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

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