**4. Results**

The method as a batch algorithm organizes all samples in the component dimensions regardless of the taphole operated. In order to process the results, moving averages of the selected principal components for the latest 20 taps (corresponding to approximately two days of operation) were considered. The average was calculated for each taphole, taking into account the taps that occurred within the latest 20-tap window. Thus, this post-processing criterion yields a quasi-time evolution. It is important to stress that the main objective of the work is to reveal similar or different behavior of the drainage from the different tapholes to gain understanding of the variability seen during operation. The left panel of Figure 6 shows a lay-out of the three tapholes in the furnace. The right top and bottom panels present the periods during which the tapholes were operated in Data set 1 and Data set 2, respectively. Each taphole is typically operated about three weeks for the blast furnace in question. This schedule results in the alternating operation of two tapholes at the time, with some overlap (where all three tapholes are used) during the transition periods. The figure also indicates the (numbered) periods that are analyzed in the following subsections.

**Figure 6.** Taphole location in the reference furnace (**left**) and operating periods of the tapholes for the Data set 1 (**right top**) and Data set 2 (**right bottom**). The sub-periods studied in following sections are also indicated.

It should be noted that the representation, because of the data compression and averaging, does not provide detailed information about single days of operation. However, the comparison between tapholes at any given point could indicate agreement or disagreement between the outflow patterns. We will present some snapshots (cf. Figures 7–10) of the motion of the averages of the principal components as time evolves. The corresponding components of the tapholes are depicted by blue line and diamonds (TH-1), red line and squares (TH-2), and green line and circles (TH-3). For the sake of clarity, the two most important components (C1 and C2) are plotted versus each other in a "phase plot" for shorter sub-periods (cf. Figures 7 and 9).

The positions of the markers on each curve indicate the average value of the components corresponding to each tapholes for the last 20 observations. For instance, a blue diamond labeled "70" indicates the average location in the principal component space of taps from TH-1 from taps 50 to 70 regardless of taphole. As the tapholes are operated alternatively, the same number label will appear next to the markers on the curves of the operating tapholes, indicating the pattern progression. For clarity, arrows show the direction of the evolution, and labels "start" and "end" are used to

indicate the first and last points of operation of a taphole if it occurs in the period. On the axes of each component, the limits of the component (lower by A, upper by B, cf. Figure 5) are also indicated. In addition to the phase plot of C1 and C2, similar averages of an additional principal component, C4 for Data set 1 (cf. Figure 8) and C3 for Data set 2 (cf. Figure 10), are plotted in a separate panel for each data set along with the average tap duration of the operating tapholes.
