Fuzzy serial-parallel stochastic configuration networks based on nonconvex dynamic membership function optimization

A fuzzy series-parallel stochastic configuration networks (F-SPSCN) is proposed based on the application of nonconvex optimization in fuzzy systems. Firstly, the kernel density estimation method is used to fit the distribution of original input data to generate dynamic nonconvex membership functions, which enhances the fuzzy system ability to handle uncertain industrial data. Then the parameters of the nonconvex membership functions are optimized based on Majorization-Minimization algorithm and Generalized Projective Gradient Descent algorithm. The optimized membership matrices and fuzzy outputs are used as inputs of the serial-parallel stochastic configuration networks to improve the overall prediction accuracy of the model. Finally, the prediction accuracy of the F-SPSCN model has been verified by performing prediction experiments with two different functions and four benchmark datasets. The F-SPSCN model demonstrates superior performance compared to other models in predicting the magnetic separation recovery ratio (MSRR) of hydrogen-based mineral phase transformation (HMPT) process for refractory iron ore.