*3.4. Multi-Mode Monitoring*

For the between-mode modeling analysis, 18 batches in mode 1, mode 2, mode 4, and mode 5 are selected respectively as historical modes. Mode 3 with 18 batches is used as the new mode for modeling. The test data are constructed by the five test batches of mode 3. According to the four-fold cross-validation method, in each phase of modeling, the number

of reserved latent variables of the traditional method and the proposed method is two. The confidence level of *α* is set to 0.99.

In order to illustrate the advantages of the method proposed in this paper, it is compared with the traditional multi-mode and multi-phase methods, in which individual models are built for a single phase within a single mode. One batch of five test batches in mode 3 is selected to show the results. The simulation results of the prediction are shown in Figure 12. The mean RMSE predicted for the five test batches under different prediction methods are shown in Table 4. The mean RMSE predicted of mode 3 by the traditional method is 0.0496, while the mean RMSE predicted by the proposed method is 0.0458, which indicates that the proposed method shows a more accurate prediction effect. The monitoring results of the injection phase and the packing-holding phase of the first test batch of mode 3 are shown in Figures 13 and 14, respectively. In Figure 13, it can be seen that *T*<sup>2</sup> and *SPE* do not exceed the control limits in the injection phase. In Figure 14, in the packing-holding phase, *T*<sup>2</sup> and *SPE* do not exceed their respective control limits.

**Figure 12.** Multi-mode online prediction of mode 3.

**Table 4.** RMSE of different prediction method.


**Figure 13.** Multi-mode online monitoring of injection phase of mode 3.

**Figure 14.** Multi-mode online monitoring of packing-holding phase of mode 3.

In addition, in order to illustrate the monitoring of new test modes by the multiphase multi-mode model, 18 batches of mode 2, mode 3, mode 4, and mode 5 are selected respectively as the historical modes for each phase, and the historical regression parameters are obtained. Mode 3 with 18 batches is used as the new mode for modeling to predict and monitor the new test batches of mode 1. The results of each phase of one batch of five test batches in mode 1 are displayed. The simulation results of quality prediction are shown in Figure 15. The mean RMSE predicted of mode 1 for the five test batches under different prediction methods are shown in Table 4. The mean RMSE predicted by the traditional method is 0.1010, while the mean RMSE predicted by the proposed method is 0.0876, which indicates that the proposed method shows a more accurate prediction effect. Figures 16 and 17, respectively, show the monitoring results of the injection phase and the packing-holding phase of one test batch of mode 1. Because the historical mode and training data do not contain the information of mode 1, when monitoring, *T*<sup>2</sup> and *SPE* in the injection phase exceed the control limit, which will lead to an alarm.

**Figure 15.** Multi-mode online prediction of mode 1.

**Figure 17.** Multi-mode online monitoring of packing-holding phase of mode 1.

In order to compare the prediction results of the single-mode model and the betweenmode model of different prediction methods, RMSE values of five test batches in mode 3 and mode 1 are used for judgment, as shown in Table 4.

According to the simulation results, it can be concluded that the between-mode model extracts the related information in the historical modes, so it contains more necessary information. It can be seen from Table 4 that the prediction results of the between-mode model are better than those of the single-mode model. Comparing the RMSE of the traditional method and the proposed method, it can be seen that the proposed method is more accurate for quality prediction. From the monitoring figures, it can be seen that if part of the mode information has been included in the modeling process, the statistics do not exceed the control limit, leading to a suitable monitoring effect. In contrast, if the modeling process does not contain the mode information, the statistics will exceed the control limits. To sum up, compared with single-mode modeling, the between-mode modeling contains more historical modal information, leading to better prediction, and can achieve the purpose of information selecting for monitoring. Therefore, for the current modes modeling, the between-mode modeling method can be selected.

For faulty batch monitoring using the between-mode modeling, the faulty batch data is consistent with the single-mode modeling faulty batch data. First, the faulty batch caused by material disturbance is monitored. The monitoring results of the traditional method and the proposed method are shown in Figure 18. Both the proposed method and the traditional method can detect the fault.

**Figure 18.** Multi-mode online monitoring of material disturbance fault.

Secondly, the monitoring effects of the traditional method and the proposed method for the sensor fault are shown in Figure 19. Compared with the traditional method, the statistics of the proposed method rise more sharply, and the amplitudes are relatively large.

**Figure 19.** Multi-mode online monitoring of sensor fault.
