An online low-dimension fuzzy modeling method for time-varying processes

Many industrial processes are full of nonlinearity and noise. Fuzzy modeling often leads to issues with dimension disaster and poor robustness for such processes. To address these issues, an online low -dimension fuzzy method (OLDF) is proposed here. First, an explicit mapping -based lowdimension fuzzy method (EMLF) is proposed to handle intricate nonlinear and noisy processes. In this method, similar fuzzy sets are combined into larger ones using a novel similarity criterion to reduce the fuzzy rules. Then, an explicit mapping strategy is developed to represent the local nonlinearities in each enlarged fuzzy set through an explicit mapping function. Subsequently, a robust objective function is constructed to improve the robustness of EMLF model. This objective function minimizes both the mean and variance of the modeling error, ensuring robust performance even in scenarios featuring non -Gaussian noise or outliers. After that, an online update strategy is designed to account for time -varying dynamics. It designs an adaptive detection mechanism to identify changes in dynamic behaviors. Following detection, global and local updating strategies are developed to dynamically update model parameters. Further analysis and proof highlight the effectiveness of the proposed method. Experiments with time -varying processes also confirm its success.