# Probabilistic Condition Monitoring of Azimuth Thrusters Based on Acceleration Measurements
## 3 Results and Discussion
### Classification Tests  
The data used for classification are shown as scatter plots between the shaft speed and feature values in Figures 13 and 14 for thrusters 1 and 2, respectively. Some of the features,  
Figure 12: Monitoring of thruster 2 by using three different sets of features during a period spanning over 466 days. such as features no. 1, 4, 7 and 9, show distinct clusters between the classes in both data sets. However, the patterns are different although the same type of damage was reported on both thrusters. For example, feature no. 5 does not show clear difference between the classes in 300-350 rpm in Figure 13, whereas Figure 14 shows some difference between the classes. Some of the features, such as features no. 2 and 3, do not show distinct differences between the classes in neither of the figures. Many features had a positive correlation with the shaft speed, but it is not fully linear, as shown by features no. 1 and 9 in Figure 14. In addition, the feature values had a discontinuity around 380 rpm shaft speed indicating there could be two separate operational areas. Figure 15 shows the classification results for the data set of thruster 1. The bearing feature set had the highest accuracy from different feature sets in general. At least 90% accuracy was reached with the bearing feature set by each method apart from the AdaBoost M1, which had low accuracy (50.18%). The highest test accuracy (95.51%) was achieved by using \"probabilistic threshold\" approach with \(\alpha\) = 0.001. The other criteria (precision, recall, specificity) reached over 94% value then as well. The time domain feature set resulted in the highest test accuracy, 88.78%, with \"two distributions\" approach. The test accuracies of the reference methods were in the range 79.46-82.92% but AdaBoost M1 suffered from overfitting because the training accuracy was 99.51%. The \"probabilistic threshold\" approach had the lowest test accuracy 56.13% (\(\alpha\) = 0.001) to 75.68% (\(\alpha\) = 0.1). Figure 13: Scatter plots of shaft speed with feature values in the data set of thruster 1. The \(x\)-axis shows the shaft speed (rpm) and the \(y\)-axis shows the feature value. The samples representing “positive class” are taken after the videoscope inspection and “negative class” represents the undamaged condition. The definitions for features no. 1–11 are given in Table 3.  
With the gear feature set, \"probabilistic threshold\" approach reached test accuracies 75.01-81.79% whereas \"two distributions\" approach had the test accuracy 84.47%. These accuracies are lower than the test accuracies of some of the reference methods, the range of  
Figure 14: Scatter plots of shaft speed with feature values in the data set of thruster 2. For interpretation, see the caption of Figure 13.  
Figure 15: Thruster 1 classification results. The plots from top to bottom show the averages of accuracy, precision, recall and specificity. The results with time domain features, bearing features and gear features are shown by using eight classification methods. The first three methods on the left apply “probabilistic threshold” approach, the fourth method applies “two distributions” approach, and the rest of the results are given by the reference classifiers. which was 83.98% (AdaBoost M1) to 89.28% (k-NN). AdaBoost M1 suffered from overfitting while the training accuracy was 97.44%. The highest test precision (98.58%) was achieved by using LDA with the bearing features as input variables. The highest recall (100%) was achieved by using \"probabilistic threshold\" approach (\(\alpha\) = 0.1) with the bearing feature set. By using \(\alpha\) = 0.05 or \"two distributions\" approach, the value was almost as high. The highest specificity (99.96%) was achieved by using AdaBoost M1 with the bearing features as input variables, but the accuracy was poor indicting that the classification was unsuccessful.