Identification of time-delay chaotic system with outliers: Fuzzy neural networks using hybrid learning algorithm

A hybrid learning algorithm is proposed to train fuzzy neural networks (FNNs) for identifying a time-delay chaotic system with outliers. In the proposed algorithm, integrating support vector regression (SVR) and annealing robust time-varying learning algorithm (ARTVLA) to optimize FNNs. In the evolutionary procedure, first, SVR is adopted to determine the number of hidden layer nodes and the initial structure of the FNNs. After initialization, ARTVLA with nonlinear time-varying learning rate is then applied to train FNNs. In ARTVLA, the determination of the learning rate would be an important work for the trade-off between stability and speed of convergence. A computationally efficient optimization method, particle swarm optimization (PSO) method, is adopted to simultaneously find optimal learning rates. Due to the advantages of SVR and ARTVLA (SVR-ARTVLA), the proposed FNNs (SVR-ARTVLA-FNNs) have good performance for identifying a time-delay chaotic system: Mackey Glass system with outliers. Simulation results are illustrated the effectiveness and feasibility of the proposed SVR-ARTVLA-FNNs.