Comparison of the effect of various clustering algorithms on the furnace profile management
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摘要: 高爐操作爐型與高爐操作、技術經濟指標等關系密切，合理的操作爐型有利于保證高爐生產的優質、低耗、高產、長壽。通過對冷卻壁溫度的聚類分析，能夠有效合理地表征高爐操作爐型的變化，對高爐生產有著重要的指導意義。分別采用K-Means、TwoStep對數據集進行聚類分析，基于兩種聚類算法的原理，結合Davies?Bouldin index（DBI）與Dunn index（DI）對聚類結果進行評價，分析不同聚類算法間的差異，得出了在所選樣本數據及數據特征基礎上，K-Means算法聚類結果更好的結論，該研究可為高爐煉鐵大數據分析中的聚類算法選擇提供有力參考。Abstract: The blast furnace operation profile is closely related to the operation, technical and economic indicators of a blast furnace. A reasonable furnace operation profile ensures high-quality hot metal, low fuel consumption, high yield, and furnace longevity. To guide the blast furnace ironmaking, cluster analysis of the stave temperature is implemented to effectively characterize the changes in the furnace operation profile. The K-Means, TwoStep, and hierarchical clustering algorithms are often used to monitor the blast furnace operation profile. The present study also shows that various clustering algorithms can help manage the blast furnace operation profile. However, the difference among the clustering results from these algorithms remains unclear. Based on the previous research, this paper compared the clustering principles and research status with various algorithms and selected two algorithms of K-Means and TwoStep, which were more applicable and compatible with the algorithm principles. The K-Means algorithm is a typical partition-based clustering algorithm with low time complexity, high clustering efficiency, and good clustering quality. It has been widely used in cluster analysis of the blast furnace operation profile. Additionally, domestic scholars had given effective improvement measures for the shortcomings of sensitivity to the initial center and requirements for data distribution. The TwoStep algorithm was an improved BIRCH (Balanced iterative reducing and clustering using hierarchies) algorithm, which reduced time complexity and can automatically determine the optimal number of clusters. The authors of this article considered the problem that indicators for evaluating the furnace operation profile were multiple and largely overlapped. Principal Component Analysis was introduced based on the TwoStep algorithm. Three new core indicators were generated from the traditional evaluation indicators for the clustering results of the furnace operation profile. For blast furnace operation profile monitoring and management, three core indicators also showed improved performance. In this paper, K-Means and TwoStep were used to cluster the data set. Based on the principles of these algorithms and combined with the Davies?Bouldin index and Dunn index, the clustering results were analyzed to judge the difference between the two clustering algorithms. The analysis based on the sample data and data characteristics selected in this article revealed that the K-Means algorithm achieved better clustering results than TwoStep. This research can provide a powerful reference for selection among various clustering algorithms in blast furnace ironmaking big data analysis.
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Key words:
- furnace profile management /
- K-Means /
- TwoStep /
- cluster evaluation index /
- big data
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圖 1 高爐各段冷卻壁位置示意圖
Figure 1. Position of a cooling stave in each section of a blast furnace
圖 2 不同聚類簇數的DBI和DI指標結果. (a) DBI評價指標； (b) DI評價指標
Figure 2. Result calculation of a cluster evaluation index for various numbers of clusters: (a) Davies-Bouldin index； (b) Dunn validity index
圖 3 K-Means聚類結果中6類爐型冷卻壁各段溫度分布
Figure 3. Temperature distribution of each cooling stave of six furnace profiles by K-Means clustering algorithm
圖 4 TwoStep聚類結果中6類爐型冷卻壁各段溫度分布
Figure 4. Temperature distribution of each cooling stave of six furnace profiles by TwoStep clustering algorithm
圖 5 TwoStep聚類結果中簇數為6、7時數據分布
Figure 5. Data distribution when the numbers of clusters are six and seven by TwoStep clustering algorithm
圖 6 K-Means聚類結果中簇數為6時數據分布
Figure 6. Data distribution when the number of clusters is six by K-Means clustering algorithm
圖 7 K-Means、TwoStep聚類結果（簇數為6）
Figure 7. K-Means, TwoStep clustering results (number of clusters is 6)
表 1 聚類算法分類及特點
Table 1. Classification and characteristics of clustering algorithms
Clustering algorithms Advantages Disadvantages K-Means Low time complexity; high computing efficiency Number of clusters needed to be preset; not suitable for
nonconvex dataBased on Hierarchy Suitable for the arbitrary data set; high scalability High time complexity; number of clusters needed to be preset SOM Diverse and developed models providing means to describe data adequately High time complexity; premise not completely correct; clustering result sensitive to the parameters of selected models TwoStep Improved BIRCH algorithm; automatically determined clustering numbers Medium computational efficiency for large-scale data; clustering algorithm cannot remerge or separate clusters to optimize
clustering results
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表 2 聚類評價指標
Table 2. Cluster evaluation index
Name Measure method or formula Compactness (CP) ${ {\overline{{\rm{CP}}} }_{{i} } }=\dfrac{1}{\left|{\varOmega }_{i}\right|}\displaystyle\sum _{ {x}_{i}\epsilon {\varOmega }_{i} }\parallel{x}_{i}-{w}_{i}\parallel $，
${\overline{ {\rm{CP} } } }=\dfrac{1}{K}\displaystyle\sum _{k=1}^{K}{\overline{\rm{CP}} }_{k}$Separation (SP) $\overline{{{\rm{SP}}} }=\dfrac{2}{ {k}^{2}-k}\displaystyle\sum _{i=1}^{k}\displaystyle\sum _{j=i+1}^{k}{\parallel{w}_{i}-{w}_{j}\parallel}_{2}$ Davies?Bouldin indicator (DBI) $\mathrm{D}\mathrm{B}\mathrm{I}=\dfrac{1}{k}\displaystyle\sum _{i=1}^{k}\underset{j\ne i}{\mathrm{max} }\left(\dfrac{\stackrel{-}{ {C}_{{i} } }+\stackrel{-}{ {C}_{{j} } } }{ {\parallel{w}_{i}-{w}_{j}\parallel}_{2} }\right)$ Dunn indicator (DI) $\mathrm{D}\mathrm{I}=\dfrac{\underset{0 < m\ne n < k}{\mathrm{min} }\left\{\left.\underset{\forall {x}_{i}\in {\varOmega }_{m},\forall {x}_{j}\in {\varOmega }_{n} }{\mathrm{min} }\left\{\left. \parallel {x}_{i}-{x}_{j}\parallel \right\}\right.\right\}\right.}{\underset{0 < m\leqslant K}{\mathrm{max} }\underset{\forall {x}_{i},{x}_{j}\in {\varOmega }_{m} }{\mathrm{max} }\left\{\left. \parallel{x}_{i}-{x}_{j}\parallel \right\}\right.}$ Silhouette coefficient Evaluate the clustering result based on the average distance between a data point and other data points in the same cluster and the average distance among various clusters, while the number of data samples among various clusters is almost the same. Notes: (1) ${\varOmega }_{i}$ stands for a collection representing a certain type of data in all clusters; (2) K stands for the total number of clusters; (3)$ k $ stands for the number of clusters; (4) $ {x}_{i},{x}_{j} $ stand for the different data point in the cluster; (5) $ {w}_{i},{w}_{j} $ stand for the different center of various clusters; (6) $ \parallel{x}_{i}-{w}_{i}\parallel $ stands for the distance from the data point to the center of a cluster; (7)$ {\parallel{w}_{i}-{w}_{j}\parallel}_{2} $ stands for the distance among various clusters; (8) $ \stackrel{-}{{C}_{t{i}}},\stackrel{-}{{C}_{{j}}} $ stand for the different average distance of all data points in the same cluster; (9)$ m,n $ stand for the different cluster; (10)$ \parallel {x}_{i}-{x}_{j}\parallel $ stands for the distance among any two data points.
下載: 導出CSV
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