**1. Introduction**

Hydrogen energy is one of the most important green energy sources. The polymer electrolyte membrane (PEM) fuel cell system can directly convert hydrogen energy into electrical energy through an electrochemical reaction and generate water and heat with minimal pollution [1]. The PEM fuel cell system is a multi-input and-output nonlinear system, and there are some auxiliary elements such as compressors, supply manifolds, return manifolds, compressors, valves, etc. For this reason, the PEM fuel cell system is vulnerable to different sets of faults that can imply its temporal or permanent damage [2]. Therefore, fault diagnosis methods are important to reduce this vulnerability as much as possible.

Considering whether the model is necessary, the diagnosis methods can be classified into two general types, i.e., model- and non-model-based methods [3,4]. The model-based method needs to develop a model to simulate the behavior of the monitored system [4] and, generally, it is performed mostly via residual evaluation, followed by a residual inference for possible fault occurrence detection [5]. Escobet and Feroldi et al. [6,7] proposed a model-based fault diagnosis methodology based on the relative fault sensitivity, and the diagnosis methodology correctly diagnosed the simulated faults in contrast with other methodologies using binary signature matrix of analytical residuals and faults. Rosich et al. [8] designed a subset of consistency relations and residual generators for a fuel cell system. Lira et al. [9] proposed a linear parameter varying (LPV) model-based fault diagnosis methodology based on the relative fault sensitivity. Laghrouche et al. [10] presented an observer-based fault reconstruction method for PEM fuel cells and the method extended the results of a class of nonlinear uncertain systems with Lipschitz nonlinearities. Damiano et al. [11] proposed the Takagi–Sugeno (TS) interval observers to solve the problem of robust fault diagnosis of PEM fuel cells. Kamal et al. [12] proposed a model-based fault detection and isolation (FDI) and found that the residual was sensitive to the fault. Steiner et al. [13] proposed the model-based diagnosis method which was based on a comparison between measured and calculated voltages and pressure drops by an Elman neural network.

A non-model-based method can detect and identify the fault through human knowledge or qualitative reasoning techniques based on a set of input and output data [3,4]. Three types of non-model-based methods include the artificial intelligence method, the statistical method, and the signal processing method. Antoni et al. [14] proposed a fault diagnosis methodology termed visual block fuzzy inductive reasoning and applied it to a fuel cell system. Shao et al. [15] proposed the artificial neural network (ANN) ensemble method based on back-propagating ANN and the Lagrange multiplier method to improve the stability and reliability of the PEM fuel cell systems. Damour et al. [16] proposed a signal-based diagnosis method, based on empirical mode decomposition (EMD). The method did not require any excitation signal or stabilization period as compared with the EIS-based method. Zheng et al. [17] used the electrochemical impedance spectroscopy (EIS) as a basis tool and proposed the double fuzzy method consisting of fuzzy clustering and fuzzy logic to mine diagnostic rules from the experimental data automatically. Ibrahim et al. [18] proposed a diagnosis method using signal-based pattern recognition. All information needed to locate the faults was drawn from the recorded fuel cell output voltage, since certain phenomena leave characteristic patterns in the voltage signal. Pahon et al. [19] used the wavelet transform to identify different patterns or fault signatures and proposed the signal-based pattern recognition approach. Mohammadi et al. [20] used a two-layer feed-forward artificial neural network and developed a reliable fault identification and localization tool for a proton exchange membrane fuel cell. Silva et al. [21] proposed a methodology based on adaptive neuro-fuzzy inference systems (ANFIS) which used, as input, the measures of the fuel cell output voltage during operation. Li et al. [22] proposed a nonlinear multivariable model of a PEM fuel cell system based on support vector regression (SVR) and used an effective informed adaptive particle swarm optimization algorithm to tune the hyper-parameters of the support vector regression (SVR) model. Pei P. et al. [23] reviewed the effect variables of pressure drop and the diagnosis method based on pressure drop was considered to be an online water fault diagnosis. Zhao, [24] proposed a fault diagnosis method based on multi-sensor signals and principle component analysis to improve the fuel cell system performance. Huang, [25] proposed a diagnostic method combining C4.5-based decision tree with a fault diagnosis expert system to solve the fault diagnosis of a fuel cell engine. Liu, [26] proposed a fault diagnosis method which combined an extreme learning machine and the Dempster–Shafer evidence theory to diagnose the faults in a PEM fuel cell system. Bougatef [27] designed the unknown input observer for a delayed LPV model to deal with the fault estimation of actuator fault for a PEM fuel cell. In addition, Wang [28,29] developed a composite support material which possessed intrinsic protonic conductivity and improved electronic conductivity together with the optimization of the microstructure structures. Wilberforce [30–33] researched the effect of humidification of reactive gases and bipolar plate geometry design on the performance of a proton exchange membrane fuel cell.

The PEM fuel cell system is a multi-input and multi-output nonlinear system. The fuel cell stack needs to be integrated with several auxiliary components to form a complete PEM fuel cell system. Therefore, the PEM fuel cell system contains the fuel cell stack, the reactant flow subsystem, heat and temperature subsystem, water management subsystem, power management system and the fuel processor subsystem. The reactant flow subsystem contains the hydrogen supply subsystem and the air supply subsystem. When the source of actual noise is multiplex, Gaussian noise can simulate actual noise well. The probability density of Gaussian noise follows the standard normal distribution. In this paper, Gaussian noise is used to simulate the interference in the PEM fuel cell model, and the

fault diagnosis effect of the method can also be verified. In this paper, when the variance of Gaussian noise is 1.0, 0.5, 0.2, 0.1 respectively, the amplitude of characteristic parameters is reduced to ±10%. By simulating the fault scenarios of the PEM fuel cell system, the original dataset is established with eight diagnosis variables. The possibilistic fuzzy C-means clustering artificial bee colony support vector machine (PFCM-ABC-SVM) method is used to diagnose the faults in the PEM fuel cell system.
