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摘要: 熱軋支持輥的健康狀態在帶鋼板形質量和軋制穩定性控制中起著關鍵作用，非線性、強耦合、少樣本等特點使得熱軋支持輥健康狀態的預測復雜，目前各大鋼廠仍以定期維護和事后維修為主。本文提出了一種支持輥虛擬健康指數的構建方法以及基于Copula函數的復雜工況健康狀態預測模型。首先結合支持輥彎竄輥數據表征支持輥健康狀態，再使用K-means聚類方法對支持輥工況進行劃分，將各工況下過程數據分別構建Copula預測模型，最后根據實際軋制計劃的排布順序融合各工況模型的預測結果。提出的基于Copula函數的預測模型在某鋼廠1780熱連軋產線得到應用，結果表明，該模型能夠準確有效的按照軋制計劃實現支持輥的健康狀態預測，以更科學的策略指導支持輥更換維護。Abstract: The health condition of hot-rolling back-up rolls plays a key role in controlling the strip profile quality and rolling stability. The characteristics of nonlinearity, strong coupling, and the use of limited samples complicate the prediction of the back-up roll health state. The current back-up roll replacement strategy of each steel mill is generally determined according to a certain rolling time or rolling kilometer, and such a maintenance mode is based on experience. In actual experience, due to different strip specifications in each rolling cycle, the degrees of wear on the back-up rolls are different. Regular maintenance methods may easily lead to excessive wear of the back-up rolls and reduce the quality of the strip shape at the end of the unit, or premature roll replacement wastes the back-up roll performance. This paper proposed a construction method for the back-up roll virtual health index and a Copula function–based model for predicting the health condition of complex working conditions. The health condition of a pair of back-up rolls was characterized by combining roll bending and shifting data, and the back-up roll condition was divided by the K-means clustering method. The Copula prediction model was constructed using the process data under each working condition, and finally, according to the actual rolling schedule, the arrangement order combines the prediction results of the working conditions. The production performance data of a 1780-mm hot rolling line were used to verify the results. The results show that the proposed Copula-based prediction model can accurately and effectively predict the health condition of the back-up roll according to the rolling schedule; thus, it can serve as the basis of a more scientific strategy to guide the replacement and maintenance of the back-up roll.
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Key words:
- back-up roll /
- health prognostics /
- Copula function /
- data-driven /
- profile and flatness
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圖 1 F7機架VHI數據（1#）表現出隨軋制計劃推進而上升的趨勢
Figure 1. Rising trend of F7 stand VHI data (1#) with the rolling schedule
圖 4 工況1支持輥VHI數據擬合降噪后結果示意圖
Figure 4. Result of noise reduction after fitting VHI data of working condition 1
圖 5 使用Copula函數預測支持輥健康狀態的建模流程圖
Figure 5. Flow chart for predicting the health of back-up roll using Copula function
圖 6 對單工況訓練集數據劃分退化等級示意圖
Figure 6. Data degradation level for single-working-condition training set
圖 7 處于不同退化等級下的分布模型適用于不同類型的Copula函數描述。（a）T12-T50, Gumbel; （b） T26?T50, Frank; （c） T46?T50, Clayton
Figure 7. Distribution models at different degradation levels fit for different types of Copula function descriptions: (a) T12?T50, Gumbel; (b) T26?T50, Frank; (c) T46?T50, Clayton
圖 8 提高模型適應性的平移處理。（a）過早失效時Copula模型無法預測；（b）Copula模型平移
Figure 8. Translation processing to improve model adaptability: (a) Copula model is unpredictable at premature failure; (b) translation of copula model
圖 10 經過VHI變尺度處理的單工況預測結果
Figure 10. Single-condition VHI prediction result after scale conversion
表 1 某鋼廠1780熱連軋產線F7機架支持輥使用情況統計
Table 1. Statistics on the use of F7 back-up roll in a 1780 hot rolling line
Data number Total number of rolled strips Total rolling weight/t Total rolling length /km 1# 15016 336000 12015 2# 16024 356000 13216 3# 17654 388900 15015 4# 14168 308000 12282 5# 16291 362300 13596 
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表 2 復雜工況下Copula模型融合預測結果
Table 2. Copula model fusion prediction results under complex conditions
Test set number Actual number of rolled strips Actual VHI Predict VHI Model error/% 5# 16291 0.726 0.769 5.85 4# 14168 0.831 0.758 ?8.74 3# 17654 0.909 0.976 7.34 2# 16024 0.825 0.862 4.42 1# 15016 0.891 0.815 ?8.54
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