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1、322Vol.32,No.2 20063ACTA AUTOMATICA SINICA March,20061(116024TP274Application of a Novel Grey Relation Analysis Algorithmto Soft SensorLI Yong SHAO Cheng(Institute of Advanced Control Technology,Dalian University of Technology,Dalian116024Abstract As an eective technique of on-line measurement,soft

2、sensor has been studied by many eorts.Being the premise of soft sensor,it is important to select secondary variables, which can directly inuence the eciency of soft sensor.Grey relation analysis gives a novel method to dig correlation between variables and is suitable to conrm the correlation degree

3、 between little-sample data in uncertain systems.Through a detailed analysis of secondary variablesselection for soft sensor,a uniform incidence degree algorithm is presented based on grey relation theory to eciently select secondary variables.And a practical method to eliminate redundant variables

4、is also proposed.Meanwhile,a practical example is given to verify the feasibility and eectiveness of the method.Simulation results show that the method is ecient and helpful to enhance the accuracy of soft sensor.Key words Soft sensor,grey relation analysis,uniform incidence degree,radiate basis net

5、work3123223131+ |x i(k|¯j (1x i(k=x i(k+1x i(k(231432m1mk=2|x z(k|,z=i,j(4x i,x j k mµijr ijkx i(kx j(k>0x i(k=x j(k=0,x i,x j kk=1,x i(kx j(k=0x i(k=x j(k,x i,x j kk=0,x i(kx j(k<0,x i,x j kk=1,v ij(k=1¯i |x j(kx j(k1|m1m1k=1kµij(k ,= 1m1l m1k1=t1k1µij(k1(7Z ij=1m1d m

6、3k3=d1k3µij(k3(9m1+m2+m3=m1(10 r ij 12315¯z <x z(k+10.8320.71µ 32 2 Û º¿¡ ¡ ÓÁ « Ç ´ ¡ Û ÅÓ ¡¶ «¹ Ý Û Å C, Ê Ý Û Å F , C ¯ Ä m ¦ n ¿¸

7、; Ó (2m n. 3 C ¯ª ¦Ó ¯Ì Á « º ¿ Ê F (É ± ¯¡ + + ¦ º Í, Ä t ¿ ¯ ¡¶ «Ì F ¯ Ä ¹ F , F ¯ Å À Û¿ Ì ¤ 4 ¬ ¹ É &

8、#206; C ¯ Ê ¯ ´ 0 n t ¿ Ì F+ ¯ ¸ ¹¡ ´ Í §¤ 5 § ¶ « ¡ ¡± ¡ §·´ ¡ ¿ » º ¿ ¤ Û ¿¡ Û º ¼ ÓÁ « ¡ Æ &

9、#206; ¡ ½ ¤ Ø ¸ ·Ó ¡ ¿¡ · ¡ ¸ ¼ Å ÇÊ ¡Ì Ó ¦ ¿¡½ Ù Ü ¤ Ê ¯ ¡ÃÇ Û ¿ ¡½Ò ¦´ Ä È Ä © 

10、9;¡ ¡ ¿¡ Å Ö¤¾ RBF ³ À ¥ ©Í ¡¾ OLS ­ © À ¥ ¤ ³ ÝÁ ¡ ¿ Ì Ó ¡´ § ¡± ¡ §·Õ ¤ ´ ¡¾ ´ §« &

11、#201; ² 2 ´ Ý ¤ ³ 2 Ö°¬ ¥ ± 316 19 50 º 14 º ¾¯Ã ¦ ¾ ´ ¿ § ¿ Table 2 Ô§ 0.21% º ¢ Experimental performance index Ô§ 0.3% ¼¢ §Ô§ 0.64% º

12、 ¢ §Ô§ 0.91% ¼¢ Á ¡ ¡ Ñ É 1. 1 (a: b: Fig. 1 Soft sensor result of grinding concentration (a: Processed real value; b: Estimation ð£Î Í ´ ÉÌ Ö ¥ £ ª £ £ 5 Î Ê ¢

13、; ¡º© Á ¡ Ñ ÂÁ ¡ ­´ Ì ¡ à դ Ì ¤ Ó ¡ ÔÕ Þ Ñ§ º© Á ¡­¦ Í © ¡ À ¾ ª ÓÁ « ¡ Ô ¡¾

14、87; ¡¤ Í § Ä » ± ¡ ¡ ¹ Ó¦ À 0.7% ¡ §·Õ ¤ « ´ ¤ Ì ¡ Ê ÒÁ ­ ÇÍ ¡ º Û ¡ Ñ ÂÛ Ê Ð ­ Ì ¡Å À

15、; Í Ä ¡ ¾Ä « ¾ Ñ º Ä ©¤ ¤ ¤ 2 ½ Í Ò¨» ¥ ÓÃ Æ Î À 317 References 1 Mejdell T, Skogestad S. Output estimation using multiple secondary measurements: High-purity distillation. Am

16、erican Institute of Chemical Engineers Journal, 1993, 39(10: 16411653 2 Park S, Han C. A nonlinear soft sensor based on multivariate smoothing procedure for quality estimation in distillation columns. Computers and Chemical Engineering, 2000, 24: 871877 3 Albertos P, Goodwin G C. Virtual sensors for

17、 control applications. Annual Reviews in Control, 2002, 26: 101112 4 Wang X H, Li S Y, Xi Y G. Research on soft sensor model for slab temperature in reheating furnace. Acta Automatic Sinica, 2004, 30(6: 928932 5 Yu J S, Liu A L, Zhang K J. Soft Sensor Technology and Its Application in Petrochemical

18、Industry. Beijing: Chemical Industry Press, 2000. 56102 6 Geladi P, Kowalski B. Partial least squares regression: A tutorial. Analytical Chemic Aeta, 1986, 185: 117 7 Liu R L, Su H Y, Zhu J. Application of soft sensing method based on PLS regression for estimating the stabilizing oil components of c

19、atalytic reform reactor. Control and Instruments in Chemical Industry, 2002, 29(5: 4447 8 Chen L D, Toru S. Data mining methods, applications, and tools. Information System Management, 2000, 17(1: 6570 9 Deng J L. Grey Theory Basis. the 2nd edition. Wuhan: Huazhong University of Science and Technolo

20、gy Press, 2002. 122154 10 Yang G B, Gao Y Y. Fuzzy Mathematics Theory and Application. Guangzhou: South China University of Technology Press, 2001. 115125 11 Li X Q. Research on the computation model of grey interconnect degree. Systems Engineering, 1995, 13(6: 5861 12 Tang W X. The concept and the

21、computation method of T s correlation degree. Mathematics Statistics and Management, 1995, 14(1: 3438 13 Wang Q Y, Zhao X H. The relational analysis of C-mode. Journal of Huazhong University of Science and Technology, 1999, 27(3: 7577 14 Li H Y. Study on the calculation method of grey relationship d

22、egree. System Engineering and Electronics, 2004, 26(9: 12311234 15 Ma B G, Cheng G Q. A formula of similarity correlation degree. Systems Engineering-Theory & Practice, 2000, 7: 6971 16 Xu X L. Improvement and Application of Grey-Relation, -Clustering, and -Prediction. Master Degree Dissertation

23、, Xiamen: Xiamen University, 2001. 6: 1722 17 Wang Q Y. The grey relational analysis of Bmode. Journal of Huazhong University of Science and Technology, 1989, 17(6: 7782 18 Wang Z H. Study on Measurement Optimization of the Internal Parameters in Ball Mill. Ph. D. Dissertation, Shenyang: Northeaster

24、n University, 2001. 7: 1925 19 Chen S, Cowan C F N, Grant P M. Orthogonal least squares learning algorithm for radiate basis function network. IEEE Transactions on Neural Network, 1991, 2(2: 302309 (LI Yong Ph. D. candidate in the Department of Control Theory and Control Engineering at Dalian University of Technology. His rese

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