A novel high level canonical piecewise linear model based on the simplicial partition and its application

Piecewise linear model has attracted more and more concerns in recent researches because it can handle the complex nonlinearity and maintain linearity in subregions. The compact representations of piecewise linear (PWL) such as hinging hyperplanes (HH), generalized hinging hyperplanes (GHH) and so on have been introduced. But during parameters training, the partitions are uncontrollable and unpredicted and will result in a large number of crossing subregions, that is so-called the curse of partitions, which makes it hard in the real world application. In this paper, a novel high level canonical piecewise linear model based on simplex partition is addressed to tackle the curse of partitions. Several numerical experiments are done to show the effectiveness of proposed model. And then, Petro-SIM is used to simulate the refinery hydro-upgrading processing units (HUPUs) and scheduling models of HUPUs are obtained with the proposed model. The simulation experiments show that the proposed model formulation can not only maintain a relatively high fitting accuracy but also effectively avoid the curse of partitions.