# Application of Machine Learning Algorithms in Real-Time Monitoring of Conveyor Belt Damage
## 3 Results and Discussion
### The Application of the Machine Learning Algorithms  
The possibility of damage identification was tested using statistical data from the registered signal of each strain gauge, namely, T1, T2, and T3, for the belt without damage, the one with three defects, and the one with five defects, respectively, as described in Section 2.3. The statistical parameters were as follows: The mean value for each strain gauge is  
\[\overline{x}=\frac{1}{N}{\sum}_{n=1}^{N}|x(n)|, \tag{1}\]  
where \(x(n)\) is the amplitude of each sampling, and \(N\) is the number of samples. The respective equations for the mean square value \(X_{ms}\), standard deviation \(\sigma\), and kurtosis \(X_{k}\) for each strain gauge were used as follows:  
\[X_{ms}=\sqrt{\frac{1}{N}{\sum}_{n=1}^{N}[x(n)]^{2}}, \tag{2}\]  
\[\sigma=\sqrt{\frac{1}{N}{\sum}_{n=1}^{N}[x(n)-\overline{x}]^{2}}, \tag{3}\]  
\[X_{k}=\frac{\frac{1}{N}{\sum}_{n=1}^{N}[x(n)-\overline{x}]^{4}}{\left(\frac{1} {N}\sum_{n=1}^{N}[x(n)-\overline{x}]^{2}\right)^{2}}. \tag{4}\]  
Figure 4: An example of the registered signal from strain gauges T1, T2, and T3. Thus, if the value of the new analyzed sample is smaller than 880.604 ADU, the sample travels the pathway and is directed to the leaf node to be classified as \"undamaged\" based on the set of training samples. Usually, \"the class represented by the majority of training samples within the leaf node subspace dictates sample classification\" [35]. The analysis of 18 features was performed using the _Diagnostic Feature Designer_ application and a one-way ANOVA. This sort of test requires the assumptions of a normal distribution and homogeneity of variance for all groups. To test the effect of a single factor on the results, it assumes the presence of one independent variable, represented by the groups studied in the experiments, and one dependent variable, represented by the results of the study. Hypotheses regarding the equality of means are tested if there are more than two analyzed groups [36]. When the abovementioned assumptions are not met, the result may become unreliable. Data transformation can be a method that allows for data normalization and variance stabilization. However, when such actions do not provide a positive result, non-parametric tests become an alternative, e.g., the Kruskal-Wallis test, which is equivalent to a one-way analysis of variance [37]. The non-parametric Kruskal-Wallis test corresponds with the parametric one-way ANOVA test and allows for post hoc testing when the null hypothesis of equality of means in the analyzed groups is rejected. When the assumptions of a parametric test are met and the distribution is normal, parametric tests appear to be more powerful than the comparable non-parametric ones, i.e., a non-parametric test is less likely to correctly define a statistically significant result [38]. Thus, it is recommended to first apply a parametric test, and if it appears improper, then a non-parametric test should be used [37]. In this research, we decided to use the Laplacian Score, variance, and monotonicity tests. The Laplacian Score used the nearest neighboring graph to determine the local data structure and the respective value for each feature. A feature with a higher Laplacian Score indicated its importance for localization [39]. Variance is the classical method of differentiation for its evaluation and has no statistical interpretation. However, it can be used for the construction of other parameters, such as central moments or the standard deviation. It is expressed as the arithmetic mean of the squares of deviations of individual values of the feature from their arithmetic mean [40]. Monotonicity is the rating method available in _Diagnostic Feature Designer_, with values ranging from 0 to 1 to describe the trend of the given function during the system's evolution. The results of the tests obtained from the five different abovementioned models are shown in Figure 6, ranked in decreasing order for different features according to the results of the one-way ANOVA.