###### Abstract  
The energy management strategy plays an essential role in improving the fuel economy and extending the energy source lifetime for fuel cell hybrid electric vehicles (FCHEVs). However, the traditional energy management strategy ignores the lifetime of the energy sources for good fuel economy. In this work, an adaptive equivalent consumption minimization strategy considering performance degradation (DA-ECMS) is proposed by incorporating fuel cell and battery performance degradation models and establishing an optimal covariate predictor based on a long short-term memory (LSTM) neural network. The comparative simulations show that, compared with the adaptive equivalent consumption minimization strategy (A-ECMS), the DA-ECMS reduces the fuel cell stack voltage degradation by 17.1%, 23.2%, and 16.6% for the Worldwide Harmonized Light Vehicle Test Procedure (WLTP), the China Light-Duty Vehicle Test Cycle (CLTC), and the New European Driving Cycle (NEDC), respectively, and the corresponding battery capacity degradation is reduced by 5.1%, 11.1%, and 11.2%. The average relative error between the hardware-in-the-loop (HIL) test and simulation results of the DA-ECMS is 5%. In conclusion, the proposed DA-ECMS can effectively extend the lifetime of the fuel cell and battery compared to the A-ECMS. fuel cell hybrid electric vehicle; energy management strategy; covariate predictor; adaptive equivalent consumption minimization strategy; degradation of energy source +
Footnote †: journal: Applied sciences  
and consequently increasing the costs. The existing energy management strategies (EMSs) for FCHEVs primarily focus on optimal power distribution between energy sources, often overlooking the lifetime of the energy sources [6]. Given the substantial production costs of fuel cells and batteries, developing energy management strategies that emphasize both high efficiency and prolonged lifetimes for FCHEV energy sources is becoming increasingly crucial [7; 8]. Typical EMSs are divided into three categories: rule-based EMSs [9], optimization-based EMSs [10], and learning-based EMSs [11]. The rule-based EMSs allocate power from hybrid sources according to predefined rules. This process is computationally light and simple to implement. The strategies predominantly include fuzzy logic control, deterministic rule-based strategies, and state machine control [12]. However, their effectiveness is often limited in complex and dynamic real-world road conditions, as the preset rules may not sufficiently adapt to rapidly changing driving environments [13]. The learning-based EMSs primarily involve reinforcement learning and deep reinforcement learning [14], and they predict the energy demand by analyzing historical and real-time data. These strategies optimize the power allocation from various energy sources using sophisticated AI algorithms that are highly adaptive [15]. However, these strategies are not conducive to solving high-dimensional problems, due to the discretization of states and actions, and they are prone to falling into local optima [16]. The optimization-based EMSs include global optimization [17] and instantaneous optimization [18]. Dynamic programming (DP) is a representative of global optimization. The core of DP is to decompose the problem into multiple sub-problems to be solved, which can achieve global optimality. However, global optimality is based on perfectly known operating conditions and is computationally intensive, making it unsuitable for real-time applications [19]. The equivalent consumption minimization strategy (ECMS) is a transient optimization strategy based on instantaneous information. The ECMS does not rely on the global operating conditions and achieves direct comparison and management between different energy types by introducing equivalence factors to convert electricity consumption to equivalent fuel consumption [20; 21].