**4. Conclusions**

In this work, based on the analysis of multi-phase multi-mode batch processes, a combination of the multi-phase quality residual recursion model for multiple phases and the between-mode model for multiple modes is proposed, and according processmonitoring strategies based on quality analysis are developed. Firstly, the critical-to-quality phases are identified and selected based on the influence of different phases on the final quality of the batch process. Then, the phase mean model is established, and based on the multi-phase quality residual recursive model, the quality predictions of critical-to-quality phases are obtained, and those phases are monitored. On the other hand, the betweenmode model is used to analyzes the regression relationship between the process variables and the quality of the new mode through the historical modes, and online monitoring is carried out on this basis. Through the simulation of the experimental data of an injection molding process, it is proved that due to better quality predictions, the proposed strategy can provide better process-monitoring results for multi-phase multi-mode batch processes.

However, the experimental data used in this paper are all processed so that the length of the same phase of different batches is equal, which is often difficult to achieve in the actual industry due to various reasons, such as the influence of climate, the quality difference of raw materials, the data acquisition system based on a non-time coordinate, etc. In order to solve this problem, the effect of this method on the data of the batch process with unequal data lengths should be considered. For this, further research will be conducted in the future.

**Author Contributions:** Conceptualization, L.Z.; methodology, L.Z., X.H. and H.Y.; software, X.H. and H.Y.; validation, L.Z; formal analysis, L.Z., X.H. and H.Y.; investigation, L.Z.; resources, L.Z.; data curation, X.H.; writing—original draft preparation, X.H. and H.Y.; writing—review and editing, L.Z. and X.H.; visualization, X.H.; supervision, L.Z.; project administration, L.Z.; funding acquisition, L.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (No. 61503069) and the Fundamental Research Funds for the Central Universities (N150404020).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are openly available in https://share. weiyun.com/GCsqQcET (accessed on 29 July 2021).

**Acknowledgments:** This work is supported in part by the National Natural Science Foundation of China (No. 61503069) and the Fundamental Research Funds for the Central Universities (N150404020).

**Conflicts of Interest:** The authors declare no conflict of interest.
