1. Introduction

2. Background

3. Methodology

3.2. Remaining Useful Life

The methodology proposed in this paper is based on the finite element method and combined with a fatigue assessment formulation [9].

3.2.1. Finite Element Method

The formulation utilized in the spatial discretization involves linear triangles [10] and bilinear quadrilaterals [11].

Figure 10. Illustration of the mechanical discretization.

Figure 10. Illustration of the mechanical discretization.

The through-thickness integration is shown in Figure 11, employing a layerwise approach, given that the materials involved in the simulation are composites.

Another crucial aspect to consider is a method that enables the real-time structural response to be obtained. To achieve this, a reduced order model (ROM) is integrated according to [12], the floating structure employed in the ROM hydroelastic analysis is the public OC4 from the DeepCwind project. The fundamental concepts can be summarized as follows:

• Assume that the nodal response of the spatial discretization can be represented by a modal basis

  $$u(x,t)=\sum _{i=1}^{\infty }{q}_i\left(t\right)·a_i\left(x\right)$$

  (1)

  where u is the displacement field, q is the temporal variation of modal amplitudes, and a is the modal basis.
• The modal basis can be obtained from the eigendecomposition of the following dynamic problem, where $\lambda$ represents the eigenvalues.

  $$M\ddot{u}+Ku=0\to \left(M^{-1}K\right)a_i={\lambda }_i{a}_i$$

  (2)
• Consequently, the entire dynamic equation becomes.

  $$M\left[\sum _{i=1}^{\infty }{\ddot{q}}_i\left(t\right)·a_i\left(x\right)\right]+C\left[\sum _{i=1}^{\infty }{\dot{q}}_i\left(t\right)·a_i\left(x\right)\right]+K\left[\sum _{i=1}^{\infty }{q}_i\left(t\right)·a_i\left(x\right)\right]=f\left(t\right)$$

  (3)

The approach is best described in Figure 12, where the OC4 deformation modes are given. For a given spectrum, the characteristic modes are computed and stored. Then, with a provided environmental load, the real-time solution can be determined based on the precomputed modes.

3.2.2. Fatigue

The objective of this article is to integrate not only to provide a framework that can obtain the real-time hydroelastic response of an offshore floating wind turbine (OFWT), but to predict the lifecycle of the OFWT. In order to monitor the lifecycle of the structure, a fatigue model proposed by Petiteau and Paboeuf [9] will be adapted to later obtain the remaining useful life (RUL) index. This model is orthotropic and designed for composite constitutive materials stacked layerwise. Each layer may consist of one or two materials, where one layer represents just a core material and a layer with two materials represents the combination of fiber and matrix materials, respectively.

In Figure 13, the characteristic stresses, ${\sigma }_p$ and ${\sigma }_s$, of a laminate layer are presented. These local stresses include the parallel component aligned with the fiber orientation and the serial component orthogonal to the fiber orientation.

The methodology by Petiteau and Paboeuf primarily focuses on transverse fatigue because the directions perpendicular to the fibers are the weakest. Consequently, a failure envelope rule is proposed for the two weakest stress components: serial stress ${\sigma }_s$ and in-plane shear stress ${\tau }_{ps}$ (refer to Figure 14). The fatigue mechanism employs a similar approach to fluency rules, where the fatigue limit decreases due to the loss of mechanical properties. As the loss region expands, the mechanical limits for in-plane shear and serial stress are reduced. The model also accounts for non-symmetric behavior in compression and tension states, although in-plane shear is considered symmetric.

The variation of the fatigue limit is characterized by the S-N curves. However, in the case of orthotropic composite materials, a separate curve must be established for each combination of fiber and matrix, volumetric fraction, and ply orientation. As a result, the extensive experimental characterization required for numerous combinations becomes costly and can be a limitation for the current application of this methodology. On the other hand, the serial-parallel theory [13] or in short SPROM, a non-linear constitutive technique, is introduced to obtain the orthotropic behavior of composites based on the isotropic properties of the constituent materials that make up the laminate (fiber and matrix). By employing this approach, it is necessary to characterize only the S-N curves in the parallel (0°) and serial (90°) directions.

The Serial-Parallel Rule of Mixtures (SPROM) can be succinctly described as follows:

• 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.

  $$\begin{array}{ccc}\sigma =\left[\begin{array}{c}{\sigma }_p\\ {\sigma }_s\end{array}\right]& ,& \epsilon =\left[\begin{array}{c}{\epsilon }_p\\ {\epsilon }_s\end{array}\right]\end{array}$$

  (4)
• Compatibility equations, also known as the Reuss-Voigt hypothesis [14,15], are defined as follows.

  $$\begin{array}{ccc}{\left[\begin{array}{c}{\sigma }_s\end{array}\right]}_{\mathrm{composite}}={\left[\begin{array}{c}{\sigma }_s\end{array}\right]}_{\mathrm{matrix}}={\left[\begin{array}{c}{\sigma }_s\end{array}\right]}_{\mathrm{fibre}}& ,& {\left[\begin{array}{c}{\epsilon }_p\end{array}\right]}_{\mathrm{composite}}={\left[\begin{array}{c}{\epsilon }_p\end{array}\right]}_{\mathrm{matrix}}={\left[\begin{array}{c}{\epsilon }_p\end{array}\right]}_{\mathrm{fibre}}\end{array}$$

  (5)
• The theory employs the Rule of Mixtures (ROM), where $\varphi$ represents the volumetric fraction.

  $${\sigma }_{\mathrm{composite}}=\varphi ·{\sigma }_{\mathrm{fibre}}+(1-\varphi )·{\sigma }_{\mathrm{matrix}}$$

  (6)
• 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.

The S-N curves can also be utilized to construct the Constant Fatigue Life (CFL) diagram, which provides information about the maximum number of cycles (N) for a given mean stress (${\sigma }_m$), alternating stress (${\sigma }_a$), and amplitude ratio (R).

Figure 15. Illustration of a Constant Fatigue Life (CFL) diagram, adapted from [16].

Figure 15. Illustration of a Constant Fatigue Life (CFL) diagram, adapted from [16].

The amplitude ratio, mean stress, and alternating stress are defined in terms of the minimum stress (${\sigma }_{\min }$) and maximum stress (${\sigma }_{\max }$).

$${\sigma }_m=\frac{{\sigma }_{\max }+{\sigma }_{\min }}{2}$$

(7)

$${\sigma }_a=\frac{{\sigma }_{\max }-{\sigma }_{\min }}{2}$$

(8)

$$R=\frac{{\sigma }_{\min }}{{\sigma }_{\max }}=\frac{{\sigma }_m-{\sigma }_a}{{\sigma }_m+{\sigma }_a}$$

(9)

The Palmgren-Miner’s rule, as described in [17,18], is employed to evaluate the cumulative damage experienced by the material.

$$D=\sum _{i=1}^k\frac{n_i}{N_i}$$

(10)

where D represents the damage index, i is the index of a cyclic interval, k is the total number of cyclic intervals, $n_i$ stands for the number of cycles, and $N_i$ represents the total number of cycles until fatigue rupture.

A stress history is recorded, and a cycle-counting algorithm is employed to evaluate the damage to a laminate layer at the Gauss point level. In marine applications, it is common to use a rainflow algorithm with 3-points or 4-points to count the cycles and utilize the cumulative damage estimation to determine the Remaining Useful Life (RUL) [19]. In this case, the cumulative damage estimation can be obtained using Equation (10). The accumulated damage is linear, although there are formulations that incorporate a non-linear additive effect [20], particularly in the context of wind turbines.

As fatigue is calculated at the Gauss point level for each ply of the laminate, it is crucial to employ a real-time cycle counting strategy (refer to Figure 16). To address this challenge, various algorithms have been proposed in an incremental form [21] or in combination with memory-reducing techniques [22].

3.2.3. Summary

In Figure 17, the methodology is summarized. The primary objective of this paper is to demonstrate the monitoring of an offshore wind turbine. To effectively track the life-cycle of the structure, the concept of Remaining Useful Life (RUL) will be utilized. The methodology to obtain the RUL is described as follows:

• 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’s rule, to establish an RUL metric.

4. Showcase

5. Implementation

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.

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.

6. Conclusions

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