The design, hence the lifetime, of wind turbines is strongly driven by the fatigue limit state; a particular interest lies with the accumulation of fatigue damage at critical zones situated around or below the mudline [1]. Directly monitoring the structural loads at these locations is often not possible, since these do not allow for easy installation, inspection, replacement or retro-fitting of sensing equipment. Model-based virtual sensing techniques could be employed to estimate the structural response at locations other than measured; effectively, this could allow to assess the health progression at arbitrary structural locations from e.g. tower response measurements and an accurate finite element model. However, uncertainties in the deterministic modelling, and/or lack of design documentation do inhibit the use of model based approaches.

Within the OWI-lab, design documentation has been digitized for several offshore wind farms [1], allowing to generate in-house developed finite element models. In recent contributions the accuracy of these models has been investigated by comparing the computed modal parameters with modal parameters as well as bending moment profiles derived from long term measurement data [2, 3]. Calibration of e.g. soil characteristics can lead to an increased model accuracy [3]. With finite element models in place, model-based response extrapolation for fatigue monitoring can be assessed.

For this study two model based virtual sensing methods will be compared on vibration response data collected on wind turbine located in the Belgian North Sea. Both methods - a modal decomposition and expansion algorithm [4,5] and a Kalman filter based Joint input state estimation algorithm [6,7]– will be used with the same best estimate finite element model for building the respective model descriptions. Furthermore the measurements which will be used as input for the algorithms will be taken from the dry part of the structure, leaving strain measurements at fatigue critical locations for validation purposes. Next to these two methods, a simple approach using a static strain profile for the extrapolation, as well as a linear regression approach [8], will be used as benchmark.

The results show that both virtual sensing methods can estimate accurate time domain stress signals. Finally, a fatigue assessment is performed to evaluate the accuracy of the considered methods regarding lifetime considerations, the required measurement data, as well as the complexity of the implementation.

A global life-cycle assessment of offshore wind structural systems should adequately treat design and maintenance aspects in order to safeguard the reliable functionality of a system at a minimum budget. While controlling environmental and societal risks that arise from deterioration mechanisms and/or accidental/extreme events, a joint design and asset management life-cycle optimization enables an effective administration of both capital and operational expenditures. However, quantifying the system reliability of an offshore wind structural system often requires high computational efforts, since the analysis should consider the complex interaction among components and many failure scenarios. Moreover, the probabilistic quantification of degradation mechanisms and structural failure events demands an exhaustive evaluation of quantities of interest (QoI), i.e., model outputs. Although time consuming, high-fidelity simulations have become essential to accurately retrieve QoIs that typically follow a natural nonlinear behavior, e.g., fatigue-corrosion deterioration, ultimate strength, and structural resistance under accidental loads. Such high-fidelity models, however, are expensive in terms of computational time, thus often prohibiting in practice the probabilistic quantification of QoIs.
Based on small datasets directly retrieved from high-fidelity engineering simulations, surrogate models are light-running analytical approximations, capable of efficiently learning mathematical relationships between uncertain input design variables and relevant output QoIs. In the literature, multi-physics engineering probabilistic designs have been implemented on wind turbine applications profiting from the computational performance of surrogate models (Slot, et al., 2020; Morán A., et al., 2022), yet most reported studies train models based on a fixed number of samples. Benefiting from built-in probabilistic metrics intrinsically featured by Gaussian-based regressors (e.g., Kriging, PC-Kriging), further computational savings can be achieved by smartly selecting the least number of informative model evaluations.
By minimizing the number of high-fidelity simulations, we propose here a surrogate-based modelling approach that can efficiently provide the model evaluations needed in a global life-cycle reliability analysis of offshore wind structural systems. More specifically, the surrogate model is actively trained by carefully resampling in domain regions selected according to an exploitation-exploration trade-off, i.e., exploiting areas near the limit state while exploring regions associated with high uncertainty. As showcased in Figure 1, the proposed framework is able to support the quantification of system structural reliability estimates, which, in turn, depend on fatigue damage predictions, global collapse analyses conducted through numerical methods, and occasional structural damage caused by accidental/extreme events.

Steel support structures for offshore wind turbines operate in a harsh chloride-containing marine environment, which can lead to surface degradation due to the formation of corrosion pits. Depending on, amongst others, the applied potential, the corrosion kinetics can either be in activation-, migration- or diffusion-controlled regime. The main aim of this work, which is part of the MAXWind project, is to identify the potential values corresponding to each of these regimes for structural steel S355 in an environment representative of the North Sea. Hereto, the PRISMS-PF open-source phase-field modelling framework is used.
Potentiodynamic polarization tests are performed for the electrochemical characterization of this material in artificial seawater. The corrosion potential and current density values obtained are -693 mV vs. Ag/AgCl and 0.005813 mA/〖cm〗^2, respectively. Open circuit potential (OCP) measurements revealed a similar result for the corrosion potential, i.e. -670 mV vs. Ag/AgCl. Besides, the effect of the applied potential on geometrical parameters (pit width and depth) and electrochemical parameters associated with the pit growth rate is studied.
For an applied potential of -600 mV (vs. Ag/AgCl) and lower, the corrosion process stays in the activation-controlled regime throughout the simulation time (1000s) and a pit will thus not change in size. Applied potentials of -550 to -400 mV (vs. Ag/AgCl) take the system to the migration-controlled regime, and above -350 mV (vs. Ag/AgCl) the system is in the diffusion-controlled regime. The higher the applied potential (towards zero), the more pitting corrosion is accelerated until it reaches a threshold where any additional increase in applied potential will not further change the pit growth rate. Numerical results are validated with experimental observations of pit depth and width on corroded specimens under temperature-controlled conditions throughout a potentiostat test.
Simulating the autonomous growth of a pit for long-term exposure using the phase-field technique is computationally expensive. Based on the preliminary results of this work, it can be assumed that the normal velocity of the pit surface will remain constant in the long term because the applied potential in the real application is lower than -600 mV (vs. Ag/AgCl), negligibly small being close to corrosion potential (no external source of current). A more simple model of pit growth can therefore be used for long-term exposure.
The authors acknowledge the financial support of the Belgian Federal Government through its Energy Transition Fund.

We present a case study on how digitalization can be utilized to optimize inspection and maintenance decisions for leading edge erosion (LEE) of wind turbine blades. The repeated impact of raindrops and other particles on the leading edge of wind turbine blades leads to initiation of erosion and progressive damage development. The initiation time and mass loss rate can be predicted using the Springer model [1] and incorporating turbine and site data such as tip speed, material properties, wind and rainfall distributions. [2]. LEE negatively impacts aerodynamic performance, thereby decreasing the power production. Furthermore, untreated LEE will eventually impact the structural integrity of the wind turbine blades, and repairs must be performed to avoid this.

Digitalization has the potential to reform the process of inspection and maintenance planning, if the information available in inspection data, maintenance reports, and operational data is utilized for optimal decision making. Relevant decisions in this context are related to timing, location and extend of inspections and repairs. Optimal risk-based decision making aims to maximize utility, or equivalently, minimize expected costs including revenues losses [3].

Within the field of inspection and maintenance planning, advanced methods have been developed recently based on e.g. partially observable Markov processes (POMDP) [4] or deep reinforcement learning [5], where decisions are flexible, and information from past inspections are taken into consideration. However, the strategies recommended by these methods lack transparency, and they are consequently not easy to understand for practitioners. Therefore, heuristic strategies are often preferred by the industry due to the transparency and simplicity of use. For time-based inspections, where the inspection times are calendar based, Bayesian networks have proved to be very efficient for optimization, and this can often be done within few seconds [6]. We propose a novel Bayesian network approach, where age-based inspections can be included, by including a count-down node for the time to the next inspection (Figure 1). This allows for including strategies, where the time to the next inspection depends on the outcome of the latest inspection in terms of the size of the defect. Due to the computational efficiency, it is possible to consider a large number of different strategies. This also enables the use of adaptive strategies, where greedy optimization has been shown capable of improving the performance of heuristic strategies [7]. This study shows how this novel heuristic approach can be applied for blade maintenance in relation to LEE.

Offshore wind turbine support structures are exposed to maritime conditions, which can lead to corrosion fatigue. This work is part of the FATCOR project funded by the Belgian Energy Transition Fund, aiming to develop a qualitative and quantitative understanding of the mechanisms of corrosion fatigue in seawater. Localized corrosion generates a geometrical defect, raising the local stresses and reducing the fatigue life. The transition from pit growth to short fatigue crack propagation occurs at a critical pit size, which depends upon the microstructure, the applied stress level and the geometry of the pit.
In linear elastic fracture mechanics, the stress intensity factor is used to describe the magnitude of the stress singularity near a crack tip caused by remote stresses and is useful for establishing a failure criterion. Literature lacks stress intensity factor solutions for cracks emanating from a three-dimensional semi-ellipsoidal pit. Fig. 1 (a) shows a schematic representation of a plate subjected to axial tensile stress with a semi-ellipsoidal pit at the center of the top surface. Two cracks in the shape of a circular arc are introduced at the pit mouth perpendicular to the loading direction (see Fig. 1 (b)). Finite element analysis is used to calculate the stress intensity factor (K₁) at the crack tip (see Fig. 2).
The displacement extrapolation method is used to quantify the effect of different pit configurations and crack lengths on K₁. This method determines K₁ from the displacement field near the crack tip. A parametric study is performed on a range of relative geometrical parameter values (a/2c, b/c) and crack lengths (r/a). It is observed that changes in the pit geometry can drastically affect the stress gradient in the vicinity of the pit, which directly influences the magnitude of K₁. For example, (a/2c) equal to 1, 0.5 and 0.25, result in K₁ values of 74.4, 71.1 and 56.6 MPa/√mm respectively, for a remote stress of 100 MPa. In future work, regression analysis will be performed to develop an equation to calculate the K₁ for a wide range of pit configurations and crack lengths.