# Time Series Feature Selection Method Based on Mutual Information
## 5 Conclusions  
Extracting effective features of a system based on mutual information values is a commonly used feature extraction method in the field of machine learning. However, one of the most challenging issues with this method is finding suitable target variables. Theoretically, these target variables must include the main performance indicators of system operation to ensure that the extracted features can effectively reflect the multiple characteristics of the system. Especially for time series, the historical data of system operation contains a large amount of information, but at the same time, there is significant redundancy and noise within this information. To solve this problem, this paper proposes a method for feature selection based on MI, in which system operability is used as a target variable. Firstly, the system operability is extracted based on PCA dimension reduction and kernel smoothing, which is monotonic and irreversible. Using it as the target variable for MI analysis is more credible compared to using individual sensor signals as the target variable. On this basis, features are filtered based on the value of mutual information between features and the target variable. In order to verify the effectiveness of the method, comparisons and analyses were conducted with F-test scores. The results show that feature extraction based on mutual information can better analyze and extract the non-linear relationship between  
Figure 8: Recognition of working conditions based on the selected features (figure drawn by seaborn): (**a**) working condition recognition based on \(s9\); (**b**) working condition recognition based on \(s9\) and s11; and (**c**) working condition recognition based on \(s9\), s11, and s12. features and target variables. Finally, to further validate the effectiveness of the method, we conducted tests on condition recognition based on the CMPASS dataset. The CMPASS dataset contains continuous operational data of the engine throughout its entire life cycle under six different operating conditions. Effectively partitioning these data between the six different operating conditions is crucial for subsequent analysis. Therefore, based on the selected feature variables, the system condition recognition was carried out. The results indicate that by using the first three extracted feature variables, the complex condition recognition of the system can be achieved. From the above analysis, we identified that the proposed method can effectively achieve system feature extraction and is suitable for feature extraction problems of time series data. However, it should be noted that one of the most critical steps of the method proposed in this paper is constructing the system operability based on sufficient historical operational data. Therefore, the method is mainly applicable to devices with a large amount of historical operating data. If the data are insufficient, the constructed system operability may not reflect the overall characteristics of the system, leading to inaccurate estimation of MI values. For example, the CMAPSS dataset FD001 used in this paper contains monitoring parameter information for the full life cycle status of 200 engines. Regarding future work, we plan to study the construction of system operability based on online data and the analysis of MI values, in order to reduce the dependence on historical operating data and improve the applicability of this method. Conceptualization, L.H. ; methodology, X.Z. ; software, L.H. ; validation, L.S. ; formal analysis, X.Z. ; investigation, L.G. ; resources, L.G. ; data curation, L.S. ; writing--original draft preparation, L.H. ; writing--review and editing, L.G. ; supervision, L.G. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable.