# American Institute of Mathematical Sciences

July  2017, 13(3): 1149-1167. doi: 10.3934/jimo.2016066

## Robust real-time optimization for blending operation of alumina production

 1 College of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou, Hunan 412007, China 2 Department of Mathematics, Shanghai University, 99 Shangda Road, Baoshan, Shanghai, China 3 Changsha University of Science and Technology, Changsha, China 4 Department of Mathematics and Statistics, Curtin University, Kent Street, Bentley, WA 6102, Australia 5 School of Information Science and Engineering, Central South University, South Lushan Road, Yuelu, Changsha, China

* Corresponding author: Changjun Yu

Received  January 2016 Published  October 2016

The blending operation is a key process in alumina production. The real-time optimization (RTO) of finding an optimal raw material proportioning is crucially important for achieving the desired quality of the product. However, the presence of uncertainty is unavoidable in a real process, leading to much difficulty for making decision in real-time. This paper presents a novel robust real-time optimization (RRTO) method for alumina blending operation, where no prior knowledge of uncertainties is needed to be utilized. The robust solution obtained is applied to the real plant and the two-stage operation is repeated. When compared with the previous intelligent optimization (IRTO) method, the proposed two-stage optimization method can better address the uncertainty nature of the real plant and the computational cost is much lower. From practical industrial experiments, the results obtained show that the proposed optimization method can guarantee that the desired quality of the product quality is achieved in the presence of uncertainty on the plant behavior and the qualities of the raw materials. This outcome suggests that the proposed two-stage optimization method is a practically significant approach for the control of alumina blending operation.

Citation: Lingshuang Kong, Changjun Yu, Kok Lay Teo, Chunhua Yang. Robust real-time optimization for blending operation of alumina production. Journal of Industrial and Management Optimization, 2017, 13 (3) : 1149-1167. doi: 10.3934/jimo.2016066
##### References:
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##### References:
 [1] H. G. Beyer and B. Sendhoff, Robust optimization -A comprehensive survey, Computer Methods in Applied Mechanics and Engineering, 196 (2007), 3190-3218.  doi: 10.1016/j.cma.2007.03.003. [2] T. Y. Chai, Optimal operational control for complex industrial processes, The 8th IFAC International Symposium on Advanced Control of Chemical Processes,, 8 (2012), 722-731. [3] X. G. Duan, C. H. Yang, H. X. Li, W. H. Gui and H. Deng, Hybrid expert system for raw materials blending, Control Engineering Practice, 16 (2008), 1364-1371.  doi: 10.1016/j.conengprac.2008.03.008. [4] S. Engell, Feedback control for optimal process operation, Journal of Process operation, 17 (2007), 203-219. [5] S. Janaqui, J. Aguilera and M. Chébre, Robust real-time optimization for the linear oil blending, RAIRO-Operations Research, 47 (2013), 465-479.  doi: 10.1051/ro/2013052. [6] C. Lim and K. L. Teo, Optimal insulin infusion control via a mathematical blood glucoregulatory model with fuzzy parameters, Cybernetics and Systems, 22 (1991), 1-16.  doi: 10.1080/01969729108902267. [7] A. Marchetti, A. Gopalakrishnan, B. Chachuat and D. Bonvin, et al, Robust real-time optimization of a solid oxide fuel cell stack Journal of Fuel Cell Science and Technology, 8 (2011), 051001. doi: 10.1115/1.4003976. [8] M. R. Naysmith and P. L. Douglas, Review of real-time optimization in the chemical process industries, Developments in Chemical Engineering and Mineral Processing, 3 (1995), 67-87.  doi: 10.1002/apj.5500030202. [9] W. Peng, R. V. Mayorga and S. Imran, A robust optimization approach for real-time multiple source drinking water blending problem, Journal of Water Supply: Research and Technology-AQUA, 61 (2012), 111-122.  doi: 10.2166/aqua.2012.037. [10] J. S. Shih and H. C. Frey, Coal blending optimization under certainty, European Journal of Operational Research, 83 (1995), 452-465. [11] A. Singh, J. Forbes, P. J. Vermeer and S. S. Woo, Model-based real-time optimization of automotive gasoline blending operations, Journal of Process Control, 10 (2000), 43-58.  doi: 10.1016/S0959-1524(99)00037-2. [12] K. L. Teo and C. C. Lim, Time optimal Control computation with application to ship steering, Journal of Optimization Theory and Applications, 56 (1998), 145-156.  doi: 10.1007/BF00938530. [13] J. H. Wiebenga, G. Klaseboer and V. D. Boogaard, A H-∞ theory and applications of robust optimization, Society for Industrial and Applied Mathematics, 53 (2011), 464-501. [14] C. H. Yang, W. H Gui, L. S Kong and Y. L. Wang, Modeling and optimal-setting control of blending process in a metallurgical industry, Computers and Chemical Engineering, 33 (2009), 1289-1297.  doi: 10.1016/j.compchemeng.2009.01.005. [15] C. H. Yang, W. H Gui, L. S. Kong and Y. L. Wang, A two-stage intelligent optimization system for the raw slurry preparing process of alumina sintering production, Engineering Applications of Artificial Intelligence, 22 (2009), 786-805.  doi: 10.1016/j.engappai.2008.11.003. [16] C. H. Yang, W. H. Gui, L. S. Kong and X. L. Wang, A genetic-algorithm-based optimal scheduling system for full-filled tanks in the processing of starting materials for alumina production, The Canadian Journal of Chemical Engineering, 86 (2008), 804-812.  doi: 10.1002/cjce.20039. [17] C. J. Yu, K. L. Teo, L. S. Zhang and Y. Q. Bai, On a refinement of the convergence analysis for the new exact penalty function method for continuous inequality constrained optimization problem, Journal of Industrial Management and Optimization, 8 (2012), 485-491.  doi: 10.3934/jimo.2012.8.485. [18] C. J. Yu, K. L. Teo, L. S. Zhang and Y. Q. Bai, A new exact penalty function method for continuous inequality constrained optimization problems, Journal of Industrial Management and Optimization, 6 (2010), 895-910.  doi: 10.3934/jimo.2010.6.895. [19] Y. Zhang, D. Monder and J. Forbes, Real-time optimization under parametric uncertainty: A probability constrained approach, Journal of Process Control, 12 (2002), 373-389.  doi: 10.1016/S0959-1524(01)00047-6.
The real-time operational control of alumina blending process
Three-time re-mixing operation
The novel robust real-time optimization for alumina blending operation
The variation of quality of recycled material
Comparison of slurry quality indices. Dotted lines-the upper and lower bounds of quality indices and their target values; solid line-quality indices of slurry produced by results of IRTO and RRTO
Target quality specification of slurry
 index $r_{1}$ $r_{2}$ $r_{3}$ $r_{1}^{\star}$ $\epsilon_{1}$ $r_{2}^{\star}$ $\epsilon_{2}$ $r_{3}^{\star}$ $\epsilon_{3}$ specification 0.96 0.01 2.193 0.03 4.66 0.03
 index $r_{1}$ $r_{2}$ $r_{3}$ $r_{1}^{\star}$ $\epsilon_{1}$ $r_{2}^{\star}$ $\epsilon_{2}$ $r_{3}^{\star}$ $\epsilon_{3}$ specification 0.96 0.01 2.193 0.03 4.66 0.03
The nominal quality of bauxites and auxiliary materials
 CaO(%) Na$_{2}$O(%) SiO$_{2}$(%) Fe$_{2}$O$_{3}$(%) Al$_{2}$O$_{3}$(%) Bauxite 1 2.24 0.50 7.08 7.52 67.2 Bauxite 2 3.20 0.42 9.48 8.80 63.4 Bauxite 3 2.80 0.40 12.73 7.27 61.4 Bauxite 4 3.00 0.46 8.57 23.4 52.0 Limestone 95.3 0.10 4.55 0.44 1.50 Anthracite 0 0 7.14 0.89 4.93 Alkali 0 98 0 0 0
 CaO(%) Na$_{2}$O(%) SiO$_{2}$(%) Fe$_{2}$O$_{3}$(%) Al$_{2}$O$_{3}$(%) Bauxite 1 2.24 0.50 7.08 7.52 67.2 Bauxite 2 3.20 0.42 9.48 8.80 63.4 Bauxite 3 2.80 0.40 12.73 7.27 61.4 Bauxite 4 3.00 0.46 8.57 23.4 52.0 Limestone 95.3 0.10 4.55 0.44 1.50 Anthracite 0 0 7.14 0.89 4.93 Alkali 0 98 0 0 0
Comparison of $SP$ for RRTO and IRTO
 Method RRTO IRTO $SP$ 98 % 82 %
 Method RRTO IRTO $SP$ 98 % 82 %
Comparison of computational time for RRTO and IRTO
 Method RRTO IRTO Time(s) 9.71 99.78
 Method RRTO IRTO Time(s) 9.71 99.78
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