Identification of nonlinear systems with outliers using wavelet neural networks based on annealing dynamical learning algorithm

This paper presents an annealing dynamical learning algorithm (ADLA) to train wavelet neural networks (WNNs) for identifying nonlinear systems with outliers. In ADLA–WNNs, wavelet-based support vector regression (WSVR) is adopted to determine the initial translation and dilation of a wavelet kernel and the weights of WNNs due to the similarity between WSVR and WNNs. After initialization, ADLA with nonlinear time-varying learning rates is applied to train the WNNs. In the ADLA, the determination of the learning rates would be a key work for the trade-off between stability and speed of convergence. A computationally efficient optimization method, particle swarm optimization (PSO), is adopted to find the optimal learning rates to overcome the stagnation in the training procedure of WNNs. Due to the advantages of WSVR and ADLA (WSVR–ADLA), the WSVR-based ADLA–WNNs (WSVR–ADLA–WNNs) can robust against outliers and achieve the promising efficiency of system identifications. Three examples are simulated to confirm the performance of the proposed algorithm. From the simulated results, the feasibility and superiority of the proposed WSVR–ADLA–WNNs for identifying nonlinear systems with artificial outliers are verified.

► Wavelet-based support vector regression determines the initial structure of WNNs.
► Propose nonlinear time-varying learning algorithm to train the initial WNNs.
► PSO method finds the optimal learning rates in time-varying learning procedure.
► Verify the efficiency of the proposed WNNs for identifying systems with artificial outliers.