*Article* **A Hybrid Prognostic Method for Proton-Exchange-Membrane Fuel Cell with Decomposition Forecasting Framework Based on AEKF and LSTM**

**Zetao Xia 1, Yining Wang 1, Longhua Ma 2, Yang Zhu 3, Yongjie Li 2, Jili Tao <sup>2</sup> and Guanzhong Tian 1,\***


**Abstract:** Durability and reliability are the major bottlenecks of the proton-exchange-membrane fuel cell (PEMFC) for large-scale commercial deployment. With the help of prognostic approaches, we can reduce its maintenance cost and maximize its lifetime. This paper proposes a hybrid prognostic method for PEMFCs based on a decomposition forecasting framework. Firstly, the original voltage data is decomposed into the calendar aging part and the reversible aging part based on locally weighted regression (LOESS). Then, we apply an adaptive extended Kalman filter (AEKF) and long short-term memory (LSTM) neural network to predict those two components, respectively. Threedimensional aging factors are introduced in the physical aging model to capture the overall aging trend better. We utilize the automatic machine-learning method based on the genetic algorithm to train the LSTM model more efficiently and improve prediction accuracy. The aging voltage is derived from the sum of the two predicted voltage components, and we can further realize the remaining useful life estimation. Experimental results show that the proposed hybrid prognostic method can realize an accurate long-term voltage-degradation prediction and outperform the single model-based method or data-based method.

**Keywords:** prognostics; proton-exchange-membrane fuel cell; hybrid method; degradation prediction; remaining useful life
