# Information Extraction from Industrial Sensor Data Using Time Series Meta-Features
## 4 Experiment and Results  
For the experiment, we used Python 3.9.12, R 4.0.5, scikit-learn 0.24.1, pandas 1.2.1, Matplotlib 3.3.4, and feasts 0.1.6. We applied the presented approach to real sensor data from TAE to find salient sensor data that indicate detached or faulty sensors. The original sensor data set under analysis contained 748 time series between 8 October 2020 07:00 and 9 October 2020 07:00, generated by 22 thermocouples mounted to 34 reduction cells in the first pot room. All 120 cells in the first pot room are fitted with shell heat exchangers to maintain the ledge of each cell during current modulation [14]. The mounting positions of the thermocouples were not considered in the analysis, as we were only interested in finding salient sensor data. The data have been resampled with a resolution of 1 min to create evenly spaced time series. For the calculation of time series meta-features, the temperature data were converted to Kelvin. We conducted three iterations, following each step in Figure 3. To create a meta-feature data set, we calculated several time series meta-features taken from [8; 15; 22; 31], which are listed in Table 2.  
A total of 432 time series had at least one meta-feature for which no value could be calculated. A visual inspection showed a constant value for each of the time series, which resulted in an exclusion of the corresponding meta-feature instances in further analyses. In the next step, a PCA was conducted using the z-transformed meta-feature instances from 316 time series. The first and second principal component were used to generate a two-dimensional feature space, which is visualized in Figure 4. Each point represents a time series, some of which are plotted as a black curve next to their corresponding point in the figure. Several points, e.g., TCWT2-1068, TCWT5-1118, TCWT3-1118, TCWT6-1118 and TCWT2-1118, diverge from the left-hand side cluster and therefore show an implausible \begin{table}
\begin{tabular}{c c} \hline \hline ACF1 & Burst \\ \hline Curvature & Linearity \\ \hline Longest flat spot & Max \\ \hline Mean & Min \\ \hline Moment & Ratio high low mean \\ \hline Ratio mean iqmean & Shift level index \\ \hline Shift level max & Shift var index \\ \hline Shift var max & Spectral entropy \\ \hline Spikiness & Var tiled mean \\ \hline Var tiled var & Variance \\ \hline \hline \end{tabular}
\end{table} 
Table 2: 20 time series meta-features were calculated for the experiment. range of temperature values. The corresponding meta-feature instances were removed from the meta-feature data set. After removing the meta-features in the first iteration, an additional PCA was conducted. The resulting first two principal components are visualized in Figure 5. The time series TCWT5-1012, TCWT4-1033 and TCWT6-1116 showed implausible characteristics. The corresponding meta-feature instances were not considered in the third iteration. The first two principal components from the third iteration are shown in Figure 6. Some time series displayed in Figure 6 exhibit a curved progress, some of which can be explained by an influence of the shell heat exchangers airflow, due to an increase in current that took place over four hours of the analysis period. Other time series, e.g., TCWT3-1061, TCWT3-1001, TCWT6-1012, and TCWT2-1115, are salient in their characteristics and should be further analyzed. In summary, Figure 6 gives an overview about the different time series characteristics of the sensor data set. Due to the generation of a two-dimensional feature space in multiple iterations, salient and implausible time series could be identified.