A robust variational mode decomposition based deep random vector functional link network for dynamic system identification

Abstract

The complexity of system identification problems has been escalated due to their diverse range of applications. In this paper, the non-linear system identification problem is addressed by proposing a deep random vector functional link network (Deep-RVFLN) based on the optimized variational mode decomposition (OVMD). The proposed method has a faster learning speed and trains the network accurately without tuning parameters. Introducing a random link network connecting the input and output layers may lead to reduction in model complexity. To enhance the accuracy and reduce errors, a random vector functional link network (RVFLN) has been implemented with an increased number of hidden layers. The variational mode decomposition (VMD) algorithm is applied to decompose the signal and select optimum modes using an improved particle swarm optimization (IPSO) algorithm. In this method, the data fidelity factor ($\alpha$) and the number of decomposition modes ($k$) are chosen by a new discrete Teaser energy operator (DTEO). The DTEO algorithm is utilized to estimate Teaser energy and it serves as a dependable indicator of overall system reliability. To test the efficacy of the model, three complex non-linear benchmark models named autoregressive (AR), moving average (MA), and autoregressive moving average (ARMA) have been considered with examples 1, 2, and 3 respectively. Based on the results and analysis, the proposed method was found to be better than other state-of-the-art methods. Finally, the proposed Deep-RVFLN identifier is implemented on a high-speed reconfigurable field-programmable gate array (FPGA) to validate the efficacy of the proposed method for non-linear system identification in the hardware platform.