A simple multi-model prediction method

The present work introduces a new multi-model state-space formulation called simultaneous multi-linear prediction (SMLP), which is suitable for systems with significant gain variation due to nonlinearity. Standard multi-model formulations usually make use of a partitioned state-space, i.e., a state-space that is divided into regions to shift parameters of the state update equation according to the current location of the state, with a view to having a better approximation of a nonlinear plant on each region. This multi-model framework, also known as linear hybrid systems framework, makes use of different boundaries or partition rules concepts, which vary from systems of linear inequalities, propositional logic rules, or a combination of these. This standard approach inevitably introduces discontinuities in the output prediction as the state update equation parameters shift noticeably. Instead, the SMLP is built by defining and updating multiple states simultaneously, thus eliminating the need for partitioning the state-input space into regions and associating with each region a different state update equation. Each state's contribution to the overall output is obtained according to the relative distance between their identification (or linearisation) point and the current operating point, in addition to a set of parameters obtained through regression analysis. Unlike the methods belonging to the hybrid systems framework, no discontinuities are introduced in the output prediction while using an SMLP system, as the weighting function is continuous and the transition between sub-models is smooth. This method presents more accurate results than the use of single linear models while keeping much of their numerical advantages and their relative ease of development. Additionally, the SMLP draws data from step response models that can be provided by commercial, black box dynamic simulators, enabling it to be applied to large-scale systems. In order to assess this methodology, an SMLP system is built for an activated sludge process (ASP) of a wastewater treatment plant, alongside a standard multi-model Piecewise Affine system generated by the same sub-models, and their output predictions are compared. The controllability analysis and the case study presented in Strutzel and Bogle (2016) are extended and updated to this multi-model approach, yielding SMLP systems describing four alternative designs for a realistically sized crude oil atmospheric distillation plant. (C) 2018 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.