## 5 Conclusions  
We focus on how to select effective features out of those extracted from composite fault signals of rolling bearings, thus making the composite fault diagnosis more accurate. We propose a feature selection approach based on the causal feature network (CFN), introducing causality into composite fault diagnosis and expressing such causality with the complex network model. With the model, we take an overall perspective in considering the features and their correlations in the rolling bearing system. Meanwhile, we use causality to express the hidden pattern of interactions within the system. First, we draw upon IAMB discovery algorithm to obtain the causal relationships between composite fault features and construct the complex network to express the causality. Then, we introduce nodes' centrality indicators to quantify the importance of composite fault features and propose new criteria of threshold selection to determine the number of selected features. At last, we undertake experiments to verify the effectiveness of our approach. Experimental results show that our feature selection approach based on causality and complex network achieves high accuracy. Comparative experiments show that our approach achieves higher accuracy with fewer features.  
The following are this paper's primary conclusions: (1) When a composite fault is diagnosed using a DNN model, the diagnostic accuracy rate often increases before declining as the number of features increases. The growth in the number of characteristics after the accuracy rate reaches its maximum causes the accuracy rate to appear to remain the same or even decline. (2) The accuracy rate is unquestionably increased at first when features are added, but as time goes on, the improvement weakens; after a certain point, adding more features has no further impact on the effectiveness of the diagnosis. (3) Our suggested feature selection approach may surpass the diagnostic effect of 20 features with just about 10 features and achieve higher accuracy with less feature information. (4) Under identical circumstances, the diagnostic accuracy of 4000 randomized trials is concentrated around 90%, whereas the accuracy of our suggested technique can reach 94.6%. Our proposed method has clear advantages for feature selection for compound defect diagnosis.  
In this study, we take a comprehensive approach to represent the hidden interaction patterns of rolling bearing systems. Then, causality is used to define the edges of complex networks. Results illustrate that our methods have clear advantages for feature selection for compound defect diagnosis. Future studies could concentrate on two aspects. On one hand, the strength of the causal relationships embedded in the network model allows further comparison of fault diagnosis results. On the other hand, the new index of node centrality should be developed to measure the important features of composite faults.  
Conceptualization, C.Y. and K.G.; methodology, Z.W. and K.G.; investigation, K.G.; data curation, K.G.; writing--original draft preparation, K.G.; writing--review and editing, M.L., Z.W., S.L. and C.Y.; supervision, C.Y. and Z.W. All authors have read and agreed to the published version of the manuscript.  
The work is supported by the National Natural Science Foundation of China (61833002).  
Not applicable.  
The data are available upon request.  
The authors declare no conflict of interest.