# Equipment Health Assessment: Time Series Analysis for Wind Turbine Performance
## 3 Results
### Deterioration Detection  
For deterioration detection, we have to find the balance between good performance on the good timeline and bad performance on the bad timeline. This needs to be achieved over a range of wind turbines (or other equipment) individually. The ensemble prediction method shows the most robust performance and therefore is our time series prediction method of choice. For deterioration detection, we use a continuous time period with good and bad timelines to test the performance of our approach. Figure 14 is showing an example test timeline for wind turbine no. 15 that has good and bad timelines. The bad timelines are labeled by the value 1 indicated by the orange line on the secondary y-axis. All labels were manually assigned according to the available information from the data provider. Figure 15 shows the power output prediction results (orange line) in regard to the actual power output (blue line). For overlaps between the actual and the predicted power, the line appears slightly grey. The predicted power outputs are obtained for each wind turbine based on the workflow presented in Figure 6 using the ensemble prediction method. We can observe that the RMSE (red line, scale on secondary y-axis), calculated for 24-h windows, is generally lower in the very beginning and in the middle of the presented test timeline. This observation matches with the time periods that we have identified as \"good timelines\" based on our domain knowledge. To detect deterioration in the performance of a wind turbine, we want to establish a prediction model performance baseline using RMSE or RMSPE metrics leveraging validation data, i.e., a known good timeline dataset that wasn't used during model training. This baseline can then be compared to the prediction performance of a test dataset where the real wind turbine output performance is unknown. Figure 16 shows an example of this process for wind turbine no. 15. The first graph shows the validation data and its RMSPE (green line on secondary y-axis). Once RMSPE value is calculated for each 24-h window hence the green line is cut off early in the plot and RMSE can be calculated in the same manner. Then, we use the obtained RMSE/RMSPE values to calculate value cutoff limits  
Figure 14: Test Data for Wind Turbine 15 with Labels for deterioration detection. Figure 13: Ensemble Prediction Results overall all bad timeline test datasets (best and worst values are highlighted per row/column as dark green: best in row, red: worst in row, light green: best in column, orange: worst in column). using simple statistics. For this research, the cutoff limits are calculated individually for each wind turbine prediction model using the 90% percentile RMSE value and the 95% percentile RMSPE value based on the validation data. Thus, dynamic cutoff limits can be calculated based on the prediction quality for each wind turbine. The cutoff limits are then used to identify if an RMSE/RMSPE value observed for the test data suggests a wind turbine performance deterioration or not. Examples of this can be seen in Figure 16 for wind turbine no. 15, where the second plot shows the RMSE based deterioration labels in red and true labels in purple. The third plot shows similar information for RMSPE with true labels in purple and identified labels in green. The two plots in the last row of Figure 16 show the confusion matrices for RMSE and RMSPE respectively. The plots give us insights into the performance deterioration classification accuracy of the two metrics. Our proposed performance deterioration approach performs better when we use the RMSPE metric. We observe 100% precision, meaning that if the wind turbine is in a good state, we are always able to classify this correctly. There are cases when the method is unable to detect deterioration correctly, especially when the expected power output is in a lower value range or at the beginning/end of a bad performing time period. Performance deterioration might therefore be harder to detect when wind speed and actual power output are low.