## 6 Conclusions  
In this paper, we propose a scheme that combined diverse CNN learners and AdaBoost tree-based ensemble classifier. The information of raw signals in the time domain, frequency domain, and time-frequency domain are employed in form of 2D images for diagnosis. Differently, samples are constructed separately and contribute to fault diagnosis simultaneously, which eliminates the situation that only one domain is focused or an elaborate feature integration across different domains must be determined in traditional vibration-based fault diagnosis, thus providing more freedom for the sample construction where each type of sample can concentrate on one aspect of the signal.  
An example based on the CWRU datasets is illustrated to prove the superiority of the proposed scheme by two steps: (1) comparing the performance between DCNN and Ada-DCNN (single DCNN embedded), and (2) comparing the performance between Ada-DCNN and hybrid Ada-DCNN (multi-DCNNs embedded). Both comparisons above are carried out under accuracy levels growing from S1 to S4. The results show that the diagnosis accuracy is averagely improved by an absolute value of 15.37%, 12.29%, 10.40%, and 5.14% from S1 to S4 by using Ada-DCNN instead of DCNN, and 29.26%, 24.59%, 18.68%, and 12.95% by using hybrid Ada-DCNN. Besides, robustness of the proposed hybrid Ada-DCNN is also investigated by dropping the performance of one or more DCNNs embedded.  
Figure 12: The accuracy changes of the hybrid Ada-DCNN, Ada-DCNNs, and DCNNs under different schemes: (**a**) Changes in accuracy with one DCNN dropped; (**b**) Changes in accuracy with two DCNNs dropped; (**c**) Changes in accuracy with three DCNNs dropped; (**d**) Reductions from the reference accuracy under each scheme.  
It presents a reduction of only 1.83%, 4.31%, and 12.29% of hybrid Ada-DCNN versus the average drop of 10.11%, 20.21%, and 26.75% of one, two, and three DCNNs, respectively.  
According to the results above, a hybrid Ada-DCNN is recommended for use in practical vibration-based fault diagnosis instead of traditional single DCNN method. The example in this paper has provided a specific way for using the proposed scheme to diagnose where the signal preprocessing and image sample construction methods can also be applied in other vibration-based analysis.  
Conceptualization, Q.Y. and B.Z.; methodology, B.Z.; software, H.Z.; validation, B.Z., H.Z.; formal analysis, Q.Y.; investigation, B.Z.; resources, H.Z.; data curation, H.Z.; writing--original draft preparation, B.Z.; writing--review and editing, B.Z., H.Z., and Q.Y.; visualization, H.Z.; supervision, Q.Y.; project administration, Q.Y.; funding acquisition, Q.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Nature Science Foundation of China, grant number 11872289, and the Key Project of Natural Science Foundation of Xi'an Jiao Tong University, grant number ZRZD2017025. And the APC was funded by the National Nature Science Foundation of China, grant number 11872289.  
The authors would like to thank the Case Western Reserve University Bearing Data Center for providing the data for this study.  
The authors declare no conflicts of interest.  
The dataset and DLM used and analyzed during the current study are available from the corresponding authors upon reasonable request.