and motions of a damaged ropax ship. Appl. Ocean. Res.
**2022**, 123, 103–153. [Google Scholar] [CrossRef] - Jiao, J.L.; Huang, S.X.; Soares, C.G. Numerical investigation of ship motions in cross waves using CFD. Ocean. Eng.
**2021**, 223, 108711. [Google Scholar] [CrossRef] - Wu, J.; Zhang, G.; Jiang, Y.; Yang, X. Numerical Simulations on the Flooding into a Damaged Compartment with a Flexible Bulkhead Based on the Mixed-Mode Function-Modified MPS Method. J. Mar. Sci. Eng.
**2022**, 10, 1582. [Google Scholar] [CrossRef] - Xu, S.M.; Gao, Z.L.; Xue, W. CFD database method for roll response of damaged ship during quasi-steady flooding in beam waves. Appl. Ocean Res.
**2022**, 126, 103282. [Google Scholar] [CrossRef] - Gao, Z.L.; Wang, Y.L.; Su, Y.; Chen, L. Numerical study of damaged ship’s compartment sinking with air compression effect. Ocean. Eng.
**2018**, 147, 68–76. [Google Scholar] [CrossRef] - Bi, X.S.; Shen, H.L.; Zhou, J.; Su, Y.M. Numerical analysis of the influence of fixed hydrofoil installation position on seakeeping of the planning craft. Appl. Ocean. Res.
**2019**, 90, 101863. [Google Scholar] [CrossRef] - Braidotti, L.; Valčić, M.; Prpić-Oršić, J. Exploring a flooding-sensors-agnostic prediction of the damage consequences based on machine learning. J. Mar. Sci. Eng.
**2021**, 9, 271. [Google Scholar] [CrossRef] - Braidotti, L.; Prpić-Oršić, J.; Valčić, M. Effect of Database Generation on Damage Consequences’ Assessment Based on Random Forests. J. Mar. Sci. Eng.
**2021**, 9, 1303. [Google Scholar] [CrossRef] - Krizhevsky, A.; Sutskever, I.; Hinton, G.E. ImageNet Classification with Deep Convolutional Neural Networks. Commun. ACM
**2012**, 60, 84–90. [Google Scholar] [CrossRef] - He, K.M.; Zhang, X.Y.; Ren, S.Q.; Sun, J. Deep Residual Learning for Image Recognition. Comput. Vis. Pattern Recognit.
**2016**, 770–778. [Google Scholar] - Sergey, V.; Vladimir, B.; Viacheslav, V. ERANNs: Efficient residual audio neural networks for audio pattern recognition. Pattern Recognit. Lett.
**2022**, 161, 38–44. [Google Scholar] - Chen, C.; Li, K.; Teo, S.G.; Zou, X.; Wang, K.; Wang, J.; Zeng, Z. Gated Residual Recurrent Graph Neural Networks for Traffic Prediction. In Proceedings of the AAAI Conference on Artificial Intelligence, Honolulu, HI, USA, 27 January–1 February 2019; Volume 33, pp. 485–492. [Google Scholar] [CrossRef]
- Michael, E.; Sander, P.A.; Mathieu, B.; Gabriel, P. Momentum Residual Neural Networks. In Proceedings of the 38th International Conference on Machine Learning, Online, 18–24 July 2021; pp. 9276–9287. [Google Scholar]
- Jiang, M.; Xu, L.; Clausi, D.A. Sea Ice–Water Classification of RADARSAT-2 Imagery Based on Residual Neural Networks (ResNet) with Regional Pooling. Remote Sens.
**2022**, 14, 3025. [Google Scholar] [CrossRef] - Ranathunga, S.; Lee, E.A.; Skenduli, M.P.; Shekhar, R.; Alam, M.; Kaur, R. Neural Machine Translation for Low-resource Languages: A Survey. ACM Comput. Surv.
**2023**, 55, 1–37. [Google Scholar] [CrossRef] - Wang, R.; Panju, M.; Gohari, M. Classification-based RNN machine translation using GRUs. Neural Evol. Comput.
**2017**, 1, 10934. [Google Scholar] - Shenoy, A.; Sardana, A. Multilogue-net: A context aware rnn for multi-modal emotion detection and sentiment analysis in conversation. arXiv
**2020**, arXiv:2002.08267. [Google Scholar] - Saha, B.N.; Senapati, A.; Mahajan, A. LSTM based Deep RNN Architecture for Election Sentiment Analysis from Bengali Newspaper. In Proceedings of the International Conference on Computational Performance Evaluation (ComPE), Shillong, India, 1–3 December 2020; pp. 564–569. [Google Scholar]
- Yao, Y. Data Analysis on the Computer Intelligent Stock Prediction Model Based on LSTM RNN and Algorithm Optimization. In Proceedings of the 2022 IEEE International Conference on Electrical Engineering, Big Data and Algorithms (EEBDA), Changchun, China, 24–26 February 2022; pp. 480–485. [Google Scholar]
- Cardona, J.L.; Howland, M.F.; Dabiri, J.O. Seeing the Wind: Visual Wind Speed Prediction with a Coupled Convolutional and Recurrent Neural Network. arXiv
**2019**, arXiv:1905.13290. [Google Scholar] - PyTorch. Torch.torchvision.model. Available online: https://pytorch.org/vision/stable/models.html (accessed on 15 October 2022).
- Zhang, Z.; Sabuncu, M. Generalized cross entropy loss for training deep neural networks with noisy labels. In Proceedings of the Advances in Neural Information Processing Systems, Montréal, QC, Canada, 3–8 December 2018; Volume 31. [Google Scholar]
- Ho, Y.S.; Samuel, W. The Real-World-Weight Cross-Entropy Loss Function: Modeling the Costs of Mislabeling. IEEE Access
**2020**, 8, 4806–4813. [Google Scholar] [CrossRef]

**Figure 6.**Flooding images of the engine room in flooding scenario 43; from left to right, the time is 1 s, 3 s, 5 s, 10 s, 30 s.

Hyperparameter | Chosen Value |
---|---|

LSTM layers | 2 |

Hidden units per LSTM layer | 256 |

Input size | 512 |

Batch size | 16 |

Epoch | 180 |

Learning late | 0.001 |

Parameters | Particulars | Model | Cruise Ship |
---|---|---|---|

Length Overall | Loa (m) | 1.517 | 303.500 |

Length between perpendiculars | Lpp (m) | 1.435 | 287.100 |

Breadth | B (m) | 0.168 | 33.500 |

Height | H (m) | 0.120 | 24.055 |

Draft | D (m) | 0.041 | 8.260 |

Displacement Tonnage | D.T (kg) | 8.375 | 6.716 × 10^{7} |

Metacentric height | GM (m) | 0.010 | 2.070 |

Height of metacenter above keel | KM (m) | 0.102 | 20.370 |

Height of Centre of Gravity above keel | KG (m) | 0.092 | 18.300 |

The Time of Input | Minimum Loss | Epoch |
---|---|---|

5 s | 24.45 | 173 |

10 s | 23.58 | 140 |

15 s | 20.68 | 123 |

20 s | 20.10 | 124 |

25 s | 23.00 | 117 |

30 s | 28.06 | 161 |

**Table 4.**The average accuracy rate of four compartments when the opening is in different compartments.

Opening Location | T_{Acc-A} | T_{Acc-B} | T_{Acc-C} | T_{Acc-D} |
---|---|---|---|---|

Compartment A | 85.31% | 93.78% | 91.47% | 95.81% |

Compartment B | 92.78% | 85.65% | 91.77% | 95.50% |

Compartment C | 92.10% | 93.86% | 86.73% | 92.74% |

Compartment D | 93.17% | 91.26% | 91.48% | 90.07% |

Flooding Scenario | Compartment | Predicted (min) | Label (min) | Time Error (min) |
---|---|---|---|---|

21 | A | 4.71 | 2.67 | −2.04 |

50 | D | 14.14 | 22.24 | 8.10 |

59 | D | 14.14 | 22.93 | 8.79 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Li, Z.; Yang, D.; Yin, G. Ship Flooding Time Prediction Based on Composite Neural Network. *J. Mar. Sci. Eng.* **2023**, *11*, 1123.
https://doi.org/10.3390/jmse11061123

**AMA Style**

Li Z, Yang D, Yin G. Ship Flooding Time Prediction Based on Composite Neural Network. *Journal of Marine Science and Engineering*. 2023; 11(6):1123.
https://doi.org/10.3390/jmse11061123

**Chicago/Turabian Style**

Li, Ze, Dongmei Yang, and Guisheng Yin. 2023. "Ship Flooding Time Prediction Based on Composite Neural Network" *Journal of Marine Science and Engineering* 11, no. 6: 1123.
https://doi.org/10.3390/jmse11061123