**4. Application Studies**

This section presents the application results of the proposed GRU-based fault detection and identification method to the datasets collected from a blast furnace (with the inner volume of 2500 m3) in China. Two case studies are studied, with Section 4.1 introduces the application of GRU-based fault detection and identification method to a hanging fault and Section 4.2 presents the application results to a fault involving fluctuation in molten iron temperature.

#### *4.1. Case 1: Hanging Fault*

The hanging fault happens in the upper part of the blast furnace, the fault caused a severe drop in the quantity of blast *u*<sup>1</sup> and pressure of blast *u*3, which subsequently resulted in an abnormal change in the composition of flue gas *u*5, *u*6, *u*7. For the purpose of model training, 2000 samples are collected under the normal operation condition and a faulty dataset containing 400 samples is considered. The sampling interval of the data is 20 min. A total of 7 process variables are considered and listed in Table 1. For comparison, the LSTM-SVDD and PCA-SVDD [20] methods are considered.


**Table 1.** The input variables for Case 1.

#### 4.1.1. Residual Generation Using the GRU Network

In order to reduce the impact of extreme values in the process data, the Hampel filter [21] is used to process the training set before feeding into the GRU network. During the training of GRU network, the mean square error loss function and 'Adam' optimizer are used [22]. The length of moving window *n* is set as 99 by trial and error. The number of hidden states in the first layer *dh* and the second layer *d <sup>h</sup>* are determined in a similar way. Figure 5 shows the modelling errors of the GRU network for *u*<sup>1</sup> under different combinations of *dh* and *d h*.

Considering both the modelling error and structure complexity, the fourth combination in Figure 5 is used so that *dh* = 32 and *d <sup>h</sup>* = 200. Also, to prevent overfitting, a dropout process is used in the training process by randomly discarding a part of units. Here, the dropout rate of *pd* = 0.2 is selected. The GRU network uses the past values to predict current values. The predicted values obtained by this model not only contains the past information, but also affected by other related variables. Therefore, when a fault happens, the predictions will deviate from the actual values. The modeling results of the GRU model are shown in Figure 6.

Figure 6 shows that there are some clear changes occurring in several variables (e.g., CO concentration, CO2 concentration and H2 concentration). the obtained residuals are then fed into the SVDD model to perform fault detection.

**Figure 5.** Prediction results for *u*<sup>1</sup> using models with different parameter settings (the red line corresponding to predictions, the blue line corresponding to true values). (**a**) Prediction results for *u*<sup>1</sup> with *dh* = 64 and *d <sup>h</sup>* = 100; (**b**) Prediction results for *u*<sup>1</sup> with *dh* = 64 and *d <sup>h</sup>* = 200; (**c**) Prediction results for *u*<sup>1</sup> with *dh* = 32 and *d <sup>h</sup>* = 100; (**d**) Prediction results for *u*<sup>1</sup> with *dh* = 32 and *d <sup>h</sup>* = 100.

**Figure 6.** The prediction results of the GRU model in Case 1 (the red lines represent prediction and the blue lines represent actual values).
