Product design for batch processes through total projection to latent structures

Abstract

Due to the short duration, batch processes are operated flexibly. With the same batch unit, a wide range of high value-added products can be produced to satisfy the demand of the rapidly varying market, within which the quick product design is of vital importance for the manufacturer. In the PLS-based product design method, a design space is available if the number of latent variables is larger than that of output variables. However, according to the development of PLS model, the latent variable may contain the output-irrelevant information, while through the model inversion, the derived latent variable only has the output-related information, so the existence condition of design space is largely relaxed and the dimension of design space may be reduced. This work introduces the total projection to latent structures (TPLS) model into the product design. The TPLS model decomposes the latent variable space into two subspaces: the output-related subspace and the output-orthogonal subspace. In the output-orthogonal subspace, the latent variable is irrelevant to the output, and it can be any value without any influence on the output, while in the output-related subspace, the latent variable is determined by the desired output, and it is derived by the model inversion. The input computed by any different output-irrelevant latent variable along with the output-related latent variable may result in the desired output, and the output-irrelevant latent variable spans the design space. Compared with the PLS-based method, the proposed TPLS-based method may derive the design space with higher dimension on less restrictive conditions. In addition, the design spaces by the two methods are compared. In the end, the validity of the method is confirmed in a numerical simulation and the penicillin fermentation simulation.