An online predictor model as adaptive habitually linear and transiently nonlinear model

Abstract

In this paper, we propose a new online predictor model for complex nonlinear processes. The proposed adaptive habitually linear and transiently nonlinear model (AHLTNM) can follow fast and significant structural variations in the process, which is caused by various sources of uncertainty. The proposed AHLTNM learning method tends to keep the model as simple as possible. While the developed model can be as complex as a TS fuzzy model with flexible precedents, it habitually tends to shrink to an adaptive linear model. The adaptive linear model evolves gradually and expands transiently to a nonlinear TS-type model, when the linear model cannot follow the variations of the process. This expansion starts and continues as long as the modeling error is higher than an adaptive threshold. The model habitually and gradually shrinks to an adaptive linear model when the modeling error becomes lower than the adaptive threshold. Evolving from a linear model to a nonlinear one and then returning to a linear model is performed through specially designed split and merge procedures, which are embedded into AHLTNM learning method. The performance of our proposed online predictor model is examined and compared with that of two well-known TS-type online identification methods in a benchmark example and two other case studies: short term prediction of electrical load time series and prediction of daily minimum temperature time series.