CIESC Journal ›› 2020, Vol. 71 ›› Issue (2): 688-697.DOI: 10.11949/0438-1157.20190359
• Process system engineering • Previous Articles Next Articles
Yuheng XIE(),Zhi LI,Minglei YANG,Wenli DU()
Received:
2019-04-08
Revised:
2019-06-19
Online:
2020-02-05
Published:
2020-02-05
Contact:
Wenli DU
通讯作者:
杜文莉
作者简介:
谢雨珩(1994—),男,硕士研究生,基金资助:
CLC Number:
Yuheng XIE, Zhi LI, Minglei YANG, Wenli DU. Surrogate model of aromatic isomerization process based on adaptive sampling algorithm[J]. CIESC Journal, 2020, 71(2): 688-697.
谢雨珩, 李智, 杨明磊, 杜文莉. 基于自适应采样算法的芳烃异构化代理模型[J]. 化工学报, 2020, 71(2): 688-697.
Add to citation manager EndNote|Ris|BibTeX
采样方法 | 采样点/个 | RMSE | 时间/s |
---|---|---|---|
自适应采样 | 20+80 | 0.078739 | 8.79 |
拉丁超立方采样 | 100 | 0.628361 | 0.196203 |
Table 1 Comparison of PK function adaptive sampling and Latin hypercube sampling results
采样方法 | 采样点/个 | RMSE | 时间/s |
---|---|---|---|
自适应采样 | 20+80 | 0.078739 | 8.79 |
拉丁超立方采样 | 100 | 0.628361 | 0.196203 |
测试函数 | 维数 | 初始采样点 | 新增采样点 |
---|---|---|---|
PK | 2 | 20 | 80 |
AlpineN.1 | 2 | 20 | 80 |
AlpineN.2 | 2 | 20 | 80 |
Hartman3 | 3 | 30 | 120 |
Shekel5 | 4 | 40 | 160 |
Shekel7 | 4 | 40 | 160 |
Hartman6 | 6 | 60 | 240 |
Ackley | 8 | 80 | 320 |
Table 2 Sampling configurations
测试函数 | 维数 | 初始采样点 | 新增采样点 |
---|---|---|---|
PK | 2 | 20 | 80 |
AlpineN.1 | 2 | 20 | 80 |
AlpineN.2 | 2 | 20 | 80 |
Hartman3 | 3 | 30 | 120 |
Shekel5 | 4 | 40 | 160 |
Shekel7 | 4 | 40 | 160 |
Hartman6 | 6 | 60 | 240 |
Ackley | 8 | 80 | 320 |
测试函数 | MASA | ASA-NNDM | SSA | ASSA-SNN |
---|---|---|---|---|
PK | 0.07506 | 0.11860 | 0.09055 | 0.06428 |
AlpineN.1 | 1.96015 | 1.75482 | 1.21713 | 1.21350 |
AlpineN.2 | 0.02524 | 0.09999 | 0.01950 | 0.04680 |
Hartman3 | 0.01351 | 0.05956 | 0.01607 | 0.01510 |
Shekel5 | 0.18186 | 0.13901 | 0.08644 | 0.07058 |
Shekel7 | 0.25594 | 0.20254 | 0.09568 | 0.07924 |
Hartman6 | 0.12602 | 0.21485 | 0.11549 | 0.10785 |
Ackley | 0.39066 | 0.41528 | 0.40963 | 0.38582 |
Table 3 Average RMSE obtained by four sampling approaches for test cases
测试函数 | MASA | ASA-NNDM | SSA | ASSA-SNN |
---|---|---|---|---|
PK | 0.07506 | 0.11860 | 0.09055 | 0.06428 |
AlpineN.1 | 1.96015 | 1.75482 | 1.21713 | 1.21350 |
AlpineN.2 | 0.02524 | 0.09999 | 0.01950 | 0.04680 |
Hartman3 | 0.01351 | 0.05956 | 0.01607 | 0.01510 |
Shekel5 | 0.18186 | 0.13901 | 0.08644 | 0.07058 |
Shekel7 | 0.25594 | 0.20254 | 0.09568 | 0.07924 |
Hartman6 | 0.12602 | 0.21485 | 0.11549 | 0.10785 |
Ackley | 0.39066 | 0.41528 | 0.40963 | 0.38582 |
测试函数 | MASA | ASA-NNDM | SSA | ASSA-SNN |
---|---|---|---|---|
PK | 15.87 | 125.68 | 32.40 | 8.87 |
AlpineN.1 | 16.41 | 124.21 | 32.71 | 8.54 |
AlpineN.2 | 15.90 | 119.78 | 28.62 | 8.57 |
Hartman3 | 55.14 | 219.46 | 162.34 | 23.12 |
Shekel5 | 148.17 | 369.43 | 669.46 | 52.17 |
Shekel7 | 150.60 | 372.50 | 652.90 | 53.17 |
Hartman6 | 650.93 | 1127.57 | 6142.58 | 189.25 |
Ackley | 2078.48 | 3028.23 | 28864.74 | 490.20 |
Table 4 Average running time obtained by four sampling approaches for test cases/s
测试函数 | MASA | ASA-NNDM | SSA | ASSA-SNN |
---|---|---|---|---|
PK | 15.87 | 125.68 | 32.40 | 8.87 |
AlpineN.1 | 16.41 | 124.21 | 32.71 | 8.54 |
AlpineN.2 | 15.90 | 119.78 | 28.62 | 8.57 |
Hartman3 | 55.14 | 219.46 | 162.34 | 23.12 |
Shekel5 | 148.17 | 369.43 | 669.46 | 52.17 |
Shekel7 | 150.60 | 372.50 | 652.90 | 53.17 |
Hartman6 | 650.93 | 1127.57 | 6142.58 | 189.25 |
Ackley | 2078.48 | 3028.23 | 28864.74 | 490.20 |
质量指标 | MASA | ASA-NNDM | SSA | ASSA-SNN |
---|---|---|---|---|
轻烃收率 | 0.001261 | 0.001115 | 0.001147 | 0.001053 |
C8+收率 | 0.001216 | 0.001123 | 0.001061 | 0.000986 |
Table 5 RMSE of important indicators for isomerization of aromatics
质量指标 | MASA | ASA-NNDM | SSA | ASSA-SNN |
---|---|---|---|---|
轻烃收率 | 0.001261 | 0.001115 | 0.001147 | 0.001053 |
C8+收率 | 0.001216 | 0.001123 | 0.001061 | 0.000986 |
质量指标 | MASA | ASA-NNDM | SSA | ASSA-SNN |
---|---|---|---|---|
轻烃收率 | 3313.04 | 4600.36 | 20404.30 | 2189.42 |
C8+收率 | 3313.02 | 4574.49 | 20429.36 | 2122.41 |
Table 6 Modeling time for important indicators of aromatic isomerization/s
质量指标 | MASA | ASA-NNDM | SSA | ASSA-SNN |
---|---|---|---|---|
轻烃收率 | 3313.04 | 4600.36 | 20404.30 | 2189.42 |
C8+收率 | 3313.02 | 4574.49 | 20429.36 | 2122.41 |
1 | 徐欧官, 傅永峰, 陈祥华. 工业异构化反应器建模及仿真[J]. 化工学报, 2011, 62(8): 2298-2302. |
Xu O G, Fu Y F, Chen X H. Modeling and simulation for an industrial reactor on hydroisomerization of C8-aromatics[J]. CIESC Journal, 2011, 62(8): 2298-2302. | |
2 | Lim D, Jin Y, Ong Y S, et al. Generalizing surrogate-assisted evolutionary computation[J]. IEEE Transactions on Evolutionary Computation, 2010, 14(3): 329-355. |
3 | Jin Y. A comprehensive survey of fitness approximation in evolutionary computation[J]. Soft Computing, 2005, 9(1): 3-12. |
4 | Box G E P, Wilson K B. On the experimental attainment of optimum conditions[J]. Journal of the Royal Statistical Society, 1951, 13(1): 1-45. |
5 | Lian Y S, Liou M S. Multiobjective optimization using coupled response surface model and evolutionary algorithm[J]. AIAA Journal, 2005, 43(6): 1316-1325. |
6 | Mullur A, Messac A. Extended radial basis functions: more flexible and effective metamodeling[J]. AIAA Journal, 2005, 43(6): 1306-1315. |
7 | Fang H B, Horstemeyer M F. Global response approximation with radial basis functions[J]. Engineering Optimization, 2006, 38(4): 407-424. |
8 | Krige D G. A statistical approach to some basic mine valuation problems on the witwatersrand[J]. Journal of the Chemical, Metallurgical and Mining Engineering Society of South Africa, 1951, 52(6): 119-139. |
9 | Cressie N. Spatial prediction and ordinary kriging[J]. Mathematical Geology, 1989, 21(4): 493-494. |
10 | Vapnik V, Golowich S E, Smola A. Support vector method for function approximation, estimation regression, and signal processing[C]// Advances in Neural Information Processing Systems 9, 1997, 9: 281-287. |
11 | Friedman J H, Roosen C B. An introduction to multivariate adaptive regression splines[J]. Statistical Methods in Medical Research, 1995, 4(3): 197-217. |
12 | Friedman J H. Multivariate adaptive regression spline[J]. The Annals of Statistics, 1991, 19(1): 1-67. |
13 | Basheer I, Hajmeer M. Artificial neural networks: fundamentals, computing, design, and application[J]. Journal of Microbiological Methods, 2000, 43(1): 3-31. |
14 | Jin Y, Li J, Du W, et al. Adaptive sampling for surrogate modelling with artificial neural network and its application in an industrial cracking furnace[J]. The Canadian Journal of Chemical Engineering, 2016, 94(2): 262-272. |
15 | Zhou B D, Yao H L, Shi M H, et al. An new immune genetic algorithm based on uniform design sampling[J]. Knowledge and Information Systems, 2012, 31(2): 389-403. |
16 | Ye K Q. Orthogonal column Latin hypercubes and their application in computer experiments[J]. Publications of the American Statistical Association, 1998, 93(444): 1430-1439. |
17 | Wang G. Adaptive response surface method using inherited Latin hypercube design points[J]. Journal of Mechanical Design, 2003, 125(2): 210-220. |
18 | Jin Y. A framework for evolutionary optimization with approximate fitness functions[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(5): 481-494. |
19 | Wang H, Jin Y, Doherty J. Committee-based active learning for surrogate-assisted particle swarm optimization of expensive problems[J]. IEEE Trans. Cybern., 2017, 47(9): 2664-2677. |
20 | Eason J, Cremaschi S. Adaptive sequential sampling for surrogate model generation with artificial neural networks[J]. Computers & Chemical Engineering, 2014, 68: 220-232. |
21 | Wei X, Wu Y Z, Chen L P. A new sequential optimal sampling method for radial basis functions[J]. Applied Mathematics and Computation, 2012, 218(19): 9635-9646. |
22 | Garud S S, Karimi I A, Kraft M. Smart sampling algorithm for surrogate model development[J]. Computers & Chemical Engineering, 2017, 96: 103-114. |
23 | Müller J, Shoemaker C A. Influence of ensemble surrogate models and sampling strategy on the solution quality of algorithms for computationally expensive black-box global optimization problems[J]. Journal of Global Optimization, 2014, 60(2): 123-144. |
24 | Sacks J, Welch W J, Toby J, et al. Design and analysis of computer experiments[J]. Statistical Science, 1989, 4(4): 409-423. |
25 | 王晓强, 罗娜, 叶贞成, 等. 基于Kriging的差分进化算法及其在苯乙烯流程优化中的应用[J]. 化工学报, 2013, 64(12): 4563-4570. |
Wang X Q, Luo N, Ye Z C, et al. Differential evolution algorithm based on Kriging and its application in styrene plant optimization[J]. CIESC Journal, 2013, 64(12): 4563-4570. | |
26 | 段星辰, 杜文莉. 基于bootstrap GEI算法的碳二加氢反应器代理模型[J]. 化工学报, 2015, 66(12): 4904-4909. |
Duan X C, Du W L. Surrogate model of acetylene hydrogenation reactor based on bootstrap GEI algorithm[J]. CIESC Journal, 2015, 66(12): 4904-4909. | |
27 | Xiao N C, Zuo M J, Guo W. Efficient reliability analysis based on adaptive sequential sampling design and cross-validation[J]. Applied Mathematical Modelling, 2018, 58: 404-420. |
28 | Gong W, Duan Q. An Adaptive Surrogate modeling-based sampling strategy for parameter optimization and distribution estimation (ASMO-PODE)[J]. Environmental Modelling & Software, 2017, 95: 61-75. |
29 | 韩忠华. Kriging模型及代理优化算法研究进展[J]. 航空学报, 2016, 37(11): 3197-3225. |
Han Z H. Kriging surrogate model and its application to design optimization: a review of recent progress [J]. Acta Aeronautica Et Astronautica Sinica, 2016, 37(11): 3197-3225. | |
30 | Jin Y. Surrogate-assisted evolutionary computation: recent advances and future challenges[J]. Swarm & Evolutionary Computation, 2011, 1(2): 61-70. |
31 | Hooke R, Jeeves T A. “Direct search” solution of numerical and statistical problems[J]. Journal of the ACM, 1961, 8(2): 212-229. |
32 |
张剑超, 杜文莉, 覃水. 基于新型自适应采样算法的催化重整过程代理模型[J]. 华东理工大学学报(自然科学版), 2018, doi: 10.14135/j.cnki.1006-3080.20180915001.
DOI URL |
Zhang J C, Du W L, Qin S. Surrogate model of catalytic reforming process based on a new adaptive sampling algorithm[J]. Journal of East China University of Science and Technology (Natural Science Edition), 2018, doi: 10.14135/j.cnki.1006-3080.20180915001.
DOI URL |
|
33 | 刘祥荣. 二甲苯异构化反应器的模拟研究[D]. 北京: 北京化工大学, 2010. |
Liu X R. The modeling and dynamic simulation of the xylene isomerization reactor[D]. Beijing: Beijing University of Chemical Technology, 2010. |
Viewed | ||||||
Full text |
|
|||||
Abstract |
|
|||||