# Principal Component Analysis of Blast Furnace Drainage Patterns

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## Abstract

**:**

## 1. Introduction

## 2. Principal Component Analysis

## 3. Method and Data Sets

#### 3.1. Pre-Processing of the Data Set

- outflow near zero for any of the phases;
- taps shorter than 40 min that may occur as a result of disturbances, stoppages, or contingencies;
- any of the phases shows an outflow rate above 2% of the production rate at all times (i.e., also during the intercast period, where there should be no liquid outflows); and
- the total outflow abruptly goes near zero as a result of measurement errors or possibly taphole clogging.

#### 3.2. Post-Processing of the Results

_{hm}, where subscript hm denotes hot metal). The third and fourth components (C3 and C4) represent changes in the share of slag during tapping. Even though the data sets were treated separately, C1 and C2 display a similar meaningful representation of the data in the principal component space. C4 in Data set 1 and C3 in Data set 2 show similar pattern ranges as well. As seen in Figure 4, the outflow patterns of the three tapholes display different trends from variable 2 to 10, and this trend can be captured by the slopes that C4 in Data set 1 and C3 in Data set 2 describe. It can be concluded that these slopes reflect how the slag share develops during the tapping when both phases flow out. Figure 5 also indicates by solid lines the pattern corresponding to the mean values for each data set, which are seen to be very similar. In the principal component space, this pattern corresponds to the interception of the components, which is referred to as the mean pattern in what follows. The dotted lines correspond to lowest values in the principal component space (denoted by A) and the dashed lines correspond to highest values (denoted by B).

## 4. Results

#### 4.1. Data Set 1

#### 4.1.1. Period 1.1

#### 4.1.2. Period 1.2

#### 4.1.3. Period 1.3

#### 4.1.4. Period 1.4

#### 4.2. Data Set 2

#### 4.2.1. Period 2.1

#### 4.2.2. Period 2.2

#### 4.2.3. Period 2.3

#### 4.2.4. Period 2.4

#### 4.2.5. Periods 2.5 and 2.6

## 5. Results of PCA and Liquid Level Model

## 6. Summary of the Analysis

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Illustration of two cases of slag delay: (

**a**) positive slag delay (for the left taphole), (

**b**) negative slag delay (for the right taphole).

**Figure 2.**Examples of liquid outflow patterns from the Data set 2: (

**a**) zero slag delay and 135 min tap duration, (

**b**) negative slag delay and 170 min tap duration, (

**c**) zero slag delay and 70 min tap duration, and (

**d**) positive slag delay and 140 min tap duration.

**Figure 3.**Slag share for the taps presented in Figure 2. Upper panels: one-minute values obtained from the measurements. Lower panels: information discretized into 10 points (solid squares) and principal component analysis (PCA) reconstruction (open circles).

**Figure 4.**Overall median curves of Data set 1 and 2 and median by taphole (TH), (

**a**) Data set 1, (

**b**) first half of Data set 2, (

**c**) second half of Data set 2.

**Figure 5.**Slag share ranges represented by the principal component (C1…C4) for Data set 1 (left panels) and Data set 2 (right panels). Solid lines represent the mean pattern, dotted lines the lowest values (labelled A), and dashed lines the highest (labelled B). The percentage of variance explained by each component is reported in the right top part of each subpanel.

**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.

**Figure 7.**First vs. second principal components progression (C1, C2) corresponding to Data set 1 at different tap labels. (

**a**) Period 1.1, (

**b**) Period 1.2, (

**c**) Period 1.3, (

**d**) Period 1.4.

**Figure 8.**Fourth principal component (C4,

**top**) and average tap duration (

**bottom**) corresponding to the four periods of Data set 1. Blue line (TH-1), red line (TH-2), and green line (TH-3).

**Figure 9.**First vs. second principal components progression (C1, C2) corresponding to Data set 2 at different tap labels. (

**a**) Period 2.1, (

**b**) Period (2.2), (

**c**) Period 2.3, (

**d**) Period 2.4, (

**e**) Period 2.5, (

**f**) Period 2.6.

**Figure 10.**Third principal component (C3,

**top**) and average tap duration (

**bottom**) corresponding to the six periods of Data set 2. Blue line (TH-1), red line (TH-2), and green line (TH-3).

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**MDPI and ACS Style**

Roche, M.; Helle, M.; Saxén, H.
Principal Component Analysis of Blast Furnace Drainage Patterns. *Processes* **2019**, *7*, 519.
https://doi.org/10.3390/pr7080519

**AMA Style**

Roche M, Helle M, Saxén H.
Principal Component Analysis of Blast Furnace Drainage Patterns. *Processes*. 2019; 7(8):519.
https://doi.org/10.3390/pr7080519

**Chicago/Turabian Style**

Roche, Mauricio, Mikko Helle, and Henrik Saxén.
2019. "Principal Component Analysis of Blast Furnace Drainage Patterns" *Processes* 7, no. 8: 519.
https://doi.org/10.3390/pr7080519