基于混合自动微分算法的缩聚反应过程优化

POLYCONDENSATION PROCESS OPTIMIZATION BASED ON HYBRID AUTOMATIC DIFFERENTIATION

针对缩聚反应过程优化模型中的分枝结构模块给求取导函数带来的困难 ,在扩展自动微分算法基础上提出了一种混合自动微分算法 .该算法结合符号自动微分算法和数值自动微分算法求取函数的导函数 ,并利用导函数计算导数 .这种求导算法不仅具有很高的精度和效率 ,且在开放式方程模型体系下可被化工过程优化领域中的各类典型优化命题调用 .

It is hard to obtain derivative functions for branched modules in polycondensation process optimization problems with current differentiation approaches, such as symbolic differentiation, extended automatic differentiation (XAD) , etc. Symbolic automatic differentiation (SAD) and numerical automatic differentiation (NAD), the two components of XAD, are integrated in a flexible way to solve this problem. The resulting derivative evaluation approach, named as hybrid automatic differentiation (HAD), is used to solve a polycondensation optimization problem. In the polycondensation model, a flash distillation process model is adopted to calculate the concentration of volatile species in the reaction mass, which is a typical branched module. So the specific module is taken apart from the main model and each of the two parts is managed in a different way. Accordingly, the derivative function obtained by HAD contains two parts: one is a NAD tool to compute the derivatives of the flash distillation process module, the other is a series of symbolic derivatives generated by SAD for derivative evaluation of the main model. Numerical results demonstrate that the HAD based optimization can significantly reduce the solution time, and is of great importance for on-line process optimization.