SyPSE: A Symbolic Computation Toolbox for Process Systems Engineering Part I─Architecture and Algorithm Development

Abstract

The main technical approaches to solving nonlinear systems are based on numerical computation in the field of process systems engineering (PSE). However, the convergence and reliability of numerical methods are not always guaranteed due to numerical instability. Symbolic computation benefits from the accuracy and completeness of the solution compared with numerical methods. However, symbolic computation has received little attention in the PSE area due to the complexity in the algorithm development and the lack of tools. An integrated symbolic computation toolbox is developed in this two-part work for PSE, including steady-state process simulation, optimization, and flexibility analysis. In part I of the two-part series, SyPSE, the symbolic computation toolbox developed in Python, is presented. The architecture and fundamental algorithm modules are described. Several strategies are also developed to improve the algorithm efficiency. A case study is presented to demonstrate the functionalities of the algorithm modules.

SyPSE: A Symbolic Computation Toolbox for Process Systems Engineering Part II─Design for PSE Applications

“…The details of model definitions and usage demonstration can be found in each subsequent section. The hardware configuration and software environment for all experiments are consistent with that in part I …”

“…SyPSE consists of two layers, namely, the bottom and top application layers. The development of the algorithm layer has been presented in part I of the two-part papers, based on which the top application layer can be implemented for different PSE problems. In this section, a unified solution strategy is initially proposed for PSE applications, including process simulation, optimization, and flexibility analysis, by using the symbolic computation method.…”

“…As described in part I of the two-part papers, a number of applications for a steady-state process can be generally formulated as types of a combination of eqs 1 –3. where f , h , and g denote the objective function, equality constraints, and inequality constraints, respectively; d , θ , z , and x represent the design parameters, uncertain parameters, control variables, and state variables, respectively.…”

“…Thus, if we can derive the projection of the feasible space on each dimension, then we can obtain the analytical solution. In part I of the two-part papers, the improvement strategy of equational constraint utilization is adopted in the algorithm modules. Thus, the symbolic computational burden has been reduced significantly when the projection and lifting modules are invoked to address process simulation problems.…”

“…The time cost of the model solution is 3.902 s. As mentioned previously, we have specially designed the projection strategy in SyPSE to make the Nonlinear Programming submodule more efficient in computation. For comparison, the computation with the original projection and lifting modules introduced in part I takes 42.815 s to find the solution. The obvious time reduction is achieved as the solution, given that a process optimization problem does not need to construct all the cells in the lifting phase; once the first valid cell is identified, the optimal solution is found, which is the global optimal solution.…”