基于自适应变步长同伦法的循环流程收敛算法

doi:10.11949/0438-1157.20231400

化工学报 ›› 2024, Vol. 75 ›› Issue (7): 2604-2612.DOI: 10.11949/0438-1157.20231400

基于自适应变步长同伦法的循环流程收敛算法

李洪瑞¹(), 黄纯西¹, 洪小东²(), 廖祖维¹(), 王靖岱¹, 阳永荣¹

^1.化学工程联合国家重点实验室，浙江大学，浙江杭州 310027
^2.功能材料智能设计与制造浙江省工程研究中心，浙江大学杭州国际科创中心，浙江杭州 311215

收稿日期:2023-12-30 修回日期:2024-03-19 出版日期:2024-07-25 发布日期:2024-08-09
通讯作者: 洪小东,廖祖维
作者简介:李洪瑞（2001—），男，硕士研究生，22328110@zju.edu.cn
基金资助:
国家自然科学基金项目(U22A20415);浙江省尖兵领雁计划项目(2022C01SA442617);浙江省自然科学基金项目(LQ24B060001)

An adaptive variable-step homotopy-based algorithm for process simulation with cyclic streams

Hongrui LI¹(), Chunxi HUANG¹, Xiaodong HONG²(), Zuwei LIAO¹(), Jingdai WANG¹, Yongrong YANG¹

^1.State Key Laboratory of Chemical Engineering, Zhejiang University, Hangzhou 310027, Zhejiang, China
^2.Engineering Research Center of Functional Materials Intelligent Manufacturing of Zhejiang Province, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 311215, Zhejiang, China

Received:2023-12-30 Revised:2024-03-19 Online:2024-07-25 Published:2024-08-09
Contact: Xiaodong HONG, Zuwei LIAO

摘要/Abstract

摘要：

包含循环流股的流程模拟面临初值难给定和传统算法收敛困难的问题。针对该问题提出了自适应变步长同伦算法，通过自适应调整同伦参数步长处理中间过程收敛失败的情形，提高收敛效率，并采用回溯线搜索法将迭代变量限制在定义域内，以提升算法的鲁棒性。构建了基于直接迭代法、Wegstein法、Broyden法和牛顿法的同伦算法，分析了同伦参数和辅助函数的影响。以淤浆法工艺生产高密度聚乙烯作为案例，模拟结果表明同伦算法可以提高模型在不同工况下的收敛性。商业流程模型软件Aspen Plus内置的求解器最高仅在21%测试工况下可以获得可行解，而同伦算法收敛案例占比可达88%。

关键词: 过程系统, 算法, 化学过程, 模拟, 同伦法

Abstract:

The simulation of processes with cyclic streams faces challenges in providing initial values and encounters difficulties in convergence with traditional algorithms. To address this issue, an adaptive variable-step homotopy-based algorithm is proposed. The algorithm adjusts the step size in the homotopy parameter during the process, handling situations where convergence fails in intermediate stages, which improve the convergence efficiency of the algorithm. A backtracking line search method is employed to constrain the iterative variables within the defined domain, enhancing the algorithm’s robustness. Homotopy algorithms are constructed based on direct iteration, Wegstein, Broyden, and Newton methods. The impact of homotopy parameters and auxiliary functions is analyzed. Taking the production of high-density polyethylene using the slurry method as a case study, simulation results indicate that the homotopy algorithm improves the convergence of the model under different operating conditions. The built-in solver of the commercial process model software Aspen Plus can only obtain feasible solutions in 21% of the test conditions, while the homotopy algorithm converges in 88% of cases.

Key words: process system, algorithm, chemical processes, simulation, homotopy method

中图分类号:

TQ 021.8

李洪瑞, 黄纯西, 洪小东, 廖祖维, 王靖岱, 阳永荣. 基于自适应变步长同伦法的循环流程收敛算法[J]. 化工学报, 2024, 75(7): 2604-2612.

Hongrui LI, Chunxi HUANG, Xiaodong HONG, Zuwei LIAO, Jingdai WANG, Yongrong YANG. An adaptive variable-step homotopy-based algorithm for process simulation with cyclic streams[J]. CIESC Journal, 2024, 75(7): 2604-2612.

图/表 7

参考文献 33

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模块	参数		初始值
反应器1	催化剂进料流率/(kg/h)		0.428
	乙烯进料流率/(kg/h)		5558
	氢气进料流率/(kg/h)		1.159
	正己烷进料流率/(kg/h)		17263
	反应器温度/℃		87
	反应器压力/bar		8.19
反应器2	乙烯进料流率/(kg/h)		4453
	氢气进料流率/(kg/h)		0.033
	正己烷进料流率/(kg/h)		9172
	反应器温度/℃		87
	反应器压力/bar		5.17
流股	氢气流率/(kmol/h)	乙烯流率/(kmol/h)	正己烷流率/(kmol/h)
R-Vap1	100	100	100
R-Vap2	100	100	100

模块	参数		初始值
反应器1	催化剂进料流率/(kg/h)		0.428
	乙烯进料流率/(kg/h)		5558
	氢气进料流率/(kg/h)		1.159
	正己烷进料流率/(kg/h)		17263
	反应器温度/℃		87
	反应器压力/bar		8.19
反应器2	乙烯进料流率/(kg/h)		4453
	氢气进料流率/(kg/h)		0.033
	正己烷进料流率/(kg/h)		9172
	反应器温度/℃		87
	反应器压力/bar		5.17
流股	氢气流率/(kmol/h)	乙烯流率/(kmol/h)	正己烷流率/(kmol/h)
R-Vap1	100	100	100
R-Vap2	100	100	100

组分	案例A		案例B
组分	R-Vap1	R-Vap2	R-Vap1	R-Vap2
氢气/(kmol/h)	41.450	19.726	69.114	52.680
乙烯/(kmol/h)	592.344	540.521	987.703	1445.184
正己烷/(kmol/h)	199.157	321.754	332.086	860.249

组分	案例A		案例B
组分	R-Vap1	R-Vap2	R-Vap1	R-Vap2
氢气/(kmol/h)	41.450	19.726	69.114	52.680
乙烯/(kmol/h)	592.344	540.521	987.703	1445.184
正己烷/(kmol/h)	199.157	321.754	332.086	860.249

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基于自适应变步长同伦法的循环流程收敛算法

An adaptive variable-step homotopy-based algorithm for process simulation with cyclic streams

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算法	同伦辅助函数	案例A			案例B
算法	同伦辅助函数	结果	流程运行次数	计算时间/s	结果	流程运行次数	计算时间/s
直接迭代法	—	失败	—	—	失败	—	—
Wegstein法	—	收敛	34	6	失败	—	—
Broyden法	—	收敛	28	5	失败	—	—
牛顿法	—	失败	—	—	失败	—	—
同伦-直接迭代法	牛顿同伦	失败	—	—	失败	—	—
同伦-直接迭代法	定点同伦	失败	—	—	失败	—	—
同伦-Wegstein法	牛顿同伦	收敛	74	35	收敛	792	374
同伦-Wegstein法	定点同伦	收敛	89	42	收敛	841	496
同伦-Broyden法	牛顿同伦	收敛	54	26	收敛	1577	874
同伦-Broyden法	定点同伦	收敛	58	28	收敛	1366	712
同伦-牛顿法	牛顿同伦	收敛	279	143	收敛	2711	1349
同伦-牛顿法	定点同伦	收敛	341	166	失败	—	—

算法	同伦辅助函数	案例C				案例D
算法	同伦辅助函数	收敛工况个数	收敛案例百分比/%	平均流程运行次数	平均计算时间/s	收敛工况个数	收敛案例百分比/%	平均流程运行次数	平均计算时间/s
直接迭代法	—	0	0	—	—	0	0	—	—
Wegstein法	—	7	13	46	8	10	18	42	7
Broyden法	—	7	13	41	7	12	21	39	7
牛顿法	—	4	7	235	43	6	11	192	36
同伦-直接迭代法	牛顿同伦	0	0	—	—	0	0	—	—
同伦-直接迭代法	定点同伦	0	0	—	—	0	0	—	—
同伦-Wegstein法	牛顿同伦	37	66	915	424	41	73	762	369
同伦-Wegstein法	定点同伦	35	63	976	488	45	80	797	391
同伦-Broyden法	牛顿同伦	45	80	1469	746	49	88	1225	641
同伦-Broyden法	定点同伦	42	75	1539	796	47	84	1376	721
同伦-牛顿法	牛顿同伦	34	61	3022	1579	38	68	2451	1365
同伦-牛顿法	定点同伦	32	57	2844	1464	33	59	2274	1217