# Black-Box Marine Vehicle Identification with Regression Techniques for Random Manoeuvres

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## Abstract

**:**

## 1. Introduction

## 2. Surface Marine Vehicle Identification

#### 2.1. Experimental System and Dataset

#### 2.2. Model Formulation

## 3. Machine Learning Techniques

#### 3.1. Ridge Regression

#### 3.2. Kernel Ridge Regression

#### 3.3. Symbolic Regression

- A random initial population is created.
- The fitness of the members of the population is evaluated.
- The ’stop if’ condition is evaluated (a given accuracy, number of generations, etc.).
- A next generation of solutions is formed by combining the selected members of the population using different operators (crossover, mutation, reproduction, etc.). Go back to step 2.

## 4. Results

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Training (blue), validation (red) and test (green) sets: (

**a**) surge speed, (

**b**) sway speed, (

**c**) yaw rate, (

**d**) rudder angle, and (

**e**) tension of the motor.

**Figure 4.**Freerun simulation diagram. At time ${t}_{0}$, the input variables are given from the sensors, and for $t>0$ the speed inputs for $t+1$ are the predicted values in t.

**Figure 5.**$\lambda $-parameter selection for kernel RBF. The units for the RMSE curves in all subplots are $m/s$ for surge speed (u) and sway speed (v), and rad/s for the yaw rate (r).

**Figure 6.**$\sigma $-parameter selection for kernel RBF. The units for the RMSE curves in all subplots are $m/s$ for surge speed (u) and sway speed (v), and rad/s for the yaw rate (r).

**Figure 7.**Validation set for the best models with the polynomial kernel (

**a**) surge speed, (

**d**) sway speed, (

**g**) yaw rate; SR (

**b**) surge speed, (

**e**) sway speed, (

**h**) yaw rate; and SOA-SR (

**c**) surge speed, (

**f**) sway speed, (

**i**) yaw rate.

**Figure 8.**Test set for best models with the polynomial kernel (

**a**) surge speed, (

**d**) sway speed, (

**g**) yaw rate; SR (

**b**) surge speed, (

**e**) sway speed, (

**h**) yaw rate; and SOA-SR (

**c**) surge speed, (

**f**) sway speed, (

**i**) yaw rate.

Parameter | Vessel [m] | Scale Ship [m] |
---|---|---|

Length between perpendiculars (${L}_{pp}$) | 74.40 | 4.389 |

Maximum beam (B) | 14.20 | 0.838 |

Mean depth to the top deck | 9.05 | 0.534 |

Design draught (${T}_{m}$) | 6.30 | 0.372 |

Model | RMSE Train [u-v-r] | RMSE Validation [u-v-r] |
---|---|---|

RBF | $0.0777-0.0739-0.0137$ | $0.1784-0.1372-0.0391$ |

Polynomial $p=1$ | $0.1059-0.0793-0.0209$ | $0.1653-0.1050-0.0154$ |

Polynomial $p=2$ | $0.0773-0.0765-0.0146$ | $0.1645-0.1148-0.0181$ |

Symbolic Regression | $0.2614-0.2422-0.1085$ | $0.3482-0.2861-0.1150$ |

Model | RMSE Validation [u-v-r] | RMSE Test [u-v-r] |
---|---|---|

Polynomial $p=2$ | $0.1645-0.1148-0.0181$ | $0.2249-0.2211-0.0654$ |

Symbolic Regression | $0.3482-0.2861-0.1150$ | $0.3279-0.3153-0.1077$ |

SOA-SR | $0.4255-0.3700-0.1895$ | $0.3403-0.3302-0.1788$ |

SOA-LSSVM (Blanke model) | $0.8835-0.3166-0.3963$ | $0.7350-0.2936-0.4169$ |

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**MDPI and ACS Style**

Moreno, R.; Moreno-Salinas, D.; Aranda, J.
Black-Box Marine Vehicle Identification with Regression Techniques for Random Manoeuvres. *Electronics* **2019**, *8*, 492.
https://doi.org/10.3390/electronics8050492

**AMA Style**

Moreno R, Moreno-Salinas D, Aranda J.
Black-Box Marine Vehicle Identification with Regression Techniques for Random Manoeuvres. *Electronics*. 2019; 8(5):492.
https://doi.org/10.3390/electronics8050492

**Chicago/Turabian Style**

Moreno, Raul, David Moreno-Salinas, and Joaquin Aranda.
2019. "Black-Box Marine Vehicle Identification with Regression Techniques for Random Manoeuvres" *Electronics* 8, no. 5: 492.
https://doi.org/10.3390/electronics8050492