Process Takagi–Sugeno model: A novel approach for handling continuous input and output functions and its application to time series prediction

In prediction, the input and output of some systems may be continuous functions, or the effect of time accumulation may need to be considered in the time series prediction. Thus, a model that can handle continuous input and output functions is required. The process Takagi–Sugeno (PTS) model is proposed in this study by improving the conventional Takagi–Sugeno (TS) model. The parameter identification algorithm of the PTS model, which contains antecedent and consequent parameter identifications, is also presented. Fuzzy clustering is used to identify the antecedent parameters. Given that the inputs of the PTS model are continuous functions, the input samples are in a function vector space wherein the fuzzy clustering should be executed. Thus, the distance in the function vector space is defined and the representation of the continuous function is presented. Fuzzy clustering can be executed on the basis of the defined distance in the function vector space. However, the computational complexity will be high if the fuzzy c-means (FCM) algorithm is used directly. Thus, the any relational clustering algorithm is used instead of the FCM algorithm to decrease the computational complexity. In the consequent parameter identification, the least square method in the function vector space is derived and the closed form of the consequent parameter vector is solved. The effectiveness of the PTS model is validated by using the Mackey–Glass time series and NN3 time series, and the PTS model is then applied to the prediction of exhaust gas temperature time series. The artificial neural network and process neural network are used for comparisons. The results validated that the PTS model can be accurate and stable, and can effectively handle the data with noise. Therefore, the PTS model is robust and has a large scope of application.