## 2 Research Methodology
### Combined Faults  
In practice, several defects exist in most instances, and diagnosing and detecting one defect presents enormous challenges since the defects can present similar features or interfere with each other's presence. This interdependence implies that the conventional diagnosis techniques, which are very efficient for single defects, would lack the necessary accuracy in handling faults that co-occur. The study by [31] investigates the application of three mathematical methods for measuring a wind turbine mast's deformation and harmonic response and compares their effectiveness. The first challenge in the study was how to estimate structural deformations of the wind turbine mast by directly using displacement sensors due to the constraints in installation and high measurement noise. As an alternative, the authors propose using accelerometer data filtered by the Kalman filter, joint input-state estimation algorithm (JISEA), and modal expansion algorithm (MEA). The algorithms imply the preprocessing of the data into a state-space representation form. The finite element method was employed to identify vibration modes:  
\[M\ddot{u}(t)+Ci(t)+Ku(t)=S_{p}(t)p(t), \tag{39}\]  
where \(u(t)\) is the vector of displacements (translations and/or rotations); \(M\), \(C\), and \(K\) are the mass, damping, and stiffness matrices of the system, respectively; \(S_{p}(t)\) is a selection matrix specifying the force locations; \(p(t)\) is a time history vector. As a result, the authors obtained deformation patterns in time, response dependencies on excitation frequencies, deformation comparisons in windward and transverse directions, and vibration mode plots (Figure 27). The experiment was evaluated experimentally on an actual wind turbine. The validation criteria were the time response agreement criterion (TRAC) and mean absolute error (MAE). The experiment revealed that, for stationary blades, all three methods provided accurate results using accelerometer data only. However, when the blades were in motion, the performance of the Kalman filter was lower compared to the JISEA and the modal expansion algorithm (MEA). Conversely, when the input parameters were set to accommodate both acceleration and deformation measurements, the accuracy of the Kalman filter was significantly enhanced and surpassed the other two methods. Concurrently, variations in the input parameters had less impact on the JISEA and MEA. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Method** & **Advantages** & **Disadvantages** & **Domain*** \\ \hline Chebyshev interval method (CIM) [64] & It works with bounded uncertainties only—no PDFs are needed. & Accuracy hinges on the chosen polynomial order and grid level; tuning remains empirical. & \\ \hline \multirow{4}{*}{
\begin{tabular}{} \end{tabular} } & Clearly separates the influence of globaland local (bearing length, unbalance phase) parameters. & Ignoring parameter correlations and fault-driven nonlinearities. & TD/FD fault-driven nonlinearities. \\ \hline Full tensor grid (FTG) [64] & Captures all interactions among interval variables exactly at sampled points. & A large number of FEA runs. & TD/FD \\ \cline{1-1} \cline{2-4}  & Offers a direct benchmark for validating surrogate methods like CIM. & May miss the true extrema between grid nodes. & TD/FD grid nodes. \\ \hline \hline \end{tabular}  
* Signal processing domain (if applicable). TD—time domain; FD—frequency domain; TFD—time-frequency domain.  
\end{table} 
Table 7: _Cont._A rotor orbit diagram is one of the most valuable instruments for detecting different faults. It can have various forms depending on system conditions, but it is hard to make any conclusions from visually exploring such diagrams. The study by [85] explores a rotor diagnostics method based on orbit analysis using the ISOMAP algorithm. Vibration sensors were installed on a test rig in two mutually perpendicular planes to generate orbit diagrams.