Abstract: A new practical approach for differentiation, named hybrid differentiation algorithm, is presented to improve the efficiency of chemical process system optimization. In this approach, the original function is partitioned into two kinds of modules:simple module and complicated module. On the one hand, automatic differentiation is used to analyze the structure of the simple modules and represent them as rooted direct trees. Then symbolic differentiation is used to obtain the symbolic derivatives of the trees, by which derivative evaluation of the simple modules can be carried out. On the other hand, finite difference is adopted to differentiate the complicated modules. Accumulation of derivatives, the critical technique of hybrid differentiation, is discussed and two approaches are developed. Numerical experiment with a distillation column optimization problem demonstrates that the efficiency of optimization is significantly improved by using hybrid differentiation.

Key words:

混合求导算法, 导数累积, 化工过程系统优化

摘要： 在符号微分法的基础上结合差商和自动微分技术提出一种实用高效的混合求导算法，提高了化工过程系统优化的效率.该算法将被求导对象的各个子模块按照是否适于用符号微分求导分为简单模块和复杂模块，对前者用符号微分求导，对后者用差商法求导.针对该算法的关键技术——子模块导数累积问题讨论了链式求导法和摄动传递法.对某厂精馏塔操作优化问题的分析和计算表明，引入混合求导算法提高了优化的效率.

关键词:

混合求导算法, 导数累积, 化工过程系统优化