Contents lists available at ScienceDirect Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour Online remaining useful lifetime prediction of proton exchange membrane fuel cells using a novel robust methodology Daming Zhou a,b,∗ , Ahmed Al-Durra c , Ke Zhang a , Alexandre Ravey b , Fei Gao b a School of Astronautics, Northwestern Polytechnical University, Xi'an, 710072, PR China b FCLAB (FR CNRS 3539), Univ. Bourgogne Franche-Comte, UTBM, Rue Thierry Mieg, Cedex, Belfort, F-90010, France c Department of Electrical and Computer Engineering, Khalifa University of Science and Technology, Sas Al-Nakhl Campus, Abu Dhabi, United Arab Emirates HIGHLIGHTS • Applicability of different prognostic approaches is considered in terms of data types. • PAM removes the non-stationary trend to obtain static time series. • The identified ARMA model filters the linear component of the stationary time series. • The remaining nonlinear component of time series is used to train TDNN. • The proposed method guarantees robustness due to proper data preprocessing. ARTICLE INFO Keywords: Remaining useful lifetime (RUL) estimation Proton exchange membrane fuel cell (PEMFC) Autoregressive and moving average (ARMA) model Nonlinear pattern of stationary time series ABSTRACT This paper proposes a novel robust prognostic approach that contains three phases for degradation prediction of proton exchange membrane fuel cell (PEMFC) performance and its remaining useful lifetime (RUL) estimation. In the first detrending phase, a physical aging model (PAM) is used to remove the non-stationary trend in the original fuel cell degradation data. In the second filtering phase, the order of autoregressive and moving average (ARMA) model is determined by autocorrelation function (ACF), partial ACF and Akaike information criterion. The linear component in the stationary time series is then filtered by the identified ARMA model. In the third prediction phase, the remaining nonlinear pattern is used to train the time delay neural network (TDNN), in order to provide the final prediction result. Since the proposed prognostic approach uses appropriate methods to analyze and preprocess the original degradation data (i.e., the PAM maintains stationary trend, and then the identified ARMA filters linear component), the remaining nonlinear pattern of stationary time series can thus guarantee a good convergence performance of TDNN. In order to experimentally demonstrate the robustness and prediction accuracy of the proposed approach, degradation tests are performed using two types of PEMFC stack. 1. Introduction Fuel cell has been considered the attractive candidate for the future power applications due to the worldwide energy crisis and environment pollution [1]. As one of the fuel cell technologies, the proton exchange membrane fuel cells (PEMFCs) have higher power density and energy efficiency at lower operating temperature and pressure [2]. Thus, they are particularly suitable for power mobile applications, such as portable power supply or fuel cell hybrid electric vehicles (FCHEVs) [3]. However, during the PEMFC operation, its performance is suffered from multiple failure mechanisms [4–6], mainly including losses of conductivity, catalyst reaction activity, and mass transfer, as shown in Fig. 1. These degradation mechanisms are generated by multiple un- certain circumstances and thus cannot be fully studied. That is the reason why the durability and reliability become the barriers to the mass deployment of the fuel cell. In order to indicate the PEMFC state of health (SOH), estimate its remaining useful lifetime (RUL), and further minimize its maintenance costs, as well as increase its utilization and operational availability, the prognostic and health management (PHM) technologies are gaining attention [7–9]. As an important part of PHM, the prognostic modeling aims at predicting the PEMFC future degradation characteristics based https://doi.org/10.1016/j.jpowsour.2018.06.098 Received 17 January 2018; Received in revised form 23 June 2018; Accepted 27 June 2018 ∗ Corresponding author. School of Astronautics, Northwestern Polytechnical University, Xi'an, 710072, PR China. E-mail addresses: daming.zhou.ubfc@gmail.com, zdm1989@hotmail.com (D. Zhou), ahmed.aldurra@ku.ac.ae (A. Al-Durra), zhangke@nwpu.edu.cn (K. Zhang), alexandre.ravey@utbm.fr (A. Ravey), fei.gao@utbm.fr (F. Gao). Journal of Power Sources 399 (2018) 314–328 0378-7753/ © 2018 Elsevier B.V. All rights reserved. T