# Digital Twin for the Prediction of Extreme Loads on a Wave Energy Conversion System

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. State of the Art

## 3. Wave Energy Converter and CFD Model

#### 3.1. CFD Model

#### 3.1.1. Numerical Methods

_{b}includes the external forces.

_{c}= min[c

_{α}|V|, max(|V|)], where c

_{α}= 1. The MULES algorithm is implemented to ensure that α $\in \text{}$[0, 1] and the interface compression scheme is used to maintain sharp interfaces during the CFD simulation.

#### 3.1.2. Force Modeling

_{line}, acting on the buoy, and it points toward the fixed anchoring position.

_{line}is the sum of the forces applied by the generator, consisting of the translator weight, the generator damping force F

_{damping}, and the force due to the compression of the upper and lower end-stop springs. In later generations of the Uppsala University WEC, only an upper end-stop spring is used, F

_{spring}, and the same setting will be used in this work. The spring force appears once the translator exceeds the upper free stroke length and hits the upper end-stop spring. When the upper spring is fully compressed, the connection line acts as an elastic cable, which adds further force, F

_{add}, to the system. The generator damping force, F

_{damping}, varies according to the generator velocity. Once the translator exceeds the lower free-stroke length, it rests at the lower position of the generator hull with the connection line being slack, leading to the uncoupled buoy–translator motion.

_{line}, as described above. In summary, the dynamics of the buoy and the generator are described by the coupled equations of motion:

_{b}is the mass of the buoy, and r is the position vector of the buoy. The equations are applied in the CFD simulation by an in-house developed restraint, capturing the physical behavior of the system. The line force F

_{line}should always point downward; otherwise, it is set equal to zero. In other words, the line can never push the buoy away, only pull the buoy toward the generator. The generator damping force, F

_{damping}, is determined as:

_{thres}is a velocity threshold. The spring force, F

_{spring}, is nonzero when the translator exceeds the free-stroke length, and the additional elastic line force, F

_{add}, is nonzero when the translator exceeds total stroke length (free stroke length + spring length):

_{spring}and k

_{mooring}is the spring and mooring line stiffness, respectively, and r

_{rest}is the line length when the buoy is resting when the water level is still. When the translator exceeds the downward stroke length, the line slacks. This is implemented through the δ

_{down}function. Table 1 provides the physical properties of the WEC in the present study. The buoy has a cylindrical shape

#### 3.1.3. Computational Domain

_{p}/Δz). The study reveals that monotonic convergence is observed and the ratio can be taken equal to A

_{p}/Δz = 17. For this choice, the inferred discretization uncertainty is less than 1%. The cells are kept orthogonal (Δx = Δy = Δz) in the refined region close the water surface to generate wave with better shape. Figure 2 also shows the enlarge area around the WEC where one can see the refined region with height of 2A

_{p}, the one level lower refinement region of 2A

_{p}, and the overset mesh. The overset dynamic mesh technique was utilized due to the extreme wave nature and the expected great structural response. The overset mesh is a cubic area surrounding the floating body with high resolution, almost equal to the resolution of the refined region in the water surface. The authors have utilized the overset method in several studies [9,10,12]. Due to the utilization of k-ω SST turbulence model, wall functions are adapted to solve the boundary layer. Therefore, good discretization is required around the WEC. The y+ is kept within the range of [30, 300] as stated by [50].

^{6}to 31 × 10

^{6}cells. All the cases were run on the Tetralith HPC cluster using 128 processors. Each case can utilize 3584–11,776 CPU hours, depending on the number of computational cells.

## 4. Digital Twin Method

**Step 1. Selection of DT input parameters.**The initial step is the identification of the DT input parameters, alongside the corresponding value range for each input parameter. These parameters are the ones mainly affecting the behavior of the mooring force. Detailed analysis is found in the Section entitled “Selection of the input parameters”.

**Step 2. Design and training of the DT model**. The DT provides the output prediction utilizing a mathematical model based on the statistical developed by [24]. The definition of the training data sets is based on the design of experiments (DoE) method as defined by the Taguchi approach [35]. Once the range of input parameters has been selected, the most suitable orthogonal array is defined. As this study focuses on extreme waves, a high-fidelity CFD model is expected to provide an accurate estimate. However, this choice poses the restraint of limited simulations due to high computational cost. As a compromise between sufficiently many simulations to provide enough training data and feasible computational cost for the CFD simulations, 25 tests will be conducted based on the L25 orthogonal array. The CFD simulations are conducted based on those experiment sets. The results are then utilized to train the DT model.

**Step 3. Validation of the DT model**. Once the DT is trained, its capability to accurately predict the output (i.e., the mooring force) has to be tested. For that reason, a new set of data is selected for testing purposes. In this study, 50 test data sets are randomly chosen. Again, CFD simulations are performed to estimate the mooring force for the testing cases. As a last step, the results obtained from the DT model for the testing data are compared with the CFD solution. An error analysis is necessary to obtain a quantitative measure of the agreement between the prediction and the solution.

#### 4.1. Selection of the Input Parameters

- Significant wave height, H
_{s}[m] - Wave peak period, T
_{p}[s] - PTO damping coefficient, γ [N]
- PTO upper end-stop spring stiffness, k
_{spring}[N/m]

**Extreme wave selection**: In offshore renewable energy engineering, a common practice for the selection of the design waves relies on the 50-year return period environmental contour for a particular study site [55]. This approach has been considered by many authors [9,56,57,58,59]. In our study, the environmental contour for the Dowsing site, shown in Figure 4, is utilized for the wave selection. The Dowsing site is located in the North Sea, 56 km from the west coast of the United Kingdom, with water depth of 22 m. The same location has been considered in previous studies, also with the focus of extreme wave characterization and survivability [10,58].

_{s}, and peak period, T

_{p}, with range of values along and inside the environmental contour line Figure 4. Therefore, the assigned ranges for these parameters are: H

_{s}= 2.5–6.8 m and T

_{p}= 8.3–14.1 s (Table 2).

_{p}A

_{p}, provided in Table 3 and Table 4 as an additional information. However, the wave steepness does not constitute an input parameter to the DT model.

#### 4.2. Digital Twin Construction

_{25}orthogonal array is used offering high resolution, examining five values for each input parameter. As a result, the L

_{25}implies that 25 CFD simulations are required to create the digital twin.

_{1}(H

_{s}

_{1}) = f

_{11}, F

_{2}(T

_{p}

_{1}) = f

_{21}, F

_{3}(γ

_{1}) = f

_{31}, F

_{4}(k

_{spring}

_{1}) = f

_{41}, etc.). The matrix defined in Equation (16) summarizes the values of each input parameter. The two matrices are combined and form the Cartesian points (Equation (17)).

_{s}, the matrix of Equation (19) takes the form of Equation (20). The continues model is shown in Figure 5, plot B. The repetition of the previous steps (step 2–4) will result to a set of four graphs with the continuous input parameter effects (step 5). The final step (step 6) integrates all the results to one single model (Equation (18)) that is able to predict the dynamic mooring force, as CFD simulations would calculate, for any set of input parameter values. Furthermore, the effect of each individual input parameter is reflected on the mooring force.

#### 4.3. Training Procedure

_{25}orthogonal array, 25 experiments are required for the creation of the digital twin model. Table 3 presents the experimental matrix based on the L

_{25}and the input parameters values. The experiments will be conducted using CFD simulations as described in the next Section entitled “CFD model”.

#### 4.4. Validation Procedure

## 5. Results

#### 5.1. Preliminary Results

#### 5.2. Results from the Enhanced Digital Twin Model2

_{initial}) and enhanced (DT

_{ench}) DTs as well as the accuracy of the additional 3 DTs, which were used to enhance the capability of the initial DT to predict more accurately the three peaks forces (Peak

_{1}, Peak

_{2}, Peak

_{3}). The average global accuracy $\overline{A}$ of the enhanced DT was calculated as 90.36% by averaging the individual accuracy of the data sets No. 1–50. The average global accuracy $\overline{A}$ of the initial DT model is 82.46%, which is significantly lower than the accuracy of the enhanced DT, underlining the importance of the enhanced DT. The peaks in the mooring force are evaluated separately and the drawn conclusion is that they are predicted with high average global accuracy $\overline{A}$ in the range 83.82–91.05%. From the 3 peaks, Peak

_{2}is the most critical, which is always the higher force acting in the mooring line. The average global accuracy $\overline{A}$ of the Peak

_{2}, as predicted by the enhanced DT, is 86.51%.

_{2}for the 50 testing data sets and how they compare to the numerical solution. The Peak

_{2}was selected because it is the most important among the three peaks, as it always presents the maximum value corresponding to the focal time of the focused wave. The data sets are depicted with red and blue dots with the latter showing better prediction when compared with the numerical results. For the red area, the prediction accuracy drops. The reason is that the red region consists of the data sets No. 26–50 for which the significant wave height, H

_{s}, is greater than the range of the training data sets. That is to say, while for training the DT, the H

_{s}= 3.5–6.8 m, some of the testing data No. 26–50 exceed this range (H

_{s}> 6.8 m). This does not happen for the testing data sets No. 1–25, which are always within the range.

#### 5.3. Sensitivity to Input Parameters

_{1}, F

_{2}, F

_{3}, and F

_{4}, respectively.

_{s}, has the maximum influence (F

_{1}= 140 kN) when H

_{s}> 7 m. For small values of H

_{s}, the mooring force is negatively affected as compared to the mean value. The wave peak period shows the maximum contribution for shorter waves, T

_{p}< 10 s, implying that steeper waves result in the increase of the mooring force. The contribution of wave period reaches up to F

_{2}= 120 KN. The influence of the PTO characteristics, F

_{3}and F

_{4}, is less compared to the wave characteristics. In particular, the maximum value of F

_{3}is 40 kN and occurs for large damping coefficient, γ, while the maximum value of F

_{4}is 30 kN and mainly appears for large spring stiffness.

_{2}. As mentioned earlier, Peak

_{2}is critical not only for the design stage but also for the safe operation of the system. Figure 10 shows the influence of each input parameter in Peak

_{2}. The wave height follows a linear trend. For H

_{s}> 5 m, the mooring force significantly increases; otherwise, for smaller waves, the force tends to get smaller values as compared to the mean. The wave period parameter presents the minimum contribution at T

_{p}= 11 s. For very short waves (T

_{p}= 8 s) and for very long waves (T

_{p}> 13 s), the influence of the wave peak period increases significantly. The PTO damping coefficient contributes to the higher increase in the mooring force (γ > 70 kN), while the stiffness of the upper end-stop spring contributes to an increasing trend for k

_{spring}> 800 kN. In the present study, the PTO damping coefficient has been kept constant throughout each wave condition, which is consistent with a no-control or passive control approach. From the results, the PTO damping affects the experienced loads. This is consistent with earlier studies, which confirmed both experimentally [62,63] and numerically [9,64] that the extreme loads depend on the applied PTO damping. In general, while the PTO damping and the spring stiffness affect the mooring line force, the influence of the wave height is several magnitudes higher.

## 6. Discussion

_{2}, was estimated with an accuracy of 86.51%.

## 7. Conclusions

_{s}> 5 m) and extreme waves, while the model gives an understanding of how to select properly the PTO characteristics in order to reduce the peaks in the mooring force.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**Left**) Illustration of the point-absorber WEC. Figure adopted from Castellucci and Strömstedt (2019) under the Creative Commons Attribution CC-BY license. (

**Right**) Illustration of the PTO system, which is a direct-driven linear generator with limited stroke length. Figure adopted from Sjökvist and Göteman (2019) with permission from Elsevier Ltd., UK.

**Figure 2.**NWT in the xz plane, showing the boundaries’ labeling and dimensions, where λ and d are the wave length and water depth, respectively. The enlargement of the area around the buoy shows the computational mesh.

**Figure 4.**50-year environmental contour for Dowsing site, UK. The waves are chosen along and inside the black line, which has been generated based on the I-FORM hybrid method. Source: Figure adopted from [10] under the Creative Commons Attribution CC-BY license.

**Figure 6.**The force in the mooring system is illustrated, as calculated by the CFD simulation and as predicted by the initial DT model. The initial DT does not give satisfactory accuracy in the peaks of the force, which motivates the construction of the enhanced DT model.

**Figure 7.**Scatter plot (numerical versus predicted) for the maximum peak in the mooring line force The test data are categorized depending on the value of the significant wave height, H

_{s}; the blue dots show the trend when the value of H

_{s}is within the range of the training data, while the red dots show the prediction when greater values are assigned to H

_{s}.

**Figure 8.**Results from the initial and enhanced digital twin model as compared to the CFD solution. As shown in Figure 7, the data sets No. 7, 24, and 25 have input parameter values within the range of the training data for the DT, which explains their good fit to the CFD results, whereas No. 28, 29, and 42 are based on input parameters outside the range of the training data, which explains their poorer fit.

**Figure 9.**Influence of the input parameters on the mooring line force. (

**A**) F1 vs. significant wave height, (

**B**) F2 vs. Wave peak period, (

**C**) F3 vs. PTO damping coefficient and (

**D**) F4 vs. Upper Spring stiffness.

**Figure 10.**Influence of the input parameters in the maximum mooring force, Peak

_{2.}(

**A**) F1 peak

_{2}vs. significant wave height, (

**B**) F2 peak

_{2}vs. Wave peak period, (

**C**) F3 peak

_{2}vs. PTO damping coefficient and (

**D**) F4 peak

_{2}vs. Upper Spring stiffness.

**Table 1.**Physical properties of the buoy and PTO. The generator damping and upper end-stop spring stiffness are input parameters, which vary for the training and testing purposes of the DT.

Parameter | Value | Unit |
---|---|---|

Buoy diameter | 3.4 | m |

Buoy height | 2.12 | m |

Buoy draft | 1.3 | m |

Buoy mass | 5736 | Kg |

Center of mass | (0, 0, 1.55) | m |

Translator mass | 6240 | Kg |

Generator damping | Input parameter | N |

Upper end-stop spring stiffness | Input parameter | N/m |

Upper end-stop spring length | 0.6 | m |

Upper/lower free stroke length | 1.2/1.2 | m |

Levels | 1 | 2 | 3 | 4 | 5 | |
---|---|---|---|---|---|---|

Significant wave height | H_{s} [m] | 2.5 | 5.2 | 6.1 | 6.8 | 7.5 |

Peak period | T_{p} [m] | 5 | 8.3 | 9.6 | 12.7 | 14.1 |

Generator damping | γ [KN] | 48.898 | 59 | 64.558 | 70.398 | 85.550 |

Spring Stiffness | k_{spring} [KN/m] | 682.238 | 728.702 | 758.938 | 844.766 | 951.856 |

**Table 3.**Assigned values for the training data sets: generator damping, γ, upper end-stop stiffness, k

_{spring}, significant wave height, H

_{s}, and peak period, T

_{p}. The waves are numerically simulated as focused waves. Information about the wave steepness, K

_{p}A

_{p}, is included; however, it is not considered as input.

No. | H_{s}[m] | T_{p}[m] | γ [ΚN] | k_{spring}[kN/m] | K_{p}A_{p}[-] |
---|---|---|---|---|---|

1 | 2.5 | 11 | 48.898 | 682.238 | 0.103 |

2 | 2.5 | 8.3 | 59.000 | 728.702 | 0.152 |

3 | 2.5 | 9.6 | 64.558 | 758.938 | 0.123 |

4 | 2.5 | 12.7 | 70.398 | 844.766 | 0.086 |

5 | 2.5 | 14.1 | 85.550 | 951.856 | 0.076 |

6 | 5.2 | 11 | 59.000 | 758.938 | 0.215 |

7 | 5.2 | 8.3 | 64.558 | 844.766 | 0.316 |

8 | 5.2 | 9.6 | 70.398 | 951.856 | 0.257 |

9 | 5.2 | 12.7 | 85.550 | 682.238 | 0.179 |

10 | 5.2 | 14.1 | 48.898 | 728.702 | 0.159 |

11 | 6.1 | 11 | 64.558 | 951.856 | 0.252 |

12 | 6.1 | 8.3 | 70.398 | 682.238 | 0.371 |

13 | 6.1 | 9.6 | 85.55 | 728.702 | 0.302 |

14 | 6.1 | 12.7 | 48.898 | 758.938 | 0.211 |

15 | 6.1 | 14.1 | 59.000 | 844.766 | 0.186 |

16 | 6.8 | 11 | 70.398 | 728.702 | 0.281 |

17 | 6.8 | 8.3 | 85.550 | 758.938 | 0.414 |

18 | 6.8 | 9.6 | 48.898 | 844.766 | 0.336 |

19 | 6.8 | 12.7 | 59.000 | 951.856 | 0.235 |

20 | 6.8 | 14.1 | 64.558 | 682.238 | 0.208 |

21 | 3.5 | 11 | 85.550 | 844.766 | 0.144 |

22 | 3.5 | 8.3 | 48.898 | 951.856 | 0.213 |

23 | 3.5 | 9.6 | 59.000 | 682.238 | 0.173 |

24 | 3.5 | 12.7 | 64.558 | 728.702 | 0.121 |

25 | 3.5 | 14.1 | 70.398 | 758.938 | 0.107 |

**Table 4.**50 datasets considered for the validation of the DT model. PTO damping, γ, spring stiffness, k

_{spring}, significant wave height, H

_{s}, and peak period, T

_{p}, are the input parameters. The magnitude of the wave steepness, K

_{p}A

_{p}, is provided as an additional description illustrating the extreme profile of the waves.

No. | γ [ΚN] | k_{spring}[KN/m] | H_{s}[m] | T_{p}[s] | K_{p}A_{p}[-] | No. | γ [ΚN] | k_{spring}[KN/m] | H_{s}[m] | T_{p}[s] | K_{p}A_{p}[-] |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 53.68 | 929.02 | 5.45 | 8.34 | 0.329 | 26 | 53.68 | 929.02 | 7.04 | 12.05 | 0.260 |

2 | 64.56 | 844.77 | 5.38 | 8.73 | 0.304 | 27 | 64.56 | 844.77 | 6.94 | 12.62 | 0.242 |

3 | 54.55 | 785.73 | 5.87 | 9.23 | 0.306 | 28 | 54.55 | 785.73 | 7.58 | 13.34 | 0.247 |

4 | 69.36 | 782.06 | 6.00 | 8.45 | 0.355 | 29 | 69.36 | 782.06 | 7.75 | 12.20 | 0.282 |

5 | 68.53 | 951.86 | 5.78 | 9.47 | 0.291 | 30 | 68.53 | 951.86 | 7.46 | 13.67 | 0.236 |

6 | 46.44 | 698.91 | 5.16 | 9.83 | 0.247 | 31 | 46.44 | 698.91 | 6.66 | 14.20 | 0.202 |

7 | 51.10 | 740.68 | 5.93 | 8.80 | 0.331 | 32 | 51.10 | 740.68 | 7.65 | 12.70 | 0.264 |

8 | 73.38 | 956.74 | 5.29 | 9.53 | 0.264 | 33 | 73.38 | 956.74 | 6.83 | 13.77 | 0.214 |

9 | 44.48 | 609.77 | 5.53 | 8.22 | 0.342 | 34 | 44.48 | 609.77 | 7.14 | 11.87 | 0.268 |

10 | 57.22 | 860.17 | 5.24 | 8.86 | 0.289 | 35 | 57.22 | 860.17 | 6.76 | 12.80 | 0.232 |

11 | 72.51 | 585.28 | 5.03 | 9.78 | 0.242 | 36 | 72.51 | 585.28 | 6.50 | 14.13 | 0.198 |

12 | 67.18 | 728.70 | 5.49 | 9.38 | 0.280 | 37 | 67.18 | 728.70 | 7.08 | 13.55 | 0.227 |

13 | 49.34 | 631.88 | 5.09 | 9.28 | 0.264 | 38 | 49.34 | 631.88 | 6.56 | 13.40 | 0.213 |

14 | 62.27 | 614.28 | 5.79 | 9.75 | 0.280 | 39 | 62.27 | 614.28 | 7.47 | 14.08 | 0.229 |

15 | 55.48 | 652.14 | 5.71 | 8.49 | 0.336 | 40 | 55.48 | 652.14 | 7.37 | 12.26 | 0.266 |

16 | 61.52 | 667.99 | 5.32 | 8.16 | 0.332 | 41 | 61.52 | 667.99 | 6.86 | 11.79 | 0.260 |

17 | 70.40 | 821.02 | 5.19 | 8.56 | 0.301 | 42 | 70.40 | 821.02 | 6.70 | 12.37 | 0.239 |

18 | 60.23 | 758.94 | 5.42 | 9.14 | 0.286 | 43 | 60.23 | 758.94 | 6.99 | 13.21 | 0.231 |

19 | 58.03 | 900.09 | 4.95 | 9.09 | 0.264 | 44 | 58.03 | 900.09 | 6.39 | 13.13 | 0.213 |

20 | 52.40 | 716.92 | 5.70 | 9.58 | 0.282 | 45 | 52.40 | 716.92 | 7.35 | 13.84 | 0.230 |

21 | 48.90 | 682.24 | 6.01 | 9.68 | 0.294 | 46 | 48.90 | 682.24 | 7.76 | 13.98 | 0.240 |

22 | 59.48 | 878.05 | 5.60 | 8.63 | 0.321 | 47 | 59.48 | 878.05 | 7.23 | 12.47 | 0.256 |

23 | 46.98 | 908.38 | 5.06 | 9.04 | 0.272 | 48 | 46.98 | 908.38 | 6.53 | 13.05 | 0.218 |

24 | 63.51 | 808.66 | 5.90 | 8.93 | 0.322 | 49 | 63.51 | 808.66 | 7.61 | 12.90 | 0.259 |

25 | 66.38 | 864.48 | 5.63 | 8.28 | 0.344 | 50 | 66.38 | 864.48 | 7.27 | 11.96 | 0.270 |

**Table 5.**Accuracy, A, of the DT model for the 50 testing datasets as estimated from the initial DT

_{init}and the enhanced DT model (DT

_{ench}). The accuracy, A, for the three main peaks (Peak

_{1}, Peak

_{2}, and Peak

_{3}) is provided based on the enhanced model.

No. | DT_{init} | DT_{ench} | Peak_{1} | Peak_{2} | Peak_{3} | No. | DT_{init} | DT_{ench} | Peak_{1} | Peak_{2} | Peak_{3} |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 81.11 | 88.83 | 91.32 | 92.35 | 91.03 | 26 | 82.68 | 89.05 | 86.12 | 74.36 | 77.70 |

2 | 80.59 | 87.79 | 89.59 | 95.80 | 93.67 | 27 | 84.41 | 90.78 | 94.94 | 68.51 | 85.93 |

3 | 78.98 | 92.02 | 85.74 | 94.36 | 95.99 | 28 | 87.45 | 94.50 | 96.60 | 79.44 | 59.31 |

4 | 80.11 | 87.16 | 87.86 | 94.80 | 91.98 | 29 | 80.54 | 87.02 | 93.21 | 83.87 | 85.25 |

5 | 79.25 | 86.40 | 86.67 | 94.73 | 81.36 | 30 | 79.86 | 93.43 | 99.72 | 79.06 | 58.82 |

6 | 82.52 | 89.93 | 79.47 | 97.20 | 92.32 | 31 | 86.57 | 93.55 | 99.81 | 82.35 | 65.79 |

7 | 78.27 | 94.09 | 88.79 | 91.83 | 86.66 | 32 | 85.78 | 93.17 | 93.23 | 85.06 | 72.90 |

8 | 80.15 | 86.85 | 88.14 | 97.24 | 83.21 | 33 | 79.90 | 93.08 | 97.66 | 76.15 | 66.31 |

9 | 83.64 | 90.88 | 94.01 | 97.54 | 65.65 | 34 | 82.74 | 90.01 | 94.41 | 74.68 | 76.16 |

10 | 80.14 | 87.13 | 88.47 | 95.84 | 85.15 | 35 | 86.29 | 93.42 | 95.46 | 73.97 | 79.07 |

11 | 81.32 | 88.54 | 84.75 | 99.91 | 78.31 | 36 | 85.43 | 92.35 | 99.88 | 91.11 | 90.41 |

12 | 79.47 | 86.15 | 84.95 | 95.75 | 95.82 | 37 | 82.17 | 90.24 | 96.96 | 68.58 | 77.14 |

13 | 82.72 | 90.44 | 86.72 | 96.92 | 76.67 | 38 | 86.50 | 93.35 | 99.67 | 81.11 | 76.03 |

14 | 76.75 | 86.50 | 85.74 | 95.12 | 91.00 | 39 | 84.48 | 91.48 | 97.54 | 65.64 | 76.68 |

15 | 81.60 | 89.44 | 90.99 | 92.07 | 79.16 | 40 | 85.25 | 92.27 | 94.89 | 79.99 | 80.95 |

16 | 83.64 | 90.53 | 91.46 | 96.43 | 77.84 | 41 | 78.62 | 90.89 | 64.14 | 72.85 | 97.08 |

17 | 81.19 | 88.18 | 90.31 | 99.17 | 98.77 | 42 | 81.17 | 92.22 | 94.32 | 78.24 | 89.09 |

18 | 79.39 | 89.11 | 85.16 | 94.67 | 91.32 | 43 | 86.99 | 93.93 | 95.46 | 67.82 | 97.56 |

19 | 80.88 | 87.14 | 86.97 | 93.79 | 91.22 | 44 | 87.70 | 94.48 | 98.61 | 82.86 | 90.31 |

20 | 81.85 | 89.10 | 82.36 | 95.86 | 92.29 | 45 | 86.53 | 93.42 | 97.59 | 73.93 | 63.28 |

21 | 81.24 | 88.62 | 84.37 | 97.33 | 95.29 | 46 | 84.99 | 91.77 | 99.59 | 72.72 | 57.50 |

22 | 79.36 | 86.95 | 88.87 | 92.62 | 92.23 | 47 | 85.04 | 92.94 | 86.71 | 80.53 | 87.16 |

23 | 81.60 | 88.79 | 90.04 | 97.35 | 90.46 | 48 | 87.15 | 94.17 | 97.29 | 83.79 | 76.06 |

24 | 78.34 | 84.97 | 87.60 | 94.68 | 99.15 | 49 | 84.08 | 91.43 | 95.24 | 82.26 | 98.82 |

25 | 83.13 | 90.00 | 90.36 | 95.76 | 97.18 | 50 | 83.34 | 89.60 | 92.83 | 77.67 | 92.09 |

Avg | 82.46 | 90.36 | 91.05 | 86.51 | 83.82 |

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**MDPI and ACS Style**

Katsidoniotaki, E.; Psarommatis, F.; Göteman, M.
Digital Twin for the Prediction of Extreme Loads on a Wave Energy Conversion System. *Energies* **2022**, *15*, 5464.
https://doi.org/10.3390/en15155464

**AMA Style**

Katsidoniotaki E, Psarommatis F, Göteman M.
Digital Twin for the Prediction of Extreme Loads on a Wave Energy Conversion System. *Energies*. 2022; 15(15):5464.
https://doi.org/10.3390/en15155464

**Chicago/Turabian Style**

Katsidoniotaki, Eirini, Foivos Psarommatis, and Malin Göteman.
2022. "Digital Twin for the Prediction of Extreme Loads on a Wave Energy Conversion System" *Energies* 15, no. 15: 5464.
https://doi.org/10.3390/en15155464