Statistical Analysis on Random Matrices of Echo State Network in PEMFC System’s Lifetime Prediction

Abstract

The data-driven method of echo state network (ESN) has been successfully used in the proton exchange membrane fuel cell (PEMFC) system’s lifetime prediction area. Nevertheless, the uncertainties of the randomly generated input and internal weight matrices in ESN have not been reported yet. In view of this, an ensemble ESN structure is proposed in this paper to analyze the effects of random matrices from a statistical point of view. For each ESN, the particle swarm optimization (PSO) method is utilized to optimize the hyperparameters of the leaking rate, spectral radius, and regularization coefficient. The statistical results of each ensemble ESN are analyzed from 100 repeated tests whose weight matrices are generated randomly. The mean value of the ensemble ESN and a confidence interval (CI) of 95% are given during the long-term lifetime prediction. The effects of two different distribution shapes, i.e., uniform distribution and Gaussian distribution, are fully compared. Finally, the effects of the ensemble structure and two different distribution shapes are tested by three experimental datasets under steady-state, quasi-dynamic, and full dynamic operating conditions.