## 5 Comparison  
For better comparison, collected data has been connected in Figure 20. Each graph was manually standardized to the same time frame.  
In Figure 20 the characteristic moment of the experiment can be noted around 120-130 s mark. A bigger change of the value visible in the temperature and visual shift of the belt position indicates the belt jerking due to contact with the bolt which caused the belt to fold and its initially tracked edge to move out of the camera's field of view. It directly explains the sudden decrease in the temperature, as the belt edge was heating up faster due to friction. After that point, the amplitude of the vibrations increases significantly due same reason.  
Since belt mistracking should be recognized as early as possible and direct contact with the frame of the conveyor can be considered a late symptom, the shortened signal in Figure 21 is presented for better visualization of the process. As can be seen, the measurement with the RGB camera provided the fastest indication of the start of belt mistracking and the exact moment when the belt edge moved out of the cylinder. The temperature started to increase a few seconds after that and continued to do so at a steady pace.  
In the case of the vibrations, detectable changes in form of the amplitude spikes happen much later and can be hardly distinguished from the natural vibrations of the conveyor. Only after the bolt friction vibrations become significant enough to indicate a potential problem. Therefore it can be noted that this method provides the least desirable results, as it only works after significant problems already occurred.  
In the final step of the data analysis authors used principal component analysis (PCA) to reduce dimensionality to a single diagnostic feature [47]. This method states that a dataset consisting of \(N\) observations spanned over \(K\) variables, can be interpreted as a point cloud in the K-dimensional space. Its goal is to obtain new information from the already obtained data by the mean of the local coordinate system rotation toward variance maximization over a new set of dimensions. Principal components can be therefore described as vectors of data in that transformed system.  
Figure 19: The differencein the compressive force between the actuators of the tensioning device in the case of belt lateral mistracking and normal operation of the conveyor.  
To obtain the principal components, Singular Value Decomposition (SVD) can be used:  
\[\frac{1}{\sqrt{n-1}}X=U\Sigma V^{T}, \tag{1}\]  
where \(U\in\mathbb{R}^{n\times n}\) and \(V\in\mathbb{R}^{m\times m}\) are unitary matrices and \(\Sigma\in\mathbb{R}^{n\times m}\) contains the nonnegative real singular values of non-increasing magnitude (\(\sigma_{1}\geq\sigma_{2}\geq\cdots\geq\sigma_{m}\geq 0\)). Principal components are the orthonormal column vectors of the matrix V, and the variance of the \(i\)-th component is equal to \(\sigma_{i}^{2}\).  
PCA has been applied to the data segment up until the moment of machine shutdown (the timestamp of 162 s of the experiment). First principal component (PC1) is presented in Figure 22. To justify the usage of only one principal component, authors present the relative informativeness of the principal components (see Figure 23). PC1 shows that the  
Figure 20: Collecteddata comparison.  
mistracking is progressing consistently over time, which was also observed in-situ during the experiment.  
Figure 21: Data comparison before 120 s mark.  
Figure 22: First principal component with eigenvalue equal to 0.91.