# Analytical and Computational Modeling for Multi-Degree of Freedom Systems: Estimating the Likelihood of an FOWT Structural Failure

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

#### 2.1. Hydro-Servo-Aero-Elastic Analysis Using FAST

#### 2.2. Hydrodynamics

#### 2.3. Structural Dynamics

#### 2.4. Dynamics of Control System

#### 2.5. Aerodynamics

#### 2.6. Multibody Simulation Using SIMPACK

## 3. System Description

#### 3.1. DTU 10-MW RWT

#### 3.2. Drivetrain’s Design

#### 3.3. Drivetrain Layout

#### 3.4. OO-Star Semi-Submersible FWT Floater with Mooring System

#### 3.5. Load Cases and Environmental Conditions

_{10}) is the significant wave height (H

_{S}), and the peak-period is (T

_{p})

- U(z): Wind speed at the level z
- U
_{ref}: Wind speed at the reference height - Z
_{ref}: Reference height - α: Empirical wind–shear exponent

## 4. Novel Reliability Method

## 5. Failure Probability Estimation

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**(

**Up**): Four-point support FWT configuration gearbox. (

**Down**): 10-MW FWT drivetrain design in MBS software [32].

**Figure 3.**OO-Star FWT wind floater’s semi-10-MW concept [31].

**Figure 4.**Illustration on how two system component processes X and Y are combined into one new synthetic vector R. The red ellipse highlights a case of simultaneous maxima for different system components.

**Figure 6.**Extrapolation of ${p}_{k}\left(\lambda \right)$ (on the y-axis) towards the critical level (marked by star) and beyond, conditioning index $k=6$. Extrapolated 95% CI marked by dotted lines. Horizontal x-axis corresponds to the non-dimensional parameter $\lambda $.

**Table 1.**DTU-10-MW RWT design summary [13].

Description | Values |
---|---|

Rating | 10 MW |

Rotor orientation and its configuration | Upwind and 3 blades |

Rotor and hub diameters | 178.3 m, 5.6 m |

FWT hub height | 119 m |

Cut-in, rated, and cut-out wind-speed | 4.0 m/s, 11.4 m/s, 25.0 m/s |

Cut-in, rated rotor speed | 6.0 RPM, 9.6 RPM |

FWT-rated tip speed | 90 m/s |

Overhang, shaft tilt, pre-cone | 7.07 m, 5°, 2.5° |

Rotor mass | 229 tons (each blade ~41 tons) |

FWT nacelle mass | 446 tons |

Tower mass | 605 tons |

Parameters | Values |
---|---|

FWT gearbox ratio | 1:50 |

Minimum rotor speed (rpm) | 6.0 |

Rated rotor speed (rpm) | 9.6 |

Rated generator speed (rpm) | 480.0 |

Electrical generator efficiency | 94.0 |

Generator inertia about high-speed shaft (kg·m^{2}) | 1500.5 |

Free–free rigid shaft torsion mode natural frequency | 4.0 |

Free–fixed rigid shaft torsion mode natural frequency | 0.6 |

Load Cases | ${\mathit{U}}_{\mathit{w}}\text{}(\mathbf{m}/\mathbf{s})$ | ${\mathit{T}}_{\mathit{I}}$ | ${\mathit{H}}_{\mathit{s}}\text{}\left(\mathbf{m}\right)$ | ${\mathit{T}}_{\mathit{p}}\text{}(\mathbf{s})$ | Samples | Simulation Length (hours) |
---|---|---|---|---|---|---|

LC1 | 8 | 0.1740 | 1.9 | 9.7 | 24 | 1 |

LC2 | 12 | 0.1460 | 2.5 | 10.1 | 24 | 1 |

LC3 | 16 | 0.1320 | 3.2 | 10.7 | 24 | 1 |

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## Share and Cite

**MDPI and ACS Style**

Gaidai, O.; Xu, J.; Yakimov, V.; Wang, F.
Analytical and Computational Modeling for Multi-Degree of Freedom Systems: Estimating the Likelihood of an FOWT Structural Failure. *J. Mar. Sci. Eng.* **2023**, *11*, 1237.
https://doi.org/10.3390/jmse11061237

**AMA Style**

Gaidai O, Xu J, Yakimov V, Wang F.
Analytical and Computational Modeling for Multi-Degree of Freedom Systems: Estimating the Likelihood of an FOWT Structural Failure. *Journal of Marine Science and Engineering*. 2023; 11(6):1237.
https://doi.org/10.3390/jmse11061237

**Chicago/Turabian Style**

Gaidai, Oleg, Jingxiang Xu, Vladimir Yakimov, and Fang Wang.
2023. "Analytical and Computational Modeling for Multi-Degree of Freedom Systems: Estimating the Likelihood of an FOWT Structural Failure" *Journal of Marine Science and Engineering* 11, no. 6: 1237.
https://doi.org/10.3390/jmse11061237