A Hybrid Derivation Algorithm in Chemical Process System Optimization

There are optimization problems at all levels of the computer integrated integrated automation system in the chemical production process. The optimization of online operations is of great significance for improving the operation level of existing devices and improving economic efficiency. Therefore, improving the efficiency of optimization calculations to meet the real-time requirements of on-line optimization is a key to whether or not chemical process system optimization can be applied in industry.

The proportion of the derivation calculation time in the optimization of the chemical process system accounted for a large proportion of the entire optimization calculation time. Therefore, the optimization draft calculation 04-23 received the first draft, and the revised draft was received on 2002-08-22.

Fund Project: The National Natural Science Foundation of China (No. 20276062) and the National Key Basic Research Development Program (No. of Chemical Journals) have become an important way to increase the speed of optimization algorithms.

Currently widely used derivation algorithms include manual derivation, finitedifference (FD), and automatic differentiation (AD). The basic idea is to decompose the computational process of the derivation program module into +, one, and x. For a series of unit operations, the derivatives of the entire model function can be accumulated by using the derivation rules (the simple rules of derivation) and the chain derivation rules of these unit operation functions. The function tree of the module can be constructed by sequentially analyzing the unit operation series obtained by auto-differentiating the decomposition function module. The generation mechanism of this function tree added in the symbol differentiation method can be used for the derivation of general program modules. Li Xiang et al discussed this combination of automatic differentiation and symbol differentiation Shao Zhijiang et al.: The other disadvantages of the symbol differentiation of a hybrid derivative algorithm in the optimization of chemical process systems belong to the inherent problems of its algorithm and cannot be overcome by improving the algorithm, and these The shortcoming is exactly the advantage of the difference business law. In order not to abandon the advantages of symbolic differentials and return to the old road of differential quotient derivation, a mixed derivative approach can be used to solve this problem: the derived model is considered to be a collection of sub-modules, some of which are It is possible to use symbolic differentiation, while others do not. The former is called a simple module and the latter is called a complex module. You can use symbolic differentiation to find the symbol derivatives of simple modules and derive them by their derivatives. Use the differential quotient method to obtain the derivatives of each complex module. In this way, the generated series of symbol derivatives and differential quotient calling programs become the derivative modules of each submodule, and they can be accumulated by the chain derivative method to obtain the derivative module of the entire model (the derivative function of program form) for calculating the derivative. .

The above derivative algorithm actually uses the advantage of the difference quotient to compensate for the lack of symbol differentiation. At the same time, the idea of ​​automatic differentiation is used in the construction of the derivative, but the automatic differentiation of the unit operation becomes a sub-module. This new method of derivation combines organically differential quotients, symbol differentials, and auto-differentiated three kinds of derivation algorithms, which can be called hybrid differentiation (HD). The computer automatically writes the generated symbol derivative into program code, and connects with the general difference quotient algorithm library and its calling program through a linking program to form a derivation function package for real-time calling of various online optimization propositions. The overall framework of the hybrid derivation algorithm is shown.

Assume a function derivation. The idea of ​​using the hybrid derivation shown is divided into two parts that are complex modules. Shown in the form of a tree. According to the above analysis, if chained derivative accumulation is used, the number of scalar calculations required is (2X2—using perturbation transfer accumulation, and the number of scalar calculations required is 1X2+1=8. The cumulative efficiency of perturbation transfer at this time is It is much higher than the cumulative efficiency of chained derivatives.

4 Example Calculations 41 Example Description and Structural Analysis Example The steady-state operation optimization of an ethylbenzene product tower in an ethylbenzene plant of a factory was constructed using a simple open-ended equation, as shown. Due to the use of local physical model equations, the phase equilibrium equation becomes simpler, while the ç„“ calculation equation is still more complicated. At the same time, the tri-diagonal equation module can be divided into two parts. The first part of the equations for the coefficient conversion, involves a relatively simple calculation, and the phase equilibrium equation constitutes a simple module; the second part is due to the recursive solution of the transformed equation, contains a complex loop statement, will cause the expansion of the sign derivative, The harmony calculation module constitutes a complex module. Energy balance equations, molecular normalization equations, and component index constraints constitute another simple module. The structure of the model is reflected in the form of a tree, omitting the nodes and edges contained between the dashed boxes.

42 Optimization of Operation Results and Analysis The number of scalar calculations performed is to solve non-Shao Zhijiang et al.: A hybrid derivation algorithm for optimization of chemical process systems. Linear programming uses SQP algorithm and is implemented by calling MATLAB optimization toolbox. The process of auto-differential analytic function structure and symbol derivative to generate symbol derivatives is implemented by XADMAT developed by the author (dissertation paper). School of Chemical Engineering, Sichuan University (School of Chemical Engineering, Sichuan University) Department of Chemical Engineering and Bioengineering, Zhejiang University School of Chemical Engineering, Dalian University of Technology School of Chemical Engineering, Zhejiang University of Technology, China State Key Laboratory of Multiphase Flow Engineering, Xi'an Jiaotong University Institute of Chemical Engineering, Shanghai Institute of Chemical Industry, Wuhan Institute of Chemical Technology, College of Chemistry and Chemical Engineering, Shanghai Jiaotong University School of Chemical Engineering, South China University of Technology, University of Petroleum, Beijing