Novel continuous function prediction model using an improved Takagi–Sugeno fuzzy rule and its application based on chaotic time series

A novel continuous function prediction model (CFPM) is proposed to resolve prediction problem whose input and output are both continuous functions (CFs). CFPM can simplify sample space reconstruction by using the coefficients of CFs, and use an improved Takagi–Sugeno (TS) fuzzy rule to predict output CF by optimizing the tendency of input CFs. The improved TS fuzzy rule handles each input CF as a consequent parameter and can obtain the nonlinear tendency. After learning process by using opinion-leader-based particle swarm optimization, output CF is determined. In the data prediction based on chaotic time series, CF can either be obtained directly or be fitted by discrete data points, thus the prediction range is enlarged because more discrete data points can be generated once output CF is determined.Two experiments and three cases based on chaotic time series are performed to validate CFPM. The Mackey–Glass chaotic time series is used to prove CFPM validation, while the NN3 time series is used to evaluate CFPM performance. The cases on exhaust gas temperature (EGT), EGT margin and delta EGT are used to show that CFPM is valuable in health status prediction for a particular aircraft engine in the practical engineering field.