# Modeling and Monitoring Erosion of the Leading Edge of Wind Turbine Blades

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## Abstract

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## 1. Introduction

- We developed a stochastic spatio-temporal erosion model of the leading edge of wind turbine blades, which is characterized by a non-homogeneous compound Poisson process across discrete states, embedded in a generator of a stochastic ensemble of degrading airfoil aerodynamic polars for use in forward aero-servo-elastic simulations. The coupled model is able to compute the aeroelastic non-stationary response of a wind turbine, thus reflecting its behavior under the effect of leading edge erosion and varying turbulent input inflow conditions over a long period of degradation.
- We adapted a deep-learning multivariate time-series-based Transformer, which employs attention mechanisms to detect and classify long-term and slow leading edge erosion processes assuming the availability of on-blade sectional monitoring data, under short- and long-term wind inflow uncertainties and aerodynamic uncertainties on the lift and drag coefficients of the airfoil sections along the span of the blade.

## 2. Review of Prior Art

#### 2.1. Modelling Leading-Edge Erosion

#### 2.2. Diagnosing Leading Edge Erosion

## 3. Modeling Erosion of the Leading Edge

#### 3.1. Non-Homogeneous Compound Poisson Process

- $N\left(0\right)=0$
- $\forall t$, $s\ge 0$, and $0\le u\le t$, ${N}_{t+s}-{N}_{t}$ is independent of ${N}_{u}$
- $\forall t$, $s\ge 0$, $P({N}_{t+s}-{N}_{t}=0)=1-\lambda \left(t\right)s+o\left(s\right)$
- $\forall t$, $s\ge 0$, $P({N}_{t+s}-{N}_{t}=1)=\lambda \left(t\right)s+o\left(s\right)$, and
- $\forall t$, $s\ge 0$, $P({N}_{t+s}-{N}_{t}\ge 2)=o\left(s\right)$

- Choose ${\lambda}_{u}$ such that $\lambda \left(t\right)\le {\lambda}_{u}\forall t\in [0,T]$
- Initialize $t=0$ and $I=0$
- Generate ${u}_{1}\phantom{\rule{3.33333pt}{0ex}}U\left(0,1\right)$
- Set $t\leftarrow t-\frac{1}{{\lambda}_{u}}log{u}_{1}$
- If $t>T$, stop; else go to next
- Generate ${u}_{2}\phantom{\rule{3.33333pt}{0ex}}U\left(0,1\right)$, independent of ${u}_{1}$
- If ${u}_{2}\le \frac{\lambda \left(t\right)}{{\lambda}_{u}}$, set $I=I+1$; $S\left(I\right)=t$
- Go to Step 3

#### 3.2. Stochastic Aerodynamic Polars Model

#### 3.3. Overview of the Algorithm

Algorithm 1: Spatio-temporal stochastic model of leading edge erosion. |

## 4. Uncertainty Modeling and Aeroelastic Simulations

#### 4.1. Stochastic Models of Inflow RVs

#### 4.2. Setup of the Aero-Servo-Elastic Simulations

#### 4.3. Retained Output from Aero-Servo-Elastic Simulations

## 5. Diagnosing LEE via Transformers

- Labeled data for LEE are hard to acquire and are scarce; as a result, any method must be designed not to suffer from over-fitting under scarce labeled data availability.
- Diagnostics shall be done with remote streaming of sensor data. Human intervention and turbine down-time should be alleviated.
- The data used in the diagnostics method intend to emulate the sensory output of a single MEMS-based aerodynamic and aero-acoustic measurement node positioned in proximity to the tip of the wind turbine blade.
- The method shall be capable of ingesting 10-min-long multivariate time-series (industry standard SCADA recording length), sampled at 100 Hz, resulting in 60,000 data-point-long sequences. A sampling rate of 100 Hz may seem excessive, but the aim is to capture even small turbulence scales.
- A supervised scheme shall be used to train a Transformer-based network by utilizing labeled data resulting from aeroelastic simulations of a turbine combined with the degradation model, as presented earlier in the article.
- Physics-constraints shall be built into the loss or likelihood function.
- The output predictions should be probabilistic in nature.

#### 5.1. Experiments and Datasets

- Are we able to learn the LEE severity classes from aerodynamic MTS data, in the general machine learning sense, with balanced data classes and no prior knowledge?
- In a continuous monitoring context, are we able to diagnose jumps in LEE severity and therefore identify the degradation path that the system takes?
- Are we able to do so in a realistic setting, with all previously described sources of uncertainty present in the simulations?

#### 5.2. Transformer Architecture

#### 5.3. Loss Functions

#### 5.4. Training Regime

## 6. Results

#### 6.1. Experiment Set 1

#### 6.2. Experiment Set 2

#### 6.3. Experiment Set 3

#### 6.4. Transferability and Curriculum Learning

- The high accuracy of transferability tests between Experiments 1.1 and 2.1 highlights the similarity of these datasets. Moreover, the balanced dataset of Experiment 1.1 improves the prediction quality for Set 2.1.
- Although both Sets 1.1 and 2.1 contained all degradation classes, networks trained on these sets do not transfer well to Test Set 3.1, undoubtedly due to the uncertainty included in this experiment.
- There was better transferability between Sets 2.1 and 3.1 than between Sets 1.1 and 3.1. This can be explained by the extra loss component which enforces monotonicity in the second and third sets of experiments.
- The first curriculum learning experiment (Set 1.1 then 2.1) yielded a large performance boost for Test Sets 1.1 and 2.1. This was to be expected due to the data-intensive nature of Transformers and the similarity between these sets.
- The first curriculum learning experiment reduced transferability to Set 3.1. This is an indication of a loss of capacity to generalize to ambiguous data.
- The best test results on Set 3.1 were obtained in the second curriculum learning experiment. This suggests that pretraining on sets with reduced stochasticity followed by fine-tuning on uncertain data is an effective approach.
- The second curriculum learning experiment yielded the best high confidence accuracy for Sets 1.1 and 2.1. Thus, adding difficult, stochastic data points of Experiment 3.1 to the training dataset helps with regularization, enabling the model to construct a better internal representation of each severity class.

## 7. Limitations and Discussion

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

$WT$ | Wind turbine |

$RV$ | Random variable |

U | Mean wind speed |

$\sigma $ | Turbulence |

$\alpha $ | Wind shear exponent |

${T}_{i}$ | Turbulence intensity |

$\mathbb{E}$ | Expected value of a random variable |

$\mathbb{V}$ | Variance of a random variable |

${C}_{L}$ | Aerodynamic lift coefficient |

${C}_{D}$ | Aerodynamic drag coefficient |

${C}_{m}$ | Aerodynamic moment coefficient |

${C}_{p}$ | Aerodynamic pressure coefficient |

$MLP$ | Multilayer perceptron |

$NHPP$ | Non-homogeneous Poisson process |

$NHCPP$ | Non-homogeneous compound Poisson process |

R | Blade radius |

$SHM$ | Structural health monitoring |

$SCADA$ | Supervisory control and data acquisition |

$EZ$ | Eroding zone |

$O\&M$ | Operation and maintenance |

$LE$ | Leading edge |

$LEE$ | Leading edge erosion |

$CNN$ | Convolutional neural network |

$RNN$ | Recurrent neural network |

$MTS$ | Multivariate time-series |

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**Figure 1.**Illustration of Aerosense, a novel MEMS-based aerodynamic surface pressure and aero-acoustic measurement system for wind turbines’ blades.

**Figure 2.**A graphical abstract of modeling and diagnosing erosion of the leading edge of wind turbine blades.

**Figure 3.**Cyclic rate function $\lambda \left(t\right)$ for the NHPP, representing the effect of weekly and seasonal variations on the rate. $\lambda \left(t\right)$ represents the rate of change in damage of LE erosion per given period.

**Figure 4.**(

**a**) Lift coefficients for $NACA64618$ for 10 severity classes of leading edge erosion. (

**b**) Drag coefficients for $NACA64618$ for 10 severity classes of leading edge erosion.

**Figure 5.**A sample of the NHCPP of the leading-edge erosion on 5 zones along the span of blade 1 over a 20-year period (240 months). Zone 5 is the outermost section along the span of the blade.

**Figure 6.**Samples of the generated stochastic aerodynamic coefficients of airfoil $NACA64618$. (

**a**) Lift coefficient. (

**b**) Drag coefficient.

**Figure 7.**(

**a**) NHCPP-generated degrading static ${C}_{L}$ for $NACA64618$. This was used as input to the aeroelastic simulations for Blade 1, Section 5. For each pre-selected degrading section on a blade, a set of such curves were generated. (

**b**) Degradation of the max lift coefficient for Blade 1, Zone 5. (

**c**) Degradation of angle of attack at max lift coefficient for Blade 1, Zone 5. (

**d**) Degradation of the lift coefficient at $\alpha ={5}^{\circ}$ for Blade 1, Zone 5.

**Figure 8.**Long-term inflow variations: (

**a**) varying mean wind speed and shape parameter ${K}_{U}$ of the Weibull distribution. (

**b**) Varying reference turbulence $Iref$.

**Figure 9.**Samples of the environmental sources of uncertainties for Degradation Period 0. $\mathbb{E}\left(U\right)=8.5$ m/s, ${K}_{U}=2.0$, ${I}_{ref}=0.09$.

**Figure 10.**Joint samples of the environmental sources of uncertainties for Degradation Period 5. $\mathbb{E}\left(U\right)=9.0$ m/s, ${K}_{U}=1.95$, ${I}_{ref}=0.12$.

**Figure 11.**Distribution of airfoils along the span of the blade. Example of the NREL5MW reference wind turbine.

**Figure 12.**(Black) beginning and (red) end of the degradation period. (

**a**) Sample hub height wind speed. (

**b**) Sample lift coefficient at the airfoil profile corresponding to $95\%$ of the span of Blade 1. (

**c**) Sample flapwise bending moment at the root of Blade 1.

**Figure 13.**(

**a**) ${C}_{L}$ for wind speeds varying between 6–16 m/s and no blade erosion. (

**b**) ${C}_{L}$ for fixed wind speed $U=11$ m/s and evolving severity of leading edge erosion.

**Figure 14.**Time-windowing architecture of the novel Transformer model. The input multivariate time-series is split along the time dimension into windows, which are then individually passed through the learnable linear embedding. The learnable class token that is added to the sequence is used in the classification MLP head to predict the level of degradation.

**Figure 15.**(

**a**) Confusion matrix of the predicted severity classes for the test data of Experiment 1.1. (

**b**) Confusion matrix of the predicted severity classes for the test data of Experiment 1.2.

**Figure 16.**Actual degradation path and predicted erosion severity classes for Experiment 2.1. (

**a**) Predictions with a likelihood greater than 70%. (

**b**) Median predictions using a three-month rolling window and upper rounding.

**Figure 17.**Actual degradation path and predicted erosion severity classes for Experiment 2.2. (

**a**) Predictions with a likelihood greater than 70%. (

**b**) Median predictions using a three-month rolling window and upper rounding.

**Figure 18.**Actual degradation path and predicted erosion severity classes for Experiment 3.1. (

**a**) Predictions with a likelihood greater than 70%. (

**b**) Median predictions using a three-month rolling window and upper rounding.

**Figure 19.**Actual degradation path and predicted erosion severity classes for Experiment 3.2. (

**a**) Predictions with a likelihood greater than 70%. (

**b**) Median predictions using a three-month rolling window and upper rounding.

**Figure 20.**Results for the curriculum learning experiment combining all datasets showing actual degradation path and predicted erosion severity classes computed on the test dataset of Experiment 2.1. (

**a**) Predictions with a likelihood greater than 70%. (

**b**) Median predictions using a three-month rolling window and upper rounding.

**Table 1.**Types and stages of leading-edge erosion with the number of pits (P), number of gouges (G), and magnitude of leading edge delamination (DL), modified from [8].

Stage 1 | Stage 2 | Stage 3 | Stage 4 | Stage 5 | |
---|---|---|---|---|---|

Type A | 100P | 200P | 400P | — | — |

Type B | — | 200P/100G | 400P/200G | 800P/400G | — |

Type C | — | — | 400P/200G/DL | 800P/400G/DL+ | 1600P/800G/DL++ |

Stage 1 | Stage 2 | Stage 3 | Stage 4 | Stage 5 | |
---|---|---|---|---|---|

Type A | 1 | 2 | 3 | — | — |

Type B | — | 4 | 5 | 6 | — |

Type C | — | — | 7 | 8 | 9 |

Sensor Name | Description |
---|---|

$Time$ | Time steps of the simulations |

$Wind1VelX$ | X-direction wind velocity at hub-height |

$B1N9Cl$ | Lift force coefficient at Blade 1, Aerosense Node at $0.96R$ |

$B1N9Cd$ | Drag force coefficient at Blade 1, Aerosense Node at $0.96R$ |

$B1N9Alpha$ | Angle of attack at Blade 1, Aerosense Node at $0.96R$ |

Parameter | Experiments | |||||
---|---|---|---|---|---|---|

1.1 | 1.2 | 2.1 | 2.2 | 3.1 | 3.2 | |

NHCPP severities | 0–9 | 0, 1, 6, 9 | 0–9 | 0–9 | 0–9 | 0–9 |

Severity type grouping | - | - | - | 0, A, B, C | - | 0, A, B, C |

Stochastic degradation | - | - | ✓ | ✓ | ✓ | ✓ |

Inflow turbulence | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |

Aerodynamic uncertainty | - | - | - | - | ✓ | ✓ |

Weather variability | - | - | - | - | ✓ | ✓ |

Num. training samples | 3360 | 3360 | 2880 | 2880 | 2880 | 2880 |

Num. validation samples | 960 | 960 | 720 | 720 | 720 | 720 |

Num. testing samples | 480 | 480 | 1200 | 1200 | 1200 | 1200 |

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

Number of windows, n | 300 |

Window size, w | 200 |

Internal Transformer dim., ${d}_{model}$ | 256 |

Transformer stack size, s | 6 |

Num. self-attention heads, h | 8 |

Self-attention head dim., ${d}_{head}$ | 64 |

Output MLP dim., ${d}_{MLP}$ | 2048 |

Experiment | Testing Accuracy (%) | |
---|---|---|

All Predictions | >70% Likelihood | |

Exp. 1.1 | 66.67 | 72.65 |

Exp. 1.1 Large | 80.63 | 85.56 |

Exp. 1.2 | 96.04 | 97.22 |

Experiment | Testing Accuracy (%) | |
---|---|---|

All Predictions | >70% Likelihood | |

Exp. 2.1 | 65.42 | 78.41 |

Exp. 2.2 | 67.75 | 69.48 |

Experiment | Testing Accuracy (%) | |
---|---|---|

All Predictions | >70% Likelihood | |

Exp. 3.1 | 35.00 | 45.75 |

Exp. 3.2 | 54.67 | 65.22 |

Training Set(s) | Test Accuracy (%) | ||
---|---|---|---|

Set 1.1 | Set 2.1 | Set 3.1 | |

Set 1.1 | – | 71.25 | 28.25 |

Set 2.1 | 65.00 | – | 29.42 |

Set 3.1 | 30.00 | 39.25 | – |

Set 1.1, then 2.1 | 77.71 | 83.50 | 20.33 |

Set 1.1, then 2.1 & 3.1 | 77.08 | 80.50 | 37.08 |

Training Set(s) | >70% Likelihood Test Accuracy (%) | ||
---|---|---|---|

Set 1.1 | Set 2.1 | Set 3.1 | |

Set 1.1 | – | 80.21 | 30.19 |

Set 2.1 | 77.11 | – | 32.86 |

Set 3.1 | 35.58 | 40.97 | – |

Set 1.1, then 2.1 | 81.35 | 87.29 | 20.52 |

Set 1.1, then 2.1 & 3.1 | 84.42 | 88.53 | 50.22 |

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## Share and Cite

**MDPI and ACS Style**

Duthé, G.; Abdallah, I.; Barber, S.; Chatzi, E.
Modeling and Monitoring Erosion of the Leading Edge of Wind Turbine Blades. *Energies* **2021**, *14*, 7262.
https://doi.org/10.3390/en14217262

**AMA Style**

Duthé G, Abdallah I, Barber S, Chatzi E.
Modeling and Monitoring Erosion of the Leading Edge of Wind Turbine Blades. *Energies*. 2021; 14(21):7262.
https://doi.org/10.3390/en14217262

**Chicago/Turabian Style**

Duthé, Gregory, Imad Abdallah, Sarah Barber, and Eleni Chatzi.
2021. "Modeling and Monitoring Erosion of the Leading Edge of Wind Turbine Blades" *Energies* 14, no. 21: 7262.
https://doi.org/10.3390/en14217262