# A Robust Wind Turbine Component Health Status Indicator
## 1 Introduction
\begin{table}
\begin{tabular}{p{56.9 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Ref** & **Models** & **Applications on** & **Main Contribution** \\ \hline
[19] & EWMA & tower, yaw, gearbox & Simple and robust. Only on large wind farms \\ \hline
[20] & EWMA, MEWMA & Power output deviation, generator & Autocorrelation is challenging. Better performance when data is independent and normally distributed. Multivariate model is the best. Limited lead time window. \\ \hline
[21] & EWMA, MEWMA & Power Curve monitoring & Robust detection of underperformance \\ \hline
[22] & LSTM-SDAE XGBoost & Generator, pitch motor, gearbox, anemometer & Average classification accuracy 92\%. Black box, not comprehensible \\ \hline
[26] & ARIMA & Gearbox & Trend propagation of the oil pump outlet pressure. Good trend predictor. Applied to one variable and one failure mode \\ \hline
[33;34] & Copula & Power curve & Good performance in outliers rejection and multivariate power curve \\ \hline
[35] & \
\begin{tabular}{l} MDAE-DTAD (deep autoencoder) \\ \end{tabular} & generator &
\begin{tabular}{l} Multivariate model. An in-depth performance comparison is made with other similar models, Semi-supervised anomaly detection models. \\ \end{tabular} \\ \hline
[36] & TWSVM & gearbox & Better performance than standard classifiers (SVM, KNN, MLPNN, DT) \\ \hline
[37] & DT & wind turbine structures & Root cause of excessive vibrations applied to big data-based applications \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary main trends in fault detection and diagnostics in wind turbines. Figure 1: Condition Monitoring. Common Data & Models. information of the system and serve as input for the copula model. Consequently, a univariate signal is generated, processed, and monitored. By analyzing and processing these signals alongside the GMCM model, the joint behavior of the variables can be evaluated, and the joint probability of anomalous events or behaviors can be determined. Moreover, as stated in the existing literature, there has been limited utilization of probabilistic models, such as copulas, specifically the GMCM model, in the context of fault detection in wind turbine components. The GMCM model enables the generation of a univariate output parameter, which facilitates the transition from condition monitoring to maintenance decision-making. This capability allows for the simultaneous monitoring of multiple variables, thereby simplifying the maintenance planning decision system by minimizing the number of health indices to be monitored (ideally, one per component). For all the aforementioned reasons, the Gaussian Mixture Copula Model (GMCM) is chosen as a solution to address the need for flexibility when working with multivariate systems and to overcome and relax the requirement of Gaussian data assumption, which is commonly imposed by many models in this field. This study aims to develop and validate a holistic methodology for generating a Failure Index (_FI_) focused on early fault detection in major wind turbine components. To conclude and highlight the main contributions of this paper to the wind energy industry and to previous work with GMCM models, this study advances the application of the Gaussian Mixture Copula Model (GMCM) by extending its use beyond the traditional power curve modeling and outlier detection with limited input variables (primarily wind speed and power). Our approach applies the GMCM to various wind turbine components, including the gearbox, generator, and blades, which represent a broader range of entities compared to previous studies. We have developed a comprehensive variable selection methodology to identify the most influential variables for representing the health of each component, utilizing up to seven variables in the final GMCM models (and many more during the variable selection process). This enhancement improves the flexibility and scalability of the GMCM method.