Online extraction of main linear trends for nonlinear time-varying processes

Linear trends of a time-varying process include useful and insight data about its temporal behaviors. In this paper, we introduce an approach for extracting the main linear trends of a nonlinear time-varying process. In this approach, originally, an adaptive linear model is utilized to estimate the temporal-linear trends of the process. Then, by using a suitable distance index, an online clustering algorithm has been developed to classify the estimated linear trends. Considering the mean and the number of members for each cluster, main linear trends are extracted for the process. Through an illustrative example, the methodology of the proposed approach in extracting main linear trends is explained and its capability is shown. Also, through two case studies –electrical load time series and pH neutralization process– the application of the proposed method in studying temporal behaviors of processes like stability, changing rate, oscillation and characteristics of transient states are explained.