A novel Physics-Based Causal Health Indicator for Fuel Cell Remaining Useful Life Online Estimation Under Dynamic Conditions

To increase the lifetime of fuel cell systems, a first step is to estimate their degradation and remaining useful life (RUL) by forecasting a health indicator (HI) until it reaches a threshold defining the end of life (EoL). In static applications, voltage or power are commonly selected as the HI. In dynamic applications, the relative power loss rate (RPLR) is considered more suitable. However, the RPLR is constructed from a simplified polarization model that does not take into account ohmic losses and is still too influenced by the short-term dynamics of the load profile. Other existing HIs based on more accurate models (stemming from physical laws to construct a Tafel-Ohmic model) cannot be computed online and do not take into account the current inside the fuel cell. To overcome the limitations of the available HIs, this work introduces a new physics-based HI based on inverting the Tafel-Ohmic model using the Lambert W function. This HI is compared to the existing ones using a pre-training metric measuring the global trend compared to local variation and a post-training metric measuring the RUL estimation performances. Compared to respectively the voltage and RPLR, the new HI has a 14 times and five times higher score in terms of global decreasing trend versus local, undesired, variations. Concerning the post-training results, it shows very good stability regarding the forecasting model parameters and has a RUL score 1.5 and 12 times higher than the voltage and RPLR, respectively.

Keywords: Health indicator, prognosis, remaining useful life, fuel cell, machine learning, Lambert function, Tafel equation, dynamic load, PEMFC