Improved MS_CMAC Neural Networks by Integrating a Simplified UFN Model

Macro_Structure_CMAC (MS_CMAC) is a variational CMAC neural network that is designed for modeling smooth functional mappings. The MS_CMAC learning strategy involves constructing virtual grid-distributed data points from random-distributed training data points, and then using the virtual data points to train a tree structure network that is composed of one-dimensional CMAC nodes. A disadvantage of the MS_CMAC is that the prediction errors near the boundary area might sometimes be unexpectedly large. Another disadvantage of the MS_CMAC is that generating virtual grid-distributed data points generally takes a long computational time. Therefore, this study develops an improved model by integrating an unsupervised fuzzy neural network (UFN) into the MS_CMAC to initialize systematically the virtual grid-distributed data points. Additionally, a new error feedback ratio function is adopted to speed up the MS_CMAC training. Several numerical problems are considered to test the improved MS_CMAC. The computed results indicate that a simplified UFN model can produce good initial values of the virtual grid-distributed data points to aggrandize MS_CMAC training. The MS_CMAC prediction is also improved by using the initialized virtual grid-distributed data points.