**1. Introduction**

Wind turbine damage has in recent years gained interest from industry and academia in an effort to keep aging wind parks around the globe productive. According to Rempel [1], in the early days of the wind energy industry there was the general misconception that once the blade is in operation, no further maintenance is required. This has changed, partly due to a considerable number of field reports that have started to surface in recent years highlighting extreme and worrying examples of early blade deterioration. For instance, Rempel states that blades as young as three years of age can show signs of wear and that blades of 87 out of 111 wind turbines in a wind farm off the shores of Denmark had to be dismantled and brought to shore after less than five years in operation due to severe leading-edge (LE) damage, as shown in Røndgaard [2].

In addition to themore common LEissues, blade's trailing edge often suffers from damage. In particular, Decoret [3] states that debonding is commonly observed at the trailing edge (TE). This phenomenon occurs when the composite layers of the blade shell separate. If this happens at the TE of the blade, its dimension is expected to greatly increase in thickness, thus decreasing the aerodynamic performance. According to Wood [4], another common source of damage at the TE happens during blade transportation and turbine assembly. Crushing of the laminate may occur as well as chipping of the TE itself, especially in the tip region where the rear of the blades is typically very thin. The impact of LE damage on AEP has been studied by various authors. Amongst the most influential research in the field, Sareen et al. [5] test in a wind-tunnel a series of LE-damaged wind turbine airfoil configurations that mimic pictures of blades that were brought in for repair. They predict massive maximum losses in AEP of up to 25%. Han et al. [6] develop a computational fluid dynamics (CFD) model of an eroded airfoil based on their inspection of a 14-year-old Vestas V47 blade using the commercial software Star CCM+. They then simulate the NREL 5 MW [7] rotor with erosion applied from 70.7% of the rotor span outwards and find AEP reductions of 3.7%. Castorrini et al. [8] develop a numerical tool to predict airfoil performance degradation due to LE erosion. The tool is tuned based on photographic evidence of damaged blades and tested on the NREL 5 MW rotor, predicting power decreases of around 8%. As also noted by Herring et al. [9], these values, and others that can be found in published literature, quantitively greatly differ between each other. This could be due to the fact that erosion has a variable impact on different airfoil shapes, turbine sizes and operating conditions, thus leading to different results. Moreover, as far as the authors are aware, no study assesses the impact of TE damage on AEP at the present time, while some of the authors recently analyzed its effects on aerodynamic performance and loads under realistic inflow conditions [10]. Some light can be shed on the discrepancies highlighted between the work of many authors by approaching the problem in a probabilistic manner rather than in a deterministic way, as done until now.

This is done in the present study by introducing two aleatory variables that model leading-edge and trailing-edge damage, respectively. That blade damage is propagated through an aero-servo-elastic model of the DTU 10 MW RWT [11] as this is a modern reference rotor design. The model response in terms of AEP and power is approximated using an arbitrary polynomial chaos (aPC) expansion. The numerical procedure that is followed will be detailed in the following sections; however, a brief rundown can be provided as follows. The damage is applied to a give airfoil through geometry modification. The lift and drag coefficients are then obtained using computational fluid dynamics (CFD). The obtained coefficients are applied to the DTU10MW blade. The turbine is then simulated using NREL's open-source code OpenFAST [12]. Finally, the model regression can be performed and response surfaces of the outputs of interest, as well as associated probability density functions (PDFs), can be estimated. An overview of the entire modelling process is provided in Figure 1.

**Figure 1.** Flowchart of the uncertainty-quantification procedure.

It should be noted that blade damage is undoubtedly not the only source of uncertainty that affects the power production of a wind farm. Other common sources of uncertainty are related to environmental conditions, with uncertainties in wind speed and turbulence intensity being the main ones. As these are not the topic of the present study, which focuses specifically on the effects of blade damage, they are not included in the uncertainty quantification; however, in order to ensure that the study is up to the present simulation standards, they are accounted for using the standard procedures of the International Electrotechnical Commission (IEC).
