Using model order reduction to accelerate optimization of multi-stage linear dynamical systems

Simulated moving bed (SMB) chromatography, an important technique for separating chemical compounds, is usually modeled by a multi-stage dynamical system. After a transient phase, an SMB usually reaches a cyclic steady state (CSS), which is of central interest in the analysis of SMB systems. Therefore, computation of the CSS under a given parameter vector requires simulating a relatively high-order SMB model repeatedly, and is therefore already computationally expensive. Optimization of the operating condition requires evaluating the CSS’s at all iterates and is computationally even more challenging. In our previous work, we proposed to use Krylov-type model order reduction methods, i.e., a straightforward method along with a partial-update strategy (Yue, Li, Feng, Seidel-Morgenstern, & Benner 2014) and a subspace-exploiting strategy (Li, Yue, Feng, Seidel-Morgenstern, & Benner 2014), to speed up SMB analysis. This paper puts these results into a more general mathematical framework of using projection-based model order reduction methods, especially Krylov-type methods, to reduce linear multi-stage systems. Special attention is paid to computation and optimization of the CSS. We also show that the two strategies can be combined to achieve an even better speedup. The efficiency of our methods is validated by numerical optimization of a linear SMB system.