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 & Management Optimization, 2017, 13 (3) : 1149-1167. doi: 10.3934/jimo.2016066
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. Google Scholar

[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. Google Scholar

[3]

X. G. DuanC. H. YangH. X. LiW. 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. Google Scholar

[4]

S. Engell, Feedback control for optimal process operation, Journal of Process operation, 17 (2007), 203-219. Google Scholar

[5]

S. JanaquiJ. 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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[9]

W. PengR. 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. Google Scholar

[10]

J. S. Shih and H. C. Frey, Coal blending optimization under certainty, European Journal of Operational Research, 83 (1995), 452-465. Google Scholar

[11]

A. SinghJ. ForbesP. 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. Google Scholar

[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. Google Scholar

[13]

J. H. WiebengaG. Klaseboer and V. D. Boogaard, A H-∞ theory and applications of robust optimization, Society for Industrial and Applied Mathematics, 53 (2011), 464-501. Google Scholar

[14]

C. H. YangW. H GuiL. 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. Google Scholar

[15]

C. H. YangW. H GuiL. 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. Google Scholar

[16]

C. H. YangW. H. GuiL. 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. Google Scholar

[17]

C. J. YuK. L. TeoL. 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. Google Scholar

[18]

C. J. YuK. L. TeoL. 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. Google Scholar

[19]

Y. ZhangD. 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. Google Scholar

show all references

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. Google Scholar

[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. Google Scholar

[3]

X. G. DuanC. H. YangH. X. LiW. 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. Google Scholar

[4]

S. Engell, Feedback control for optimal process operation, Journal of Process operation, 17 (2007), 203-219. Google Scholar

[5]

S. JanaquiJ. 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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[9]

W. PengR. 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. Google Scholar

[10]

J. S. Shih and H. C. Frey, Coal blending optimization under certainty, European Journal of Operational Research, 83 (1995), 452-465. Google Scholar

[11]

A. SinghJ. ForbesP. 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. Google Scholar

[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. Google Scholar

[13]

J. H. WiebengaG. Klaseboer and V. D. Boogaard, A H-∞ theory and applications of robust optimization, Society for Industrial and Applied Mathematics, 53 (2011), 464-501. Google Scholar

[14]

C. H. YangW. H GuiL. 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. Google Scholar

[15]

C. H. YangW. H GuiL. 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. Google Scholar

[16]

C. H. YangW. H. GuiL. 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. Google Scholar

[17]

C. J. YuK. L. TeoL. 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. Google Scholar

[18]

C. J. YuK. L. TeoL. 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. Google Scholar

[19]

Y. ZhangD. 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. Google Scholar

Figure 1.  The real-time operational control of alumina blending process
Figure 2.  Three-time re-mixing operation
Figure 3.  The novel robust real-time optimization for alumina blending operation
Figure 4.  The variation of quality of recycled material
Figure 5.  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
Table 1.  Target quality specification of slurry
index $r_{1}$$r_{2}$$r_{3}$
$r_{1}^{\star}$ $\epsilon_{1}$ $r_{2}^{\star}$ $\epsilon_{2}$ $r_{3}^{\star}$ $\epsilon_{3}$
specification0.960.012.1930.034.660.03
index $r_{1}$$r_{2}$$r_{3}$
$r_{1}^{\star}$ $\epsilon_{1}$ $r_{2}^{\star}$ $\epsilon_{2}$ $r_{3}^{\star}$ $\epsilon_{3}$
specification0.960.012.1930.034.660.03
Table 2.  The nominal quality of bauxites and auxiliary materials
CaO(%)Na$_{2}$O(%)SiO$_{2}$(%)Fe$_{2}$O$_{3}$(%)Al$_{2}$O$_{3}$(%)
Bauxite 12.240.507.087.5267.2
Bauxite 23.200.429.488.8063.4
Bauxite 32.800.4012.737.2761.4
Bauxite 43.000.468.5723.452.0
Limestone95.30.104.550.441.50
Anthracite007.140.894.93
Alkali098000
CaO(%)Na$_{2}$O(%)SiO$_{2}$(%)Fe$_{2}$O$_{3}$(%)Al$_{2}$O$_{3}$(%)
Bauxite 12.240.507.087.5267.2
Bauxite 23.200.429.488.8063.4
Bauxite 32.800.4012.737.2761.4
Bauxite 43.000.468.5723.452.0
Limestone95.30.104.550.441.50
Anthracite007.140.894.93
Alkali098000
Table 3.  Comparison of $SP$ for RRTO and IRTO
MethodRRTOIRTO
$SP$98 % 82 %
MethodRRTOIRTO
$SP$98 % 82 %
Table 4.  Comparison of computational time for RRTO and IRTO
MethodRRTOIRTO
Time(s)9.7199.78
MethodRRTOIRTO
Time(s)9.7199.78
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