Particle Swarm Response Surface Modeling Method In ASPEN Multivariate Optimization

It is easy to establish the approximate mathematical model between the experimental factors and the response values for the Response Surface Methods(RSM),, and it makes the analysis possible for the optimization problem of the response values. So, this method is frequently applied to the field of the engineering and scientific experiments currently.The number of tests and the test dot structure influence the accuracy of the RSM obviously,and the number of tests will affect the test cycle and the investment funds.So, it is particularly important to use the limited test data to obtain a more accurate response surface model.This article through studying the Least Squares Methods(LSM) which can solve response surface models found that the principle of LSM was to solve the coefficients of regression equations by finding the minimum of the sum of square of the variance according to the test data.After grasping this mechanism of the mathematics deeply,this article proposed a new method to found responsesurface models which was called the particle swarm response surface modeling method(PSORSM) through combining the high performance of PSO in the randomness, the convergence rate, the nonlinear, and the stability with the mechanism of LSM.In the paper,the aqueous acetic acid was the research object,the PSORSM was used to build the response surface model of the acetic acid separation experiments.The process simulation software, Aspen Plus, was used to simulate the crafts process of the extraction distillation of the acetic acid.The article also analyzed the six factors, such as,the raw material feed position X1, the extractant feed position X2, the reflux ratio X3 and the extractant feed rate X4 of the extractive distillation column, the raw material feed position X5 and the reflux ratio X6 of the solvent recovery column, which influenced the energy consumption and the quality score of the acetic acid in product,and did sensitivity analysis.Then the best ranges of the six factors were determined,and divided into five levels to do the orthogonal test.It reduced the number of the design point effectively by this way.The paper applied the method of undetermined coefficients and the PSORSM to set up the response surface models of the quality score of the acetic acid in product and the total energy consumption of the two columns.The results showed that the method of undetermined coefficients could not receive correct fitting equation when the problem had more parameter and complex polynomial.But the PSORSM could do with this problem well,and get satisfied models.According to the industryrequirement,the acetic acid content in product should not be less than 99.5%.So it was treated as the restrictions,and the minimum of the total energy consumption was treated as the optimization goal,then the PSO was used to do constrained optimization,finally it found the smallest total energy consumption which met the quality score requirements of the product and the appropriate operating conditions.The results showed that the total energy consumption was5372 kW with the mass fraction of acetic acid 0.9982. It was much less than the result 6545 kW calculated in other paper with the single factor sensitivity analysis. It suggests that the particle swarm response surface method is effective in the complex rectification column system and can be applied to other industrial production.