Fuzzy Elman Wavelet Network: Applications to function approximation, system identification, and power system control

Abstract

Fuzzy Wavelet Neural Networks (FWNNs) have recently gained popularity as a powerful tool for various applications. Although the literature contains several effective FWNNs, there is still scope for improvement. This research proposes and implements a novel modification called the Fuzzy Elman Wavelet Network (FEWN), which combines the appealing properties of Elman Neural Networks (ENNs), wavelet functions, and fuzzy membership functions (MFs). The integration suggests the use of interval type-2 fuzzy MFs and wavelet functions with self-recurrent and ENN's cross-coupled feedback loops to handle system uncertainties while accurately representing the intrinsic cross-coupled interferences of real dynamic nonlinear systems. However, it is worth noting that the proposed integration has no detrimental effect on the computational network load, which is critical for online applications.Furthermore, a thorough stability analysis is conducted, and the novel network is implemented and tested in various applications. Finally, the effectiveness of the proposed novel network is evaluated through extensive simulation studies using well-known benchmark functions and dynamic systems. These studies demonstrate the proposed FEWN's efficacy in function approximation, system identification, and as a damping controller for two benchmark large-scale nonlinear power systems.