A random-effects model for long-term degradation analysis of solid oxide fuel cells

Solid oxide fuel cells (SOFCs) are electrochemical devices converting the chemical energy into electricity with high efficiency and low pollutant emissions. Tough very promising, this technology is still in a developing phase, and degradation at the cell/stack level with operating time is still an issue of major concern. Methods to directly observe degradation modes and to measure their evolution over time are difficult to implement, and indirect performance indicators are adopted, typically related to voltage measurements in long-term tests. In order to describe long-term degradation tests, three components of the voltage measurements should be modelled: the smooth decay of voltage over time for each single unit; the variability of voltage decay among units; and the high-frequency small fluctuations of voltage due to experimental noise and lack of fit. In this paper, we propose an empirical random-effects regression model of polynomial type enabling to evaluate separately these three types of variability. Point and interval estimates are also derived for some performance measures, such as the mean voltage, the prediction of cell voltage, the reliability function and the cell-to-cell variability in SOFC stacks. Finally, the proposed methodology is applied to two real case-studies of long-term degradation tests of SOFC stacks.