**Figure 9.** *Cont*.

**Figure 9.** Performance comparison. Numbers in parentheses are the *p*-values of the Mann–Whitney U test.

From Figure 9, in all process patterns, the proposed method is better than UMPCA-BC, though only slightly better at *F*1. To further test whether the proposed method outperforms the alternative method significantly in all process patterns, Mann–Whitney U tests are conducted, and their *p*-values are also presented in Figure 9. If the 1% level of significance is taken, the superiority of the proposed model is significant except *F*1. There are two reasons for this situation. Firstly, the rounding operation of the grayscale image makes the *F*1 process lose detail information, which further makes our model not sensitive to a small shift in abnormal process pattern *F*1. Secondly, in practical production, the failure of the acid spouting system does have a grea<sup>t</sup> impact on the thickness uniformity of plates in a short time. In other words, the variation of thickness uniformity in *F*1 is usually small in a limited size of identification window, which increases the similarity between normal pattern and *F*1 pattern. As a result, the performance of the proposed method has a limited improvement at *F*1. However, in general, the CNN method proposed in this paper can identify the abnormal process with spatial-temporal data more accurately than the UMPCA-BC method.

To further verify the reliability of the proposed model, sensitivity analysis is carried out and the effect of noise on performance is studied. The white Gaussian noise is generated and added to the original test data as follows:

$$\mathbf{x}\_{i,j}^{noise} = \mathbf{x}\_{i,j} + \mathbf{g}\_{\prime}\mathbf{g} \sim N(0, \sigma^2),\tag{9}$$

where *xi*,*j* is the value at row *i* and column *j* of original data matrix, and *g* refers to the noise that obeys normal distribution with a mean of zero and a standard deviation of *σ*. In this example, the specification limits of plate thickness are 1.75 ± 0.02, and only the values of *σ* at 0 to 0.02 are considered. For convenience, five scenarios, including 0, 0.005, 0.01, 0.015, and 0.002 are implemented, shown in Table 5.


**Table 5.** The performance comparison for various noise levels.

The recognition accuracy of the proposed method and UMPCA-BC is inevitably decreased with an increase of *σ*. However, from Table 5, the proposed method still outperforms UMPCA-BC with an increasing noise level. Therefore, the CNN method proposed in this paper can identify the abnormal process with spatial-temporal data with better results.

#### **6. Limitations of the Proposed Methodology**

Some aspects may limit the application and assessment of the proposed framework, such as the following ones:


#### **7. Conclusions and Further Work**

This paper develops a general framework based on the CNN model to detect the abnormal pattern and diagnose the causes in the pasting process with spatial-temporal data. Different from traditional schemes, the main contribution of our proposed framework makes full use of both normal and abnormal information from historical data, and it overcomes the dilemma of multiple data types in real applications. The proposed model is tested on the example of the pasting process and achieved a better recognition performance than the alternative method. Experimental results demonstrated that better performance can be achieved at all abnormal process patterns in the pasting process. In addition, the sensitivity analysis of noise is also provided to verify the superiority of the proposed method. In addition, the procedure for constructing the recognition model is convenient. Our proposed CNN recognition model shows the good potential of online monitoring and tracing the root cause simultaneously. Benefiting from the CNN model, the spatial and temporal interrelationship of abnormal information can be captured and all the historical information can be utilized by the proposed CNN model.

However, there are two outstanding issues on this topic. First, although this paper focuses on the pasting process, the CNN recognition framework we proposed could be applied to any other abnormal process monitoring and diagnosis, where the observations are spatial-temporal data. In order to improve the performance of the CNN recognition model, the CNN model should be investigated further to make the proposed framework more suitable for other general situations. Second, the parameter optimization of the CNN model is a challenging work in the deep learning domain. However, it is not our concern in current work, thus the parameters of the CNN model only for the pasting process are determined in our paper. In fact, the architecture parameters are related to the data type, shape of the abnormal patterns, and the number of the data sample, thus more suggestions for determining proper parameters are needed. Some other advanced parameter optimization techniques should be added to the CNN framework to improve the recognition accuracy further. Therefore, future improvements can be conducted in the following ways. First, this framework can be modified to identify the process of other general situations by using the transfer learning method. Second, other advanced techniques for hyper-parameters optimization can be studied further to replace the manual method, such as heuristic search algorithms and design of experiments' techniques.

**Author Contributions:** Conceptualization, Z.Z. and Y.L.; methodology, Z.Z.; software, S.Z.; validation, Y.L.; formal analysis, Y.L. and Z.Z.; investigate Z.Z.; resources, Y.L.; data curation, Z.Z.; writing—original draft preparation, Z.Z.; writing—review and editing, Y.L.; visualization, Z.Z.; supervision, U.J.; project administration, Y.L.; funding acquisition, Y.L. 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 Grant No. 71672182, U1604262, U1904211, and 71672209.

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