Nonlinear methods for evaluating and online predicting the lifetime of fuel cells

Lifetime evaluation and prediction is a key topic for proton exchange membrane (PEM) fuel cells, which can contribute to prolong the durability and accelerate the commercialization of fuel cells. In this paper, a linear formula to evaluate the maximum service lifetime of fuel cells for vehicle applications and several nonlinear formulas to predict the lifetime of fuel cells are presented. The terminal voltage of fuel cells at the rated condition is defined as the average cell voltage decreasing by ca. 10% from the start rated voltage at the rated condition. A nonlinear formula based on the variation of the hydrogen crossover is derived, which reveals that the variation of the hydrogen crossover is the main factor for the nonlinear lifetime degradation of fuel cells. The nonlinear formula based on the time response of first-order control systems (FOCS) for the overall process is proposed, and the segment point between linear and nonlinear degradation is also defined by this formula. Then a more accurate segmented formula with linear lifetime formula and nonlinear lifetime formula based on the time response of FOCSs for the local process is derived. Finally, the segmented formula is verified by experiment results of the single cell and fuel cell stacks and practical operating results of fuel cell vehicles. Moreover, methods for lifetime evaluation in the laboratory and online prediction in the vehicle are proposed.