# Model of Bio-Colonisation on Mooring Lines: Updating Strategy Based on a Static Qualifying Sea State for Floating Wind Turbines

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## Abstract

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## 1. Introduction

- a reduction of mooring line’s minimum tension, leading to an increased risk of “slack event” [7] (fast tensioning of the line).
- a reduction of line’s buoyancy, accelerating wearing by rubbing with the seabed.
- a shift of natural frequencies towards larger periods at which the floater has larger response amplitudes [8].
- an increase of effective tension’s variance [8].

## 2. Materials and Methods

#### 2.1. An a Priori Spatial Distribution of Bio-Colonisation

#### 2.1.1. Data

**th${}_{ext}$**, as defined in Figure 3, is obtained. This is an important remark because considering thickness as t or

**th${}_{ext}$**as an impact on the considered volume of bio-colonisation and so on the considered range of density of bio-colonisation. In the following, the thickness is defined as

**th${}_{ext}$**.

- Mussels colonisation is a so-called hard macro-colonisation. The fluid interaction with a solid body, instead of a soft body, can be modelled through the Morison equation.
- The settlement of mussels after the installation of the offshore structure is fast, usually in one year.
- Mussels are plentiful in the first 20 m under the Mean Water Level (MWL), but can also colonise deeper (cf. data from Spraul et al. [8]) because they sustain a wide range of temperature.
- In a certain extent, mussels can resist to mooring lines perturbations reinforcing their byssal threads, with which they attach themselves to the mooring line or others mussels. Mussels could then occupy the space during a long term [20].

#### 2.1.2. Modelling

- A decrease of thickness with depth.
- The emergence of bulbs or lumps identifiable by peaks and deeps of thickness along the line.
- A correlated geospatial process.

#### 2.1.3. Parameters Identification & Model Uncertainty

#### 2.1.4. Density of Bio-Colonisation

#### 2.2. Reduction of the Uncertainty of our Prior Model

- the storms which can result in high accelerations and vibrations of the mooring lines and so lead to the unhooking of mussels clusters.
- the natural unhooking of multi-layered mussels clusters when they reach a critical size. The external layers can come down during a slack event of the line due to their fragile connection with below layers, which are directly hooked to the mooring line. This phenomenon is well-known by mussel farmers, who remove these external layers before they come down and let the underneath mussels grow.
- the mortality due to attacks of predators such as sea stars (Asterias rubens) or sparus fishes (Sparus aurata).
- the non-monotonous supply of phytoplankton which is depending on phytoplankton bloom and currents.
- The mortality or growth due to extreme variations of environmental parameters such as temperature.
- Pollution or diseases.

- define a realistic case study by presenting the chosen anchoring geometry, by configuring a tension sensing network on it and finally by proposing different realistic scenarii of bio-colonisation called reference mass distributions.
- present the methodology to build samples of posterior distributions of thickness and density parameters, which will depend on the number and the measurement error of tension sensors, and also on the reference mass distribution of bio-colonisation.
- introduce a robust estimator to quantify the reduction of uncertainty between prior and posterior distributions.

#### 2.2.1. Realistic Mass Distributions of Bio-Colonisation and Parametrisation of Distributed Sensors on a Monitored Mooring Line of a FWT

- Only one tension sensor close to the fairlead (red in Figure 15).
- Two tension sensors (green). One close to the fairlead and a second in the middle of the line.
- Three tension sensors (orange). One close to the fairlead, a second at one-third of the line and a last at two-third of the line.
- Four tension sensors (blue). One close to the fairlead, a second at one-quarter of the line, a third in the middle of the line and a last at three-quarter of the line.

#### 2.2.2. Updating a Priori Model from Measurements

- installation uncertainties:
- −
- the position of the anchor which influences $\alpha $ and the pretension.
- −
- the position, orientations and draft of the floater which also influence $\alpha $ and the pretension $Pt$.

- manufacturing uncertainties:
- −
- the length and the diameter of the mooring line which influence the mass and volume of the mooring line.

#### 2.2.3. Estimate for Uncertainty Reduction from SHM

## 3. Results and Discussion

- On which parameter uncertainty (a, b, ${\sigma}_{residuals}$, ${l}_{c}$ or $\rho $) does the proposed methodology (cf. Figure 16) act?
- Does the uncertainty narrow around the reference value (cf. Table 4)?
- For parameters whose uncertainty is reduced, is the metric linked with: the reference case? The error of measurement? The number of sensors?

#### 3.1. Efficiency of the Methodology

#### 3.2. Sensitivity Analysis

- the reduction of uncertainty on a is strongly correlated with the number of sensors, strongly uncorrelated with the case of colonisation and uncorrelated with the error of measurement.
- the reduction of uncertainty on b is strongly correlated with the case of colonisation, correlated with the number of sensors and dimly correlated with the error of measurement.
- the reduction of uncertainty on $\rho $ is correlated with the number of sensors, dimly correlated with the error of measurement and strongly uncorrelated with the case of colonisation.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ADF | Augmented Dickey-Fuller |

AIC | Akaike Information Criterion |

cdf | cumulative density function |

CoV | Coefficient of Variation |

DFT | Discrete Fourier Transform |

FFT | Fast Fourier Transform |

FPU | Floating Production Unit |

FWT | Floating Wind Turbine |

GEV | Generalised Extrem Value |

KPSS | Kwiatkowski-Phillips-Schmidt-Shin |

KS | Kolmogorov-Smirnov |

LSE | Least-Squares Estimation |

MCS | Monte-Carlo Sampling |

MLE | Maximum Likelihood Estimation |

MWL | Mean Water Level |

probability density function | |

QSS | Qualifying Sea State |

RLHS | Random Latin Hypercube Sampling |

SCAP | Spatial Correlation Assessment Procedure |

SHM | Structural Health Monitoring |

Std | Standard deviation |

VIV | Vortex Induced Vibrations |

## Appendix A. Experimental Trajectories

#### Appendix A.1. From a Previous Article on the SEMREV Test Site

**Figure A1.**Thickness of mussels colonisation on mooring lines of the SEMREV before summer 2017 [8].

#### Appendix A.2. From Videotapes

## Appendix B. Generation of the Thicknesses for the Deeps

- First (I), we generate a Gaussian field for the residuals at peak positions (blue), following Equation (2) but with ${\mu}_{residuals}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}0.0195$ m $>\phantom{\rule{3.33333pt}{0ex}}0$.
- Second (II), for each peak thickness, now considered to be the reference value $T{h}_{peak,\phantom{\rule{3.33333pt}{0ex}}ref}$ ($=9$ in Figure A5), we generate correlated samplings of deep and peak thicknesses from uniform distributions around the reference value, using a Gaussian copula and a correlation coefficient ${\rho}_{Deep/Peak}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}0.78083$. Peak thicknesses are uniformly sampled between $T{h}_{peak}\phantom{\rule{3.33333pt}{0ex}}-\phantom{\rule{3.33333pt}{0ex}}\delta $ and $T{h}_{peak}\phantom{\rule{3.33333pt}{0ex}}+\phantom{\rule{3.33333pt}{0ex}}\delta $. The upper and lower bounds for the sampling of deep thicknesses (doted lines) are respectively the antecedents of $T{h}_{peak}\phantom{\rule{3.33333pt}{0ex}}+\phantom{\rule{3.33333pt}{0ex}}\delta $ and $T{h}_{peak}\phantom{\rule{3.33333pt}{0ex}}-\phantom{\rule{3.33333pt}{0ex}}\delta $ by the linear fit of experimental thicknesses of the deep-peak pairs (cf. Figure 9).
- Third (III), we stop the generation of samplings when we find a sampling whose peak thickness $T{h}_{peak,\phantom{\rule{3.33333pt}{0ex}}sampling}$ is close enough to the reference value ($|T{h}_{peak,\phantom{\rule{3.33333pt}{0ex}}ref}-T{h}_{peak,\phantom{\rule{3.33333pt}{0ex}}sampling}|\phantom{\rule{3.33333pt}{0ex}}<\phantom{\rule{3.33333pt}{0ex}}0.0005$ m). The deep thickness of the selected sampling (7 in Figure A5) is then assigned to the deep position upstream the peak position of the reference peak thickness.

## Appendix C. Differential Entropy of a Truncated Normal Distribution

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**Figure 3.**Definition of thickness (t) commonly used in standards vs. Practical measurement of thickness (

**th${}_{ext}$**) on-site.

**Figure 4.**Photograph of bio-colonisation on East cardinal buoy mooring chain of the SEMREV test site in February 2018.

**Figure 5.**Trajectory of the bio-colonisation thickness on East cardinal buoy mooring chain in February 2018.

**Figure 14.**Density ${\rho}_{ocp}$ (kg·m${}^{-3}$) of mussels colonisation depending on its thickness.

**Figure 16.**Building samplings of posterior distributions of thickness and density parameters in calm sea state from tension measurements.

**Figure 18.**Histograms of the conditional entropy metric for ${\sigma}_{residuals}$ and ${l}_{c}$ (56 scenarii).

**Figure 19.**Histograms of the conditional entropy metric considering (a, b and $\rho $) parameters depending on the number of sensors.

**Figure 20.**Histograms of the conditional entropy metric considering only (a) parameter depending on the number of sensors.

a (m) | b | |
---|---|---|

East Mooring before summer 2017 | $0.044;\phantom{\rule{3.33333pt}{0ex}}a\phantom{\rule{3.33333pt}{0ex}}\in \phantom{\rule{3.33333pt}{0ex}}[0.030;0.059]$ | $-0.0010;\phantom{\rule{3.33333pt}{0ex}}b\phantom{\rule{3.33333pt}{0ex}}\in \phantom{\rule{3.33333pt}{0ex}}[-0.002;0]$ |

West Mooring before summer 2017 | $0.036;\phantom{\rule{3.33333pt}{0ex}}a\phantom{\rule{3.33333pt}{0ex}}\in \phantom{\rule{3.33333pt}{0ex}}[0.018;0.054]$ | $-0.0003;\phantom{\rule{3.33333pt}{0ex}}b\phantom{\rule{3.33333pt}{0ex}}\in \phantom{\rule{3.33333pt}{0ex}}[-0.0016;0.0009]$ |

East Mooring in February 2018 | $0.082;\phantom{\rule{3.33333pt}{0ex}}a\phantom{\rule{3.33333pt}{0ex}}\in \phantom{\rule{3.33333pt}{0ex}}[0.069;0.094]$ | $-0.0016;\phantom{\rule{3.33333pt}{0ex}}b\phantom{\rule{3.33333pt}{0ex}}\in \phantom{\rule{3.33333pt}{0ex}}[-0.0030;-0.0002]$ |

East Mooring in May 2018 | $0.140;\phantom{\rule{3.33333pt}{0ex}}a\phantom{\rule{3.33333pt}{0ex}}\in \phantom{\rule{3.33333pt}{0ex}}[0.113;0.166]$ | $-0.0051;\phantom{\rule{3.33333pt}{0ex}}b\phantom{\rule{3.33333pt}{0ex}}\in \phantom{\rule{3.33333pt}{0ex}}[-0.0074;-0.0029]$ |

**Table 2.**Identification of ${\sigma}_{residuals}^{2}$ and ${l}_{c}$ and their $95\%$ confidence bounds.

${\mathit{\sigma}}_{\mathit{r}\mathit{e}\mathit{s}\mathit{i}\mathit{d}\mathit{u}\mathit{a}\mathit{l}\mathit{s}}^{2}$ (m${}^{2}$) | ${\mathit{l}}_{\mathit{c}}$ (m) | ||
---|---|---|---|

East Mooring before summer 2017 | MLE | $4.3\times {10}^{-4};\phantom{\rule{3.33333pt}{0ex}}{\sigma}^{2}\phantom{\rule{3.33333pt}{0ex}}\in \phantom{\rule{3.33333pt}{0ex}}[6.7\times {10}^{-5};7.9\times {10}^{-4}]$ | $2.38;\phantom{\rule{3.33333pt}{0ex}}{l}_{c}\phantom{\rule{3.33333pt}{0ex}}\in \phantom{\rule{3.33333pt}{0ex}}[-0.20;4.96]$ |

West Mooring before summer 2017 | MLE | $6.4\times {10}^{-4};\phantom{\rule{3.33333pt}{0ex}}{\sigma}^{2}\phantom{\rule{3.33333pt}{0ex}}\in \phantom{\rule{3.33333pt}{0ex}}[1.2\times {10}^{-4};1.2\times {10}^{-3}]$ | $2.38;\phantom{\rule{3.33333pt}{0ex}}{l}_{c}\phantom{\rule{3.33333pt}{0ex}}\in \phantom{\rule{3.33333pt}{0ex}}[-0.16;4.52]$ |

East Mooring in February 2018 | LSE | $2.1\times {10}^{-3};\phantom{\rule{3.33333pt}{0ex}}{\sigma}^{2}\phantom{\rule{3.33333pt}{0ex}}\in \phantom{\rule{3.33333pt}{0ex}}[2.0\times {10}^{-3};2.2\times {10}^{-3}]$ | $1.24;\phantom{\rule{3.33333pt}{0ex}}{l}_{c}\phantom{\rule{3.33333pt}{0ex}}\in \phantom{\rule{3.33333pt}{0ex}}[1.14;1.33]$ |

East Mooring in May 2018 | MLE | $1.5\times {10}^{-3};\phantom{\rule{3.33333pt}{0ex}}{\sigma}^{2}\phantom{\rule{3.33333pt}{0ex}}\in \phantom{\rule{3.33333pt}{0ex}}[-4.8\times {10}^{-4};3.5\times {10}^{-3}]$ | $0.78;\phantom{\rule{3.33333pt}{0ex}}{l}_{c}\phantom{\rule{3.33333pt}{0ex}}\in \phantom{\rule{3.33333pt}{0ex}}[-0.29;1.85]$ |

**Table 3.**Definition of three different densities depending on interstitial and intervalvular waters.

Interstitial Water Volume | Intervalvular Water Mass | |
---|---|---|

The “open porosity” density (${\rho}_{op}$) | ✓ | × |

The “closed porosity” density (${\rho}_{cp}$) | × | ✓ |

The “open and closed” porosity density (${\rho}_{ocp}$) | ✓ | ✓ |

Name of the Scenario | ${\mathit{a}}_{\mathit{r}\mathit{e}\mathit{f}}$ (m) | ${\mathit{b}}_{\mathit{r}\mathit{e}\mathit{f}}$ | ${\mathit{\sigma}}_{\mathit{r}\mathit{e}\mathit{s}\mathit{i}\mathit{d}\mathit{u}\mathit{a}\mathit{l}\mathit{s},\phantom{\rule{3.33333pt}{0ex}}\mathit{r}\mathit{e}\mathit{f}}$ (m) | ${\mathit{l}}_{\mathit{c},\phantom{\rule{3.33333pt}{0ex}}\mathit{r}\mathit{e}\mathit{f}}$ (m) | ${\mathit{\rho}}_{\mathit{r}\mathit{e}\mathit{f}}$ (kg·m${}^{-3}$) |
---|---|---|---|---|---|

Unfavourable site (US) | $0.09$$\left(\updownarrow \right)$ | $-0.018$$\left(\downarrow \right)$ | $0.034$$\left(\updownarrow \right)$ | $1.8$$\left(\uparrow \right)$ | 720 $\left(\uparrow \right)$ |

Favourable site after some months (FS) | $0.04$$\left(\downarrow \right)$ | $-0.0025$$\left(\uparrow \right)$ | $0.018$$\left(\downarrow \right)$ | $1.1$$\left(\updownarrow \right)$ | 380 $\left(\downarrow \right)$ |

Full developed in favourable site (FD) | $0.17$$\left(\uparrow \right)$ | $-0.006$$\left(\updownarrow \right)$ | $0.05$$\left(\uparrow \right)$ | $1.1$$\left(\updownarrow \right)$ | 550 $\left(\updownarrow \right)$ |

After a storm (AS) | $0.035$$\left(\downarrow \right)$ | $-0.0017$$\left(\uparrow \right)$ | $0.06$$\left(\uparrow \right)$ | 2 $\left(\uparrow \right)$ | 550 $\left(\updownarrow \right)$ |

Name of the Scenario | 1 Sensor (kg) | 2 Sensors (kg) | 3 Sensors (kg) | 4 Sensors (kg) |
---|---|---|---|---|

Unfavourable site | 465 | $[465;0]$ | $[465;0;0]$ | $[465;0;0;0]$ |

Favourable site after some months | 848 | $[848;0]$ | $[795;53;0]$ | $[648;200;0;0]$ |

Full developed in favourable site | $\mathrm{12,600}$ | $[\mathrm{10,375};2225]$ | $[8184;3594;822]$ | $[6761;3614;1791;434]$ |

After a storm | 2863 | $[2863;0]$ | $[1676;1187;0]$ | $[1512;1351;0;0]$ |

Probabilistic Distribution | |
---|---|

a (m) | Uniform $[0.01;0.2]$ |

b | Uniform $[-0.02;-0.0017]$ |

${\sigma}_{residuals}$ (m) | Truncated normal (Mean: $0.034$ m; Std: $0.013$ m; ${\sigma}_{max}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}0.06$ m; ${\sigma}_{min}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}0.008$ m) |

${l}_{c}$ (m) | Truncated normal (Mean: $1.1$ m; Std: $0.45$ m; ${l}_{c,\phantom{\rule{3.33333pt}{0ex}}max}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}2$ m; ${l}_{c,\phantom{\rule{3.33333pt}{0ex}}min}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}0.2$ m) |

$\rho $ (kg·m${}^{-3}$) | Uniform $[300;800]$ |

Differential Entropy in Nats | Source | |
---|---|---|

$X\phantom{\rule{3.33333pt}{0ex}}\sim $ Uniform $\left(\right)$ | $H\left(X\right)\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}ln\left(\right)open="("\; close=")">{U}_{2}-{U}_{1}$ | [27] |

$X\phantom{\rule{3.33333pt}{0ex}}\sim \phantom{\rule{3.33333pt}{0ex}}$ Truncated normal $\mathrm{Mean}:\phantom{\rule{4.pt}{0ex}}\mu ;\phantom{\rule{4.pt}{0ex}}\mathrm{Std}:\phantom{\rule{4.pt}{0ex}}\sigma ;$ $\phantom{\rule{4.pt}{0ex}}\mathrm{Min}:\phantom{\rule{4.pt}{0ex}}{t}_{1};\phantom{\rule{4.pt}{0ex}}\mathrm{Max}:\phantom{\rule{4.pt}{0ex}}{t}_{2}$ | $H\left(X\right)\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}{\displaystyle \frac{1}{2}}ln\left(\right)open="("\; close=")">2\pi {\sigma}^{2}$ $\frac{1}{\sqrt{2\pi}}}{\displaystyle \frac{{T}_{1}{e}^{-{\displaystyle \frac{{T}_{1}^{2}}{2}}}-{T}_{2}{e}^{-{\displaystyle \frac{{T}_{2}^{2}}{2}}}+\sqrt{{\displaystyle \frac{\pi}{2}}}\left(\right)open="("\; close=")">erf\left({\displaystyle \frac{{T}_{2}}{\sqrt{2}}}\right)-erf\left({\displaystyle \frac{{T}_{1}}{\sqrt{2}}}\right)}{}2\left(\right)open="("\; close=")">\mathsf{\Phi}\left(\right)open="("\; close=")">{T}_{2}-\mathsf{\Phi}\left(\right)open="("\; close=")">{T}_{1}$ $ln\left(\right)open="("\; close=")">\mathsf{\Phi}\left(\right)open="("\; close=")">{T}_{2}$ | Appendix C |

Reference Mass Distribution | Number of Sensors | Relative Error $\mathsf{\Delta}$ of Tension Measurement$(\%)$ |
---|---|---|

Favourable site after some months | 4 | 5 |

Full developed in favourable site | 3 4 | 5 5 |

After a storm | 3 3 4 4 4 | 5 10 5 10 15 |

**Table 9.**Student’s t-test: the alternative hypothesis ($h\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}1$) is that the mean of the metric is greater than 0.

a | b | ${\mathit{\sigma}}_{\mathit{r}\mathit{e}\mathit{s}\mathit{i}\mathit{d}\mathit{u}\mathit{a}\mathit{l}\mathit{s}}$ | ${\mathit{l}}_{\mathit{c}}$ | $\mathit{\rho}$ | |
---|---|---|---|---|---|

h | 1 | 1 | 0 | 0 | 1 |

p-value | $2.25\times {10}^{-22}$ | $5.30\times {10}^{-7}$ | $9.99\times {10}^{-1}$ | $9.71\times {10}^{-1}$ | $5.2\times {10}^{-3}$ |

Nb Sensors | a | b | $\mathit{\rho}$ | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | ||

US | $\Delta =5\%$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | × | × | × | × |

$\Delta =10\%$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | × | × | × | × | |

$\Delta =15\%$ | × | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | × | × | × | × | |

$\Delta =20\%$ | ✓ | × | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | × | × | × | × | |

FS | $\Delta =5\%$ | ✓ | ✓ | ✓ | □ | × | × | × | □ | ✓ | ✓ | ✓ | □ |

$\Delta =10\%$ | ✓ | ✓ | ✓ | ✓ | × | × | × | ✓ | ✓ | ✓ | ✓ | ✓ | |

$\Delta =15\%$ | ✓ | ✓ | ✓ | ✓ | × | × | × | ✓ | ✓ | ✓ | ✓ | ✓ | |

$\Delta =20\%$ | ✓ | ✓ | ✓ | ✓ | × | × | × | ✓ | ✓ | ✓ | ✓ | ✓ | |

FD | $\Delta =5\%$ | ✓ | ✓ | □ | □ | ✓ | ✓ | □ | □ | Reference value | |||

$\Delta =10\%$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |||||

$\Delta =15\%$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |||||

$\Delta =20\%$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | Prior mean = | ||||

AS | $\Delta =5\%$ | × | × | □ | □ | × | × | □ | □ | Reference value | |||

$\Delta =10\%$ | × | × | □ | □ | × | × | □ | □ | |||||

$\Delta =15\%$ | × | × | ✓ | □ | × | × | ✓ | □ | |||||

$\Delta =20\%$ | × | × | ✓ | ✓ | × | × | ✓ | ✓ | Prior mean = |

Colonisation Case | Number of Sensors | Error of Measurement $\left(\mathsf{\Delta}\right)$ | |
---|---|---|---|

Pearson | Corr $=0.0067$ p-value $=0.9608$ | Corr $=0.5797$ p-value $=2.8381\times {10}^{-6}$ | Corr $=0.1205$ p-value $=0.3765$ |

Spearman | Corr $=-0.0274$ p-value $=0.8411$ | Corr $=0.5695$ p-value $=4.64\times {10}^{-6}$ | Corr $=0.0435$ p-value $=0.7503$ |

Colonisation Case | Number of Sensors | Error of Measurement $\left(\mathsf{\Delta}\right)$ | |
---|---|---|---|

Pearson | Corr $=0.4352$ p-value $=8.0251\times {10}^{-6}$ | Corr $=0.3970$ p-value $=0.0025$ | Corr $=0.1774$ p-value $=0.1908$ |

Spearman | Corr $=0.4026$ p-value $=0.0021$ | Corr $=0.2045$ p-value $=0.1305$ | Corr $=0.2626$ p-value $=0.0506$ |

Colonisation Case | Number of Sensors | Error of Measurement $\left(\mathsf{\Delta}\right)$ | |
---|---|---|---|

Pearson | Corr $=0.0032$ p-value $=0.9814$ | Corr $=0.4114$ p-value $=0.0016$ | Corr $=0.0728$ p-value $=0.5939$ |

Spearman | Corr $=0.0384$ p-value $=0.7790$ | Corr $=0.2057$ p-value $=0.1283$ | Corr $=0.2944$ p-value $=0.0276$ |

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## Share and Cite

**MDPI and ACS Style**

Decurey, B.; Schoefs, F.; Barillé, A.-L.; Soulard, T.
Model of Bio-Colonisation on Mooring Lines: Updating Strategy Based on a Static Qualifying Sea State for Floating Wind Turbines. *J. Mar. Sci. Eng.* **2020**, *8*, 108.
https://doi.org/10.3390/jmse8020108

**AMA Style**

Decurey B, Schoefs F, Barillé A-L, Soulard T.
Model of Bio-Colonisation on Mooring Lines: Updating Strategy Based on a Static Qualifying Sea State for Floating Wind Turbines. *Journal of Marine Science and Engineering*. 2020; 8(2):108.
https://doi.org/10.3390/jmse8020108

**Chicago/Turabian Style**

Decurey, Benjamin, Franck Schoefs, Anne-Laure Barillé, and Thomas Soulard.
2020. "Model of Bio-Colonisation on Mooring Lines: Updating Strategy Based on a Static Qualifying Sea State for Floating Wind Turbines" *Journal of Marine Science and Engineering* 8, no. 2: 108.
https://doi.org/10.3390/jmse8020108