# A Combined Anomaly and Trend Detection System for Industrial Robot Gear Condition Monitoring
## 2 Materials and Methods
### Method for Anomaly and Trend Detection Model Selection
#### 2.2.3 Model Evaluation  
To measure the models' performance, the ROC curves (receiver operating characteristic curves) for different parameter choices of the models were determined. This means that different model parameters were varied and the True Positive Rate (TPR) and False Positive Rates (FPR) of the models for the synthetic data were determined. More precisely, the models were presented with slices of the time series and had to determine, whether trends or anomalies were present in the time series. For the trend detection task, these slices were increased in size per time series with a window size of 1008 samples and an initial size of 2016 samples. This is equivalent to 24 measurements per day for a length of 12 weeks for the initial window. For the anomaly detection, the first 168 values were used to train the models. This is equivalent to 24 measurements per day for one week. The models were then tested on time series with a length of 6720 samples. The parameters that were varied for the different models are summarized in Table 11. The most robust models with high TPR and low FPR and high average AUC values (area under the curve) were then applied to data sets from accelerated robot gear wear tests. A data set, which is based on an accelerated wear test with an ABB IRB 6600-255/2.55, was used to test the trend detection models (Accelerated wear test 1). The experiment caused different faults in the robot gear of the second axis. In total, 2425 measurements over a time span of roughly one year were used from the experiment; these were acquired with an acceleration sensor at the robot gear cap. From this data the HI described in [3] was derived. For more information regarding the experiment, see [39; 40]. The same data set and another data set, which was acquired during another accelerated wear test with an ABB IRB 7600-340/2.8, to test the anomaly detection models (Accelerated wear test 2). Here, 920 measurements were acquired over three months at the second axis gear cap with an acceleration sensor, and the same HI was calculated and various gear faults were subsequently detected in the second axis gear. As no obvious trend could be seen in this data set, it was just used for the AD model evaluation.  
More information regarding this experiment is given in [3]. Figure 5 presents the various faults of both accelerated wear tests. For analyzing these data sets, the models' parameters were chosen that yielded the best compromise in TPR and FPR during the experiments with the synthetic data. In a real world setup, other parameter sets could be more reasonable in respect of the trade-off between false alarms and undetected faults. A method of how to choose the best parameters given the maintenance circumstances of an individual robot is discussed in Section 4. Based on the results of the accelerated wear test experiments, a suggestion of which models to use for trend and anomaly detection in the CM system is made. The detailed model evaluation method based on synthetic data is depicted in Figure 6.