An efficient latent variable optimization approach with stochastic constraints for complex industrial process

For complex chemical processes, process optimization is usually performed on causal models from first principle models. When the mechanism models cannot be obtained easily, restricted model built by process data is used for dynamic process optimization. A new strategy is proposed for complex process optimization, in which latent variables are used as decision variables and statistics is used to describe constraints. As the constraint condition will be more complex by projecting the original variable to latent space, Hotelling T2 statistics is introduced for constraint formulation in latent space. In this way, the constraint is simplified when the optimization is solved in low-dimensional space of latent variable. The validity of the methodology is illustrated in pH-level optimal control process and practical polypropylene grade transition process.

Graphical abstractWith latent variable optimization approach the number of optimization variables will decrease while the constraint will become more complex. The constraints can be simplified by introducing Hotelling T2 statistics, and the original feasible region in parallelogram is replaced by the region in the ellipse. The optimal profiles of output variables for pH neutralization process are given, in which two constraint expressions, the original physical variable constraint and the Hotelling T2 statistics constraint, are used. The dotted lines denote the result with original physical variable constraint, while the solid lines with the Hotelling T2 statistics constraint. The elapsed time for optimization calculation is 4.805 s with the simplified Hotelling T2 statistics constraint while it is 8.079 s with the original physical variable constraint. Similar optimization result can be obtained by using the simplified T2 statistics constraint, while the computing time is greatly reduced.Figure optionsDownload full-size imageDownload as PowerPoint slide