# Simulating Ship Manoeuvrability with Artificial Neural Networks Trained by a Short Noisy Data Set

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Description of the Manoeuvring Tests

_{C}and η

_{C}for the manoeuvre’s starting point (Figure 2):

_{R}is the rudder angle, r is the yaw rate, V is the speed of the ship, V

_{A}is the relative wind speed, β

_{A}is the wind drift angle, and χ

_{A}is the wind course angle.

## 3. Neural Network Training

- Rudder angle θ(k);
- RPM(k);
- Sway velocity at previous time step v(k − 1);
- Heading angle at previous time step $\psi $(k − 1);
- x position at previous time step x(k − 1);
- y position at previous time step y(k − 1);

- Heading angle at current time step $\psi $(k);
- x position at current time step x(k);
- y position at current time step y(k).

_{k}is the error in the k

^{th}exemplar and e is the vector of the elements e

_{k}. If the discrepancy between the preceding weight vector and the current one is small, the vector of the errors can be approximated to the first order using Taylor series expansion:

^{T}J

## 4. Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ANN | Artificial neural network |

RNN | Recursive neural network |

MMG | Manoeuvring Mathematical Group |

LSTM | Long short-term memory |

SVM | Support vector machine |

CMU | Command and monitoring unit |

CCU | Communication and control unit |

HMI | Human–machine interface |

IES | Industrial Ethernet switch |

MLP | Multilayer perceptron |

RPM | Revolutions per minute |

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Chemical Tanker | Real Ship | Model |
---|---|---|

Length (m) | 170 | 2.588 |

Breadth (m) | 28 | 0.426 |

Draft (estimated at the tests) (m) | 6.7 | 0.102 |

Propeller diameter (m) | 5.4 | 0.082 |

Design speed (m/s) | 8 | 0.984 |

Scaling coefficient | - | 65.7 |

# | Parameter | Unit | Equipment |
---|---|---|---|

1 | Geographical coordinates | deg | Real-time kinematic GPS |

2 | Surge and sway | m | IXSEA inertial sensor |

3 | Roll and pitch angles | deg | IXSEA inertial sensor |

4 | Heading angle | deg | IXSEA inertial sensor |

5 | Relative wind speed | m/s | Ultrasonic anemometer |

6 | Relative wind direction | deg | Ultrasonic anemometer |

7 | Rudder angle | deg | Incremental encoder |

8 | Propeller rev. | rpm | Incremental encoder |

Maneuvere | Data Points Available | Rudder Angle Range (Degrees) | Average RPM | Average Realwind Speed (Knots) | Wind Conditions |
---|---|---|---|---|---|

ZigZag1 | 748 | [−30, 30] | 856 | 2.7 (max 8.6) | Light Air to Gentle Breeze |

ZigZag2 | 614 | [−30, 30] | 873 | 2.2 (max 7.9) | Light Air to Gentle Breeze |

ZigZag3 | 565 | [−20, 20] | 844 | 2.1 (max 8.3) | Light Air to Gentle Breeze |

ZigZag4 | 954 | [−20, 20] | 669 | 3.0 (max 10.4) | Light Air to Gentle Breeze |

Turning1 | 992 | [0, 20] | 487 | 1.3 (max 11.4) | Light Air to Moderate Breeze |

Turning2 | 1356 | [0, 26] | 492 | 1.2 (max 11.8) | Light Air to Moderate Breeze |

Set | ||||
---|---|---|---|---|

Method | Training | Validation | Test | All |

Levenberg–Marquardt | 0.99332 | 0.994538 | 0.99202 | 0.99333 |

Scaled Conjugate Gradient | 0.99339 | 0.990813 | 0.9961 | 0.9934 |

Bayesian Regularization | 0.99259 | 0.993147 | 0.99753 | 0.99314 |

Set | ||||
---|---|---|---|---|

Method | Training | Validation | Test | All |

Levenberg–Marquardt | 0.99998 | 0.999978 | 0.99998 | 0.99998 |

Scaled Conjugate Gradient | 0.99998 | 0.999981 | 0.99998 | 0.99998 |

Bayesian Regularization | 0.99998 | 0.99998 | 0.99998 | 0.99998 |

Set | ||||
---|---|---|---|---|

Method | Training | Validation | Test | All |

Levenberg–Marquardt | 0.99995 | 0.999954 | 0.99995 | 0.99995 |

Scaled Conjugate Gradient | 0.99995 | 0.999949 | 0.99995 | 0.99995 |

Bayesian Regularization | 0.99995 | 0.999948 | 0.99995 | 0.99995 |

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**MDPI and ACS Style**

Moreira, L.; Guedes Soares, C.
Simulating Ship Manoeuvrability with Artificial Neural Networks Trained by a Short Noisy Data Set. *J. Mar. Sci. Eng.* **2023**, *11*, 15.
https://doi.org/10.3390/jmse11010015

**AMA Style**

Moreira L, Guedes Soares C.
Simulating Ship Manoeuvrability with Artificial Neural Networks Trained by a Short Noisy Data Set. *Journal of Marine Science and Engineering*. 2023; 11(1):15.
https://doi.org/10.3390/jmse11010015

**Chicago/Turabian Style**

Moreira, Lúcia, and C. Guedes Soares.
2023. "Simulating Ship Manoeuvrability with Artificial Neural Networks Trained by a Short Noisy Data Set" *Journal of Marine Science and Engineering* 11, no. 1: 15.
https://doi.org/10.3390/jmse11010015