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

作　　者：李洪瑞 黄纯西 洪小东 廖祖维[1] 王靖岱[1] 阳永荣[1] LI Hongrui;HUANG Chunxi;HONG Xiaodong;LIAO Zuwei;WANG Jingdai;YANG Yongrong(State Key Laboratory of Chemical Engineering,Zhejiang University,Hangzhou 310027,Zhejiang,China;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)

机构地区：[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

出　　处：《化工学报》2024年第7期2604-2612,共9页CIESC Journal

基　　金：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)。

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%。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.

关 键 词：过程系统 算法 化学过程 模拟 同伦法 

分 类 号：TQ021.8[化学工程]