# A Digital Twin for Assessing the Remaining Useful Life of Offshore Wind Turbine Structures

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Background

## 3. Methodology

#### 3.1. Digital Twin Platform

#### 3.2. Remaining Useful Life

#### 3.2.1. Finite Element Method

- 1.
- Assume that the nodal response of the spatial discretization can be represented by a modal basis, as follows:$$u(x,t)=\sum _{i=1}^{\infty}{q}_{i}\left(t\right)\xb7{a}_{i}\left(x\right)$$
- 2.
- The modal basis can be obtained from the eigendecomposition of the following dynamic problem, where $\lambda $ represents the eigenvalues.$$M\ddot{u}+Ku=0\to \left({M}^{-1}K\right){a}_{i}={\lambda}_{i}{a}_{i}$$
- 3.
- Consequently, the entire dynamic equation is as follows:$$M\left[\sum _{i=1}^{\infty}{\ddot{q}}_{i}\left(t\right)\xb7{a}_{i}\left(x\right)\right]+C\left[\sum _{i=1}^{\infty}{\dot{q}}_{i}\left(t\right)\xb7{a}_{i}\left(x\right)\right]+K\left[\sum _{i=1}^{\infty}{q}_{i}\left(t\right)\xb7{a}_{i}\left(x\right)\right]=f\left(t\right)$$

#### 3.2.2. Fatigue

- Similar to the behavior described in Figure 13, the behavior of a laminate ply is characterized by its serial and parallel components, where stresses ($\sigma $) and deformations ($\epsilon $) can be described as follows:$$\sigma =\left[\begin{array}{c}{\sigma}_{p}\\ {\sigma}_{s}\end{array}\right]\phantom{\rule{1.em}{0ex}},\text{\hspace{0.33em}}\epsilon =\left[\begin{array}{c}{\epsilon}_{p}\\ {\epsilon}_{s}\end{array}\right]$$
- Compatibility equations, also known as the Reuss–Voigt hypothesis [17,18], are defined as follows:$${\left[{\sigma}_{s}\right]}_{\mathrm{composite}}={\left[{\sigma}_{s}\right]}_{\mathrm{matrix}}={\left[{\sigma}_{s}\right]}_{\mathrm{fibre}}\phantom{\rule{1.em}{0ex}},\text{\hspace{0.33em}}{\left[{\epsilon}_{p}\right]}_{\mathrm{composite}}={\left[{\epsilon}_{p}\right]}_{\mathrm{matrix}}={\left[{\epsilon}_{p}\right]}_{\mathrm{fibre}}$$
- The theory employs the rule of mixtures (ROM), where $\varphi $ represents the volumetric fraction.$${\sigma}_{\mathrm{composite}}=\varphi \xb7{\sigma}_{\mathrm{fibre}}+(1-\varphi )\xb7{\sigma}_{\mathrm{matrix}}$$
- Consequently, the transverse serial stress of the fiber must be equal to that of the matrix (Equation (5)). Combined with Equation (6), this poses a minimization problem. This results in a formulation where both the serial and parallel stresses depend on the deformation of the matrix phase. If the constitutive model is elastic, then the classical orthotropic constitutive matrix is obtained. The advantage of the SPROM is that it allows for simulating damage (non-linear constitutive models) based on the damage rheology of its fiber and matrix phases.

#### 3.2.3. Summary

- Utilizing a finite element method approach to obtain the stress history at the Gauss point level.
- Implementing a cycle-counting algorithm, such as the rainflow algorithm, adapted to avoid excessive data storage and to enable real-time cycle prediction.
- Applying a fatigue damage model, such as the Palmgren–Miner rule, to establish the RUL metric.

## 4. Showcase

#### 4.1. Environmental Load Monitoring

#### 4.2. Predictive Maintenance

## 5. Implementation

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Tao, F.; Zhang, H.; Liu, A.; Nee, A.Y. Digital Twin in Industry: State-of-the-Art. IEEE Trans. Ind. Inform.
**2019**, 15, 2405–2415. [Google Scholar] [CrossRef] - Issa, R.; Hamad, M.S.; Abdel-Geliel, M. Digital Twin of Wind Turbine Based on Microsoft
^{®}Azure IoT Platform. In Proceedings of the 2023 IEEE Conference on Power Electronics and Renewable Energy, CPERE, Luxor, Egypt, 19–21 February 2023. [Google Scholar] [CrossRef] - AWS Architecture Blog. Physics on AWS: Optimizing Wind Turbine Performance Using OpenFAST in a Digital Twin. Available online: https://aws.amazon.com/blogs/architecture/physics-on-aws-optimizing-wind-turbine-performance-using-openfast-in-a-digital-twin/ (accessed on 24 March 2024).
- Haghshenas, A.; Hasan, A.; Osen, O.; Mikalsen, E.T. Predictive digital twin for offshore wind farms. Energy Inform.
**2023**, 6, 1. [Google Scholar] [CrossRef] - Wiser, R.; Bolinger, M.; Hoen, B.; Millstein, D.; Rand, J.; Barbose, G.; Darghouth, N.; Gorman, W.; Jeong, S.; Paulos, B. Land-Based Wind Market Report: 2023 Edition; Lawrence Berkeley National Laboratory (LBNL): Berkeley, CA, USA, 2023.
- Arvesen, A.; Hertwich, E.G. Assessing the life cycle environmental impacts of wind power: A review of present knowledge and research needs. Renew. Sustain. Energy Rev.
**2012**, 16, 5994–6006. [Google Scholar] [CrossRef] - Arvesen, A.; Hertwich, E.G. Environmental implications of large-scale adoption of wind power: A scenario-based life cycle assessment. Environ. Res. Lett.
**2011**, 6, 045102. [Google Scholar] [CrossRef] - Wagner, H.J.; Baack, C.; Eickelkamp, T.; Epe, A.; Lohmann, J.; Troy, S. Life cycle assessment of the offshore wind farm alpha ventus. Energy
**2011**, 36, 2459–2464. [Google Scholar] [CrossRef] - CORDIS|European Commission. Development, Engineering, Production and Life-Cycle Management of Improved FIBRE-Based Material Solutions for Structure and Functional Components of Large Offshore Wind EnerGY and Tidal Power Platform|FIBREGY Project|H2020|. Available online: https://cordis.europa.eu/project/id/952966 (accessed on 24 March 2024).
- OSI4IOT Platform. Available online: https://github.com/osi4iot/osi4iot (accessed on 24 March 2024).
- Di Capua, D.; Pacheco, R.; García-Espinosa, J.; Pastor, A. OSI4IOT: An Advanced Open-Source Platform for Sensor-Driven IoT and Digital Twins Deployment. Available online: https://www.researchgate.net/publication/372883021_OSI4IOT_An_Advanced_Open-Source_Platform_for_Sensor-driven_IoT_and_Digital_Twins_Deployment (accessed on 24 March 2024).
- Petiteau, J.C.; Paboeuf, S. Fatigue assessment of composites partsfor Marine Renewable Energy converters. In Proceedings of the 15th International Symposium on Practical Design of Ships and Other Floating Structures PRADS 2022, Dubrovnik, Croatia, 9–13 October 2022. [Google Scholar]
- Pacheco, R.; Di Capua, D.; Garcia, J.; Casals, O. Methodology and application to assess thermo-mechanical buckling in composite marine structures. Ocean Eng.
**2023**, 267, 113002. [Google Scholar] [CrossRef] - Pacheco-Blazquez, R.; Di Capua, D.; García-Espinosa, J.; Casals, O.; Hakkarainen, T. Thermo-mechanical analysis of laminated composites shells exposed to fire. Eng. Struct.
**2022**, 253, 113679. [Google Scholar] [CrossRef] - García-Espinosa, J.; Serván-Camas, B.; Calpe-Linares, M. High Fidelity Hydroelastic Analysis Using Modal Matrix Reduction. J. Mar. Sci. Eng.
**2023**, 11, 1168. [Google Scholar] [CrossRef] - Rastellini, F.; Oller, S.; Salomón, O.; Oñate, E. Composite materials non-linear modelling for long fibre-reinforced laminates. Comput. Struct.
**2008**, 86, 879–896. [Google Scholar] [CrossRef] - Voigt, W. Ueber die Beziehung zwischen den beiden Elasticitätsconstanten isotroper Körper. Ann. Phys.
**1889**, 274, 573–587. [Google Scholar] [CrossRef] - Reuss, A. Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle. ZAMM-J. Appl. Math. Mech./Z. Angew. Math. Und Mech.
**1929**, 9, 49–58. [Google Scholar] [CrossRef] - Sutherland, H.J.; Mandell, J.F. Optimized Constant-Life Diagram for the Analysis of Fiberglass Composites Used in Wind Turbine Blades. J. Sol. Energy Eng.
**2005**, 127, 563–569. [Google Scholar] [CrossRef] - Miner, M.A. Cumulative Damage in Fatigue. J. Appl. Mech.
**1945**, 12, A159–A164. [Google Scholar] [CrossRef] - Palmgren, A. Die lebensdauer von kugellagern. Z. Vereins Dtsch. Ingenieure
**1924**, 68, 339–341. [Google Scholar] - Mérigaud, A.; Ringwood, J.V. Condition-based maintenance methods for marine renewable energy. Renew. Sustain. Energy Rev.
**2016**, 66, 53–78. [Google Scholar] [CrossRef] - Yi, X.; Ng, C.; McKeever, P.; Little, C.; Hillmansen, S. Life estimation modelling for power electronics used in wind turbines. In Proceedings of the 7th IET International Conference on Power Electronics, Machines and Drives (PEMD 2014), Manchester, UK, 8–10 April 2014. [Google Scholar] [CrossRef]
- Antonopoulos, A.; Drarco, S.; Hernes, M.; Peftitsis, D. Challenges and strategies for a real-time implementation of a rainflow-counting algorithm for fatigue assessment of power modules. In Proceedings of the 2019 IEEE Applied Power Electronics Conference and Exposition—APEC, Anaheim, CA, USA, 17–21 March 2019; pp. 2708–2713. [Google Scholar] [CrossRef]
- Musallam, M.; Johnson, C.M. An efficient implementation of the rainflow counting algorithm for life consumption estimation. IEEE Trans. Reliab.
**2012**, 61, 978–986. [Google Scholar] [CrossRef] - Vasconcelos, D.; Vieira, M.; Dias, D.; Reis, L. Structural Evaluation of the DeepCWind Offshore Wind Foundation. Frat. Ed Integrità Strutt.
**2020**, 14, 24–44. [Google Scholar] [CrossRef] - Berdugo-Parada, I.; Servan-Camas, B.; Garcia-Espinosa, J.; Berdugo-Parada, I.; Servan-Camas, B.; Garcia-Espinosa, J. Numerical Framework for the Coupled Analysis of Floating Offshore Multi-Wind Turbines. J. Mar. Sci. Eng.
**2023**, 12, 85. [Google Scholar] [CrossRef]

**Figure 1.**OPEX Cost Trends. The “2022” label pertains to data acquired during the 2022 survey, not to data collected in the years preceding the survey, adapted from [5].

**Figure 2.**Median O&M cost versus project age and the combined impact of digital twins and wind turbines. Adapted from [5].

**Figure 3.**Greenhouse gas emissions for offshore and onshore wind turbines, adapted from [7].

**Figure 7.**Blender serves as the de facto external tool for generating the metadata and geometry data required to construct the digital twin in the web platform.

**Figure 8.**The platform incorporates Grafana technology for seamless integration. Grafana’s dashboards enable the visualization of data ingested from sensors.

**Figure 15.**Illustration of a constant fatigue life (CFL) diagram, adapted from [19].

**Figure 16.**A cycle-counting algorithm is used to determine the number of cycles based on the stress history.

**Figure 19.**The wind load, the stress history for the region with maximum fatigue, and the remaining useful life.

**Figure 20.**Two snapshots of the FEM mesh for the von Misses stress. In accordance with the load history from Figure 19. (

**a**) One hour ago. (

**b**) Now.

**Figure 21.**Two snapshots of the mesh for the RUL results. In accordance with the load history from Figure 19. (

**a**) One hour ago. (

**b**) Now.

**Figure 22.**Sensor data displayed in a Grafana dashboard. The displayed measures of interest include strains, accelerations, and a safety factor calculated based on the ratio between the allowable stress and the maximum stress recorded.

**Figure 26.**The W2POWER structure, real footage and reconversion. (

**a**) The W2POWER floating wind turbine from EnerOcean. (

**b**) Reconverted carbon tower.

**Figure 27.**The geographical representation of the W2POWER wind turbine deployment using OSI4IOT GIS, showcasing its location in the Oceanic Platform of the Canary Islands (PLOCAN) in Spain.

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Pacheco-Blazquez, R.; Garcia-Espinosa, J.; Di Capua, D.; Pastor Sanchez, A.
A Digital Twin for Assessing the Remaining Useful Life of Offshore Wind Turbine Structures. *J. Mar. Sci. Eng.* **2024**, *12*, 573.
https://doi.org/10.3390/jmse12040573

**AMA Style**

Pacheco-Blazquez R, Garcia-Espinosa J, Di Capua D, Pastor Sanchez A.
A Digital Twin for Assessing the Remaining Useful Life of Offshore Wind Turbine Structures. *Journal of Marine Science and Engineering*. 2024; 12(4):573.
https://doi.org/10.3390/jmse12040573

**Chicago/Turabian Style**

Pacheco-Blazquez, Rafael, Julio Garcia-Espinosa, Daniel Di Capua, and Andres Pastor Sanchez.
2024. "A Digital Twin for Assessing the Remaining Useful Life of Offshore Wind Turbine Structures" *Journal of Marine Science and Engineering* 12, no. 4: 573.
https://doi.org/10.3390/jmse12040573