Experimental gradient estimation of multivariable systems with correlation by various regression methods and its application to modifier adaptation. (October 2018) - Jeong, Dong Hwi; Lee, Chang Jun; Lee, Jong Min
Highlights: Existing experimental gradient estimation methods are not suitable for highly multivariate systems. Regression-based methods such as MLR, PCA and PLS are utilized to estimate the gradient and moving average input update strategy is proposed. The regression-based approach is combined with modifier adaptation scheme to address a problem of optimization under model-plant mismatch and shows improved performances. Its applicability is confirmed with several simulations of fed-batch bioreactor having a large number of manipulated variables. Abstract: In process optimization, model-plant mismatch is an important issue because it is closely related to the economic competitiveness of the product. To handle this issue, experimental gradient-based methods, such as modifier adaptation scheme, that ensure the necessary conditions of optimality for the plant equations have been utilized. However, gradient estimation methods may not work properly for the conventional modifier adaptation scheme in the case of multivariable systems with correlation. In this paper, we compare the optimization performance of gradient estimation for conventional modifier adaptation approaches and regression methods, such as multivariable linear regression, partial least squares regression, and principal component analysis. The moving average input update strategy and latent variable space model based algorithm are proposed to suppress excessive updates and improve the convergence rate and stability near the Karush-Kuhn-Tucker (KKT) point. Several simulation results of fed-batch operation of a bioreactor show that regression-based methods, especially latent variable space modelling, outperform conventional methods in the optimization of the multivariable system with correlation. In addition, the simulations show that both fast convergence and stability near the KKT point can be achieved by using the proposed latent variable space model-based algorithm.