4.1.2. Fault Detection and Identification

From the previous subsection, the GRU model can be used to generate residuals. As is shown in the Figure 6, there is an obvious change after the 2000th sample. In order to detect this change, SVDD is used here. The parameters of SVDD are set as *σ* = 10, *C* = 0.01. With 99% of confidence limit, the monitoring results using SVDD are shown in Figure 7a.

**Figure 7.** Monitoring results for the hanging fault. (**a**) Monitoring results of GRU-SVDD, (**b**) Monitoring results of LSTM-SVDD, (**c**) Monitoring results of principal component analysis (PCA)-SVDD.

From Figure 7a it can be seen that significant violation of the confidence limit can be observed, indicating that there is a fault happening in the blast furnace system. This is in accordance with the fact that the last 400 samples correspond to a hanging fault. For comparison, the monitoring results using LSTM-SVDD and PCA-SVDD are shown in Figure 7b,c. The LSTM network has the same structure and parameters as GRU-SVDD. For PCA-SVDD, PCA is first performed on the training data and SVDD is used to detect the residual subspace. The number of principal components retained for PCA is 3. Comparing Figure 7a–c, it can be seen that GRU-SVDD and LSTM-SVDD has higher sensitivity than PCA-SVDD. The detection rates of the three methods are shown in Table 2.


**Table 2.** Comparison of detection rate for different methods.

Table 2 confirms the finding that GRU-SVDD and LSTM-SVDD have better detection rates. Considering the simpler structure of GRU, obviously GRU-SVDD is a better method. After the hanging fault is detected, fault identification is then performed based on the GRU residuals. Figure 8 shows the sample by sample GRU residuals, with deeper color indicating greater residuals.

**Figure 8.** The sample by sample normalized GRU residuals in Case 1.

For a clearer inspection, Figure 9 presents the accumulated normalized GRU residuals. Figure 9 shows that the hanging fault has significant impact on the concentration of flue gas, with the most significant change happening in the CO2, CO, H2 concentration. This will lead experienced operators to inspect the gas flow and see whether there is any kind of hanging fault happening in the system.

**Figure 9.** The fault contribution rate for each variable in Case 1.

#### *4.2. Case 2: Abnormal Molten Iron Temperature*

In this subsection, a faulty condition from the same blast furnace is considered. The fault involves an abnormal fluctuation of the molten iron temperature, which caused the operators to adjust the quantity of blast *u*<sup>1</sup> as well as the temperature of blast *u*2, resulting in change in a series of variables. In the later stage, the fault was corrected, however the temperature of blast was kept at a relatively low level for the sake of safety. Similar to the hanging fault, 2000 samples were collected under the normal operating conditions for model training, and a faulty dataset containing 1000 samples is considered. The fault involves an abnormal molten iron temperature, which caused reduction in blast quantity,

blast temperature and fluctuation in a series of variables related to the gas flow. This time, 10 process variables are considered and listed in Table 3.


**Table 3.** The input variables for Case 2.

Comparing to Table 1, it can be seen that three additional variables, the temperature of cold blast (*u*5), the top pressure (*u*6) and the pressure of cold blast (*u*10) are also included. it should be noted some of them are redundant variables (*u*<sup>5</sup> and *u*10) that are highly related with other variables. The purpose for introducing these variables is to show the capability of the proposed method in dealing with variable redundancy.

Similar to Section 4.1, the proposed GRU method is applied, with the same parameter values. And the prediction results for the 10 variables are shown in Figure 10. For a clearer exhibition, only the 1000 faulty samples are presented. It can be seen that for the first 200 samples, the prediction accuracy is acceptable. After that, an obvious fluctuation can be observed and the prediction accuracy deteriorated. After the 2450th sample, the prediction accuracy for all variables except *u*<sup>2</sup> return normal.

After the predictions are obtained, SVDD is applied and the monitoring results are shown in Figure 10b. It can be seen that the fault was successfully detected since significant number of violations can be observed after the 2250th sample. This again indicates the good capability for the proposed method in fault detection. It should be noted that violations can still be observed even after the fault was corrected after 2450th sample. This can be explained, as to avoid further fault, the operators decided to reduce the temperature of blast(*u*2), which caused the violations. This can be confirmed by the subsequent fault identification results in Figure 11.

In Figure 11, the first plot involves the fault identification results from samples from 2250 to 2450, while the second plot involves the identification results for samples from 2450 till 3000. As can be seen from the first plot of Figure 11, it can be clearly seen all variables except *u*<sup>4</sup> have significant contribution to the fault, indicating a significant anomaly arises. This is expected, as to correct the fault, both the quantity of blast and the temperature of blast are reduced, resulting in changes in other variables. From the second plot, it can be seen that after the fault was corrected, the contribution of other variables reduced significantly while that of *u*<sup>2</sup> remains. This is in accordance with our previous analysis that the operators reduced the temperature of blast to avoid further fault. The application results of the second faulty case also confirmed the performance of the proposed method.

**Figure 10.** Prediction results using GRU and monitoring results using SVDD for Case 2. (**a**) Prediction results using GRU, (**b**) Monitoring results using SVDD.

**Figure 11.** The fault contribution rate for each variable in Case 2. (**a**) The Contribution of different variables in observations 2250 to 2450, (**b**) The Contribution of different variables in observations 2450 to 3000.

#### **5. Conclusions**

This paper introduces a fault detection and identification method for blast furnace ironmaking process based on the GRU network and SVDD. The GRU model is capable of handling multi-dimensional inputs to make predictions for future inputs. The residuals between the actual inputs and predictions are then monitored using SVDD. A fault identification method is further developed by inspecting the accumulated normalized residuals. The proposed method is tested on a hanging fault observed in a real blast furnace in China. Application results show that the proposed GRU-SVDD model can successfully detect the hanging fault. Compared with the PCA-SVDD model, GRU-SVDD has a higher detection rate. The method proposed in this article is very suitable for monitoring systems with strong dynamics and non-Gaussianity.

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

**Funding:** The authors would like to thank financial support from National Natural Science Foundation of China (Grant Nos. 61673358 and 61973145).

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