Grinding process particle size modeling method using robust RVFLN-based ensemble learning
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摘要: 作為磨礦過程的主要生產質量指標, 磨礦粒度是實現磨礦過程閉環優化控制的關鍵.將磨礦粒度控制在一定范圍內能夠提高選別作業的精礦品位和有用礦物的回收率, 并減少有用礦物的金屬流失.由于經濟和技術上的限制, 磨礦粒度的實時測量難以實現.因此, 磨礦粒度的在線估計顯得尤為重要.然而, 目前我國所處理的鐵礦石大多數為性質不穩定的赤鐵礦, 其礦漿顆粒存在磁團聚現象, 所采集的數據存在大量異常值, 使得利用數據建立的磨礦粒度模型存在較大誤差.同時, 傳統前饋神經網絡在磨礦粒度數據建模過程中存在收斂速度慢、易于陷入局部最小值等缺點, 且單一模型泛化性能較差, 現有的集成學習在異常值干擾下性能嚴重下降.因此, 本文在改進的隨機向量函數鏈接網絡(random vector functional link networks, RVFLN)的基礎上, 將Bagging算法與自適應加權數據融合技術相結合, 提出一種基于魯棒隨機向量函數鏈接網絡的集成建模方法, 用于磨礦粒度集成建模.所提方法首先通過基準回歸問題進行了實驗研究, 然后采用磨礦工業實際數據進行驗證, 表明其有效性.
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關鍵詞:
- 磨礦粒度 /
- 隨機向量函數鏈接網絡 /
- 集成學習 /
- 魯棒性 /
- 數據融合
Abstract: As a key production quality index of grinding process, particle size is of great importance to closed-loop optimization and control. This is because controlling particle within a proper range can improve the concentrate grade, enhance the recovery rate of useful minerals, and reduce the loss of metal in the sorting operation; thus, the particle size determines the overall performance of the grinding process. In fact, it is not easy to optimize or control the practical industrial process because the optimal operation largely depends on a good measurement of particle size of grinding process; however, it is difficult to realize the real-time measurement of particle size because of limitations of economy or technique. Employing soft sensor techniques is necessary to solve the problem of particle size estimation, which is particularly important for the actual grinding processes. Considering that soft sensors are applicable in many fields, the data-driven soft sensor will be a useful tool for achieving particle size estimation. However, most of the iron ores processed in China are characterized by hematite with unstable properties, and the slurry particles exhibit magnetic agglomeration, giving rise to a large number of outliers in the collected data. In this case, there are gross errors in the particle size estimation model constructed based on the data and thus unreliable measurements. Meanwhile, the traditional feedforward neural networks have the disadvantages of slow convergence speed and easily fall into local minimum during the prediction process. A single model tends to lack superiority in sound generalization, and the performance of existing ensemble learning methods will be worse under outlier interference. Therefore, in this study, based on the improved random vector functional link networks (RVFLN), the Bagging algorithm is incorporated into an adaptive weighted data fusion technique to develop an ensemble learning method for particle size estimation of grinding processes. Experimental studies were first conducted through benchmark regression issues and then validated by the samples collected from an actual grinding process, indicating the effectiveness of the proposed method.-
Key words:
- particle size /
- random vector functional link networks /
- ensemble learning /
- robustness /
- data fusion
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圖 1 磨礦過程工藝流程
α1—球磨機給礦量，t·h-1；α2—球磨機入口給水量，m3·h-1；α3—螺旋分級機溢流質量分數；c1—球磨機電流，A；c2—螺旋分級機電流，A；T—檢測儀；W—質量；F—流量；C—電流；D—密度
Figure 1. Flow diagram of grinding process
圖 2 批次磨礦試驗下的磨礦速率與磨礦濃度關系
Figure 2. Relationship between grinding rate and mill density based on batch grinding experiment
圖 3 分級機溢流質量分數與磨礦粒度的關系
Figure 3. Relationship between classifier overflow concentration and particle size
圖 6 ξ=20%時函數近似比較試驗. (a) 直接平均隨機向量函數鏈接網絡集成；(b) 數據融合隨機向量函數鏈接網絡集成；(c) 數據融合魯棒隨機向量函數鏈接網絡集成
Figure 6. Comparison experiments of function approximation at ξ=20%: (a) RVFLN-based direct average ensemble learning; (b) RVFLN-based data fusion ensemble learning; (c) robust RVFLN-based data fusion ensemble learning
圖 7 基準回歸比較試驗. (a) combined cycle power plant；(b) concrete；(c) wine
Figure 7. Comparison experiments of benchmark regression: (a) combined cycle power plant; (b) concrete; (c) wine
圖 8 ξ=30%時磨礦粒度估計.(a) 直接平均隨機向量函數鏈接網絡集成；(b) 數據融合隨機向量函數鏈接網絡集成；(c) 數據融合魯棒隨機向量函數鏈接網絡集成
Figure 8. Particle size estimation of grinding process at ξ=30%: (a) RVFLN-based direct average ensemble learning; (b) RVFLN-based data fusion ensemble learning; (c) robust RVFLN-based data fusion ensemble learning
表 1 函數近似集成建模性能比較
Table 1. Performance comparison of ensemble learning for function approximation
數據集 集成建模方法 模型參數, L 模型參數, λ mean, t/s 異常值水平0 異常值水平10% 異常值水平20% 異常值水平30% 直接平均隨機向量函數鏈接網絡集成 500 20 8.2×10-4, 0.143 0.008, 0.138 0.011, 0.156 0.013, 0.147 非線性復合函數 數據融合隨機向量函數鏈接網絡集成 500 20 8.1×10-4, 0.143 0.007, 0.140 0.010, 0.145 0.012, 0.144 數據融合魯棒隨機向量函數鏈接網絡集成 500 50 8.9×10-4, 0.408 0.003, 0.409 0.005, 0.411 0.008, 0.419 
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表 2 磨礦粒度集成建模性能比較
Table 2. Performance comparison of ensemble learning for particle size of grinding process
數據集 集成建模方法 模型參數, L 模型參數, λ mean, t/s 異常值水平0 異常值水平10% 異常值水平20% 異常值水平30% 直接平均隨機向量函數鏈接網絡集成 50 1 0.095, 0.063 0.183, 0.063 0.212, 0.062 0.231, 0.063 實際工業磨礦過程 數據融合隨機向量函數鏈接網絡集成 50 1 0.086, 0.063 0.168, 0.062 0.201, 0.623 0.224, 0.063 數據融合魯棒隨機向量函數鏈接網絡集成 50 1 0.009, 0.118 0.035, 0.113 0.072, 0.120 0.106, 0.119
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參考文獻
[1] Chen X S, Li Q, Fei S M. Supervisory expert control for ball mill grinding circuits. Expert Syst Appl, 2008, 34(3): 1877 doi: 10.1016/j.eswa.2007.02.013 [2] Zhou P, Dai W, Chai T Y. Multivariable disturbance observer based advanced feedback control design and its application to a grinding circuit. IEEE Trans Control Syst Technol, 2014, 22(4): 1474 doi: 10.1109/TCST.2013.2283239 [3] Wang X L, Gui W H, Yang C H, et al. Wet grindability of an industrial ore and its breakage parameters estimation using population balances. Int J Miner Process, 2011, 98(1-2): 113 doi: 10.1016/j.minpro.2010.11.008 [4] Meyer E J, Craig I K, The development of dynamic models for a dense medium separation circuit in coal beneficiation, Miner Eng, 2010, 23(10): 791 doi: 10.1016/j.mineng.2010.05.020 [5] Sun Z, Wang H G, Zhang Z K. Soft sensing of overflow particle size distributions in hydrocyclones using a combined method. Tsinghua Sci Technol, 2008, 13(1): 47 doi: 10.1016/S1007-0214(08)70008-7 [6] Wang X H, Gui W H, Wang Y L, et al. Prediction modeling for particle size of grinding circuit of mixture kernels SVM. Comput Eng Appl, 2010, 46(12): 207 doi: 10.3778/j.issn.1002-8331.2010.12.062王新華, 桂衛華, 王雅琳, 等. 混合核函數支持向量機的磨礦粒度預測模型. 計算機工程與應用, 2010, 46(12): 207 doi: 10.3778/j.issn.1002-8331.2010.12.062 [7] Qiao J H, Chai T Y. Soft measurement model and its application in raw meal calcination process. J Process Control, 2012, 22(1): 344 doi: 10.1016/j.jprocont.2011.08.005 [8] Igelnik B, Pao Y H. Stochastic choice of basis functions in adaptive function approximation and the functional-link net. IEEE Trans Neural Netw, 1995, 6(6): 1320 doi: 10.1109/72.471375 [9] Huang G B, Chen Y Q, Babri H A. Classification ability of single hidden layer feedforward neural networks. IEEE Trans Neural Netw, 2000, 11(3): 799 doi: 10.1109/72.846750 [10] Zhang S Y, Bao Y P, Zhang C J, et al. Prediction model of aluminum consumption with BP neural networks in IF steel production. Chin J Eng, 2017, 39(4): 511 https://www.cnki.com.cn/Article/CJFDTOTAL-BJKD201704005.htm張思源, 包燕平, 張超杰, 等. BP神經網絡IF鋼鋁耗的預測模型. 工程科學學報, 2017, 39(4): 511 https://www.cnki.com.cn/Article/CJFDTOTAL-BJKD201704005.htm [11] Pao Y H, Phillips S M, Sobajic D J. Neural-net computing and the intelligent control of systems. Int J Control, 1992, 56(2): 263 doi: 10.1080/00207179208934315 [12] Scardapane S, Wang D H. Randomness in neural networks: An overview. WIREs Data Min Knowl Disc, 2017, 7(2): e1200 doi: 10.1002/widm.1200 [13] Ditterrich T G. Machine learning research: four current direction. Artif Intell Mag, 1997, 4: 97 http://ci.nii.ac.jp/naid/10020896742 [14] Kearns M J, Valiant L G. Learning Boolean Formulae or Finite Automata is as Hard as Factoring. Cambridge: Harvard University, Center for Research in Computing Technology, Aiken Computation Laboratory, 1988 [15] Schapire R E. The strength of weak learnability. Mach Learn, 1990, 5(2): 197 doi: 10.1109/SFCS.1989.63451 [16] Schwenk H, Bengio Y. Boosting neural networks. Neural Comput, 2000, 12(8): 1869 doi: 10.1162/089976600300015178 [17] Martínez-Mu?oz G, Suárez A. Out-of-bag estimation of the optimal sample size in bagging. Pattern Recognit, 2010, 43(1): 143 doi: 10.1016/j.patcog.2009.05.010 [18] Dai W, Chai T Y, Yang S X. Data-driven optimization control for safety operation of hematite grinding process. IEEE Trans Ind Electron, 2015, 62(5): 2930 doi: 10.1109/TIE.2014.2362093 [19] Dai W, Liu Q, Chai T Y. Particle size estimate of grinding processes using random vector functional link networks with improved robustness. Neurocomputing, 2015, 169: 361 doi: 10.1016/j.neucom.2014.08.098 [20] Rao C R. Generalized Inverse of Matrices and its Applications. New York: Wiley, 1971 [21] Wang D H, Alhamdoosh M. Evolutionary extreme learning machine ensembles with size control. Neurocomputing, 2013, 102: 98 doi: 10.1016/j.neucom.2011.12.046 -
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