Degradation Identiﬁcation and Prognostics of Proton Exchange Membrane Fuel Cell Under Dynamic Load

Proton exchange membrane (PEM) fuel cell has seen its recent increasing deployment in both automotive and stationary applications. However, the unsatisﬁed durability of the fuel cell has barriered in the way of its successful commercialization. Recent research on prognostics and predictive maintenance has demonstrated its e ﬀ ectiveness in predicting the system failure and improving the durability of the PEM fuel cell. This paper contributes to developing a degradation identiﬁcation method for the PEM fuel cell operating under dynamic load. A degradation indicator is proposed based on the polarization model and the nonlinear regression method is applied to extract the degradation feature by segmenting the voltage measurement. To perform prognostics, a machine learning method based on a multi-step echo state network is developed, in which a sliding window is used to recursively reformulate the input sequence with predicted values in the prediction phase. The length of the sliding window is optimized by a genetic algorithm. The proposed method is veriﬁed on the experimental PEM fuel cell degradation data and improves the prediction performance on both accuracy and computation speed when comparing with other prognostics methods.


Introduction
Although fossil fuels still account for the majority of global 2 energy demand, an energy transition is taking place.Hydro-3 gen, as one of the cleanest fuels, has driven increasing attention 4 around the world, which is regarded as a potential solution to 1 Corresponding author.E-mail address: meiling.yue@femto-st.frdegradation rate.An accelerated degradation test is conducted in [6] with normal vehicle driving cycles where signification degradation of the fuel cell has been observed.Varying thermal/humidity state, changing reactant demand and potential voltage cycling are identified as the principal reasons for PEM fuel cell degradation in dynamic operating conditions [7].
Fuel cell performance loss can be easily observed by evaluating the stack voltage degradation and under constant operating conditions, it is measured directly.Various works on PEM fuel cell degradation estimation and prognostics have been conducted using the stack voltage as the direct health indicator [8,9].For example, Bressel et al. have proposed to estimate the health state of the PEM fuel cell using an observerbased prognostics algorithm and a state variable was created to track its degradation [10].Wu et al. have predicted the stack voltage degradation of PEM fuel cells by developing a selfadaptive relevance vector machine, which is able to provide 20 hours ahead forecast time [11].Both model-based and datadriven prognostics methods have been developed.For example, Pan et al. have proposed a model-based prognostics method based on Electrochemical Impedance Spectroscopy (EIS) measurement and an analytical equivalent circuit model, in which the parameters are obtained by linear regression [12].A semiempirical model-based prognostics method based on the adaptive unscented Kalman filter (AUKF) algorithm has been proposed in [13] to improve the initial parameters setting problem.Recent researches have seen increasing interests in developing data-driven prognostics methods, which can reflect the inherent relationships between the input and output by simulating neural networks and avoid the study of complicated physical mechanisms.Data-driven methods have gradually become the main methodology for fuel cell prognostics due to their easyto-use and flexible modelling properties [14,15,16,17].For example, echo state network (ESN) has been deployed to fuel cell prognostics in recent works thanks to its improve computation efficiency [18,19,20].It was first applied to the prediction of the mean cell voltage of a degrading fuel cell in [21] where the accuracy and the computation time are studied regarding the ESN parameters.Furthermore, for predicting the fuel cell health state, a multi-reservoir ESN has been developed in [22] to optimize the parameterization process and in [23], an advanced structure of using moving weight matrix has been proposed to improve the prediction accuracy.However, these studies are limited to the stack level and have not fully considered variable and dynamic loads that may exist in most automotive applications.In those cases, the degradation of the PEM fuel cells cannot be easily quantified using the measured stack voltage, whose value is also affected by system operating dynamics [24].A degradation indicator reflecting intrinsic degradation level in dynamic operating conditions is required.Some researchers have proposed hybrid degradation indexes in multi-time scales for online operation, however, they are limited to certain components and the accuracy is not satisfying [25].Li et al. have proposed to represent the dynamic voltage response of the PEM fuel cell using linear parameter-varying models, and then obtained a real-time health indicator based on the online identified model [18].However, the proposed health index in [18] only evaluates the overall performance loss and lacks the insights of fuel cell intrinsic degradation analysis.As the degradation of the fuel cell is related not only to the ageing phenomenon but also to the time-varying online operating conditions, developing a degradation identification method adapted to random external conditions is required.This paper contributes to proposing an innovative degradation identification method for the PEM fuel cell operating in real time, especially under dynamic load.A degradation indicator is proposed based on the fuel cell polarization model, which is extracted using a non-linear regression process regardless of the operation conditions.Following that, a multi-step windowsliding ESN prognostics method is applied to predict the future evolution of the degradation indicator which is identified online.The parameterization of the ESN is optimized by a genetic algorithm that ensures improved prediction performance.
The proposed degradation identification and prognostics methods are verified with a long-term operation experimental dataset of PEM fuel cell.As there is no additional device to integrate into the embedded fuel cell system, the prognostics can thus be performed in real time.As the measurements are obtained non-intrusively and the proposed method uses directly the output voltage signal, the prognostics can thus be performed in real time.
The main contributions of this paper can be summarized as follows:

65
The rest of the paper is organized as follows: Section 2 66 describes the long-term fuel cell degradation experiment and 67 the dataset used to validate the proposed method.Section 3 68 explains the degradation identification method and Section 4 69 presents the enhanced multi-step window-sliding ESN prognos-70 tics strategy.Finally, Section 5 concludes the paper.

72
A long-term fuel cell degradation experiment was carried 73 out in FCLAB Research Federation2 , France, and supported 74 by the PRODIG project, which received funding from region 75 Aquitaine, France.The test bench consists of a hydrogen tank, 76 a pressure reducer, purge valves and hydrogen inlet valves, DC 77 electric loads, DC power modules, two fuel cell stack mod-78 ules, a compact data acquisition system and a computer for con-79 trol and data logging.The structure of the two-fuel-cell-stack-80 module is shown in Figure 1.One of the stack modules is used 81 for the dynamic load test, which is supposed to be applied in 82 electric bicycles and is, therefore, tested using a dynamic load 83 profile acquired in real operating conditions.The fuel cell stack 84 is designed with an open cathode and dead-end anode structure 85 and a 24 Vdc air fan is integrated with the stack for air supply 86 and temperature regulation.The speed of the air fan is regu-87 lated by varying the duty cycle of an input PWM signal of 25 88 kHz so that the temperature is controlled at the optimal level.89 Moreover, in the cathode side, the air is supplied with an air 90 fan.With the air fan, sufficient quantity of air is guaranteed in 91 normal operation.In other words, the fuel cells always work in 92 the high stoichiometry mode.The pressure in the cathode side 93 is kept equal to the atmosphere pressure.On the anode side, the 94 pressure of hydrogen is fixed and a purge is performed every 30 95 seconds.The fuel cells are self-humidified.Some critical pa-96 rameters of the studied fuel cell stack module are listed in Table 97 1.

98
The dynamic load profile is obtained in real operating condi-99 tions of a hydrogen bike, which is supplied by a 36 V battery, 100 while the fuel cell is used as a range extender, connected in par-101 allel with the battery.Both are used to supply the bike with an 102 average power demand of 53.6 W. A 2.5-hour operation profile 103 is shown in Figure 2, in which the fuel cell starts up to charge 104 the battery until the battery's state-of-charge (SOC) gets to a 105 pre-defined threshold and shuts down when the battery is fully 106 charged.Based on this profile, the current load profile for the 107  The performance loss process of the PEM fuel cell stack 14 shown in Figure 3 may be due to different causes, e.g., varying 15 thermal and humidity state, fuel starvation, cycling with large 16 voltage dynamics, etc.It is hard to represent its performance 17 loss by the stack voltage evolution as it is also dependent on 18 the load characteristics and system dynamics.Confronted with 19 this problem, a time-varying degradation indicator is proposed 20 in this section to evaluate the degradation of the PEM fuel cell 1 operating under such dynamic load.V ohmic , the concentration losses V conc : A detailed parametric model of V cell is derived in [26,27]: where R is the gas constant, T is the operating temperature, F 11 is the Faraday constant, a is charge transfer coefficients of the 12 electrodes, i loss is the stack internal current, which is assumed  the membrane water concentration and temperature [28].by the potential cycles [30].
i L : The limiting current on the cathode varies due to the changes on the diffusivity of oxygen, the gas pressure and the thickness of the gas diffusion layer [31].The diffusivity and the pressure of the oxygen at the cathode are dominated cause of the concentration loss, which are influenced by the gas and water accumulation and can be recovered or mitigated by proper water management.The thickness of the gas diffusion layer cannot change over some nanometers, therefore, it can be ignored [27].
Some works have modelled the variation of the three parameters using physical models or semi-empirical models, however, some of them are developed with assumptions, which have not been validated [27].Moreover, complex parameters bring difficulties when performing prognostics and some measurements needed in the model are not economically or technically feasible, therefore, establishing a degradation indicator that can track the degradation of the PEM fuel cell is necessary.

Degradation indicator α
Figure 5 plots the polarization curves measured in the 2nd, 4th, 5th, 8th and 9th weeks, which indicates different degrees of fuel cell degradation.The polarization curves were obtained by varying the current value between 0 and the maximum (10 A). 8 current values, as shown in Figure 5, were set increasingly to the test stack through an electronic load.For each test point, the current value was maintained for 10 minutes to get a stable voltage measurement.Then the polarization curves were formed by interconnecting the 8 test points in current-voltage coordinate plane.
The model of (2) is identified with different values of R eq , i 0 and i L , whereas the evolutions of the parameters are shown in Figure 6.From Figure 6, it is found that the equivalent resistance R eq increases by approximately 80%, while the exchange current i 0 decreases by a rather same value.The fitting result of i L has remained nearly constant.It is due to that under the dynamic cycling load, the water accumulation is well managed and contributes rarely to the concentration loss.This observation inspires us to assume the same linear evolution of R eq and i 0 and assign a constant value to i L .Therefore, a unique timevarying variable α(t) is chosen to describe the deviation of the parameters, which reflects the state of health of the fuel cell: The introduction of variable α(t) ensures the identification of the fuel cell degradation level in the dynamic operation of the fuel cell.Even if the stack is operated under random load and the degradation cannot be directly identified by the voltage signal, α(t) can be used as a degradation indicator to predict indicate the health state of the fuel cell.
As degradation can only be observed over long periods of at least several hundred hours, the fuel cell degradation is supposed to be quasi-constant on a short time scale, i.e., several hours [10,32].It allows us to segment the operation time into

25
A data-driven prognostics method based on neural network 26 modelling is proposed in this section.The idea is to use the 27 available dataset to build the system behaviour model and to 28 project the current system state to the future.Data-driven prog-29 nostics methods have the model-free advantage that can be ap-30 plied regardless of the physical characteristics of the system.In 31 this section, a typical recurrent neural network (RNN), i.e., the 32 ESN, is adapted for the prognostics purpose.The ESN has seen its wide use in time-series prediction ap-35 plications [34].Different from traditional RNNs, the ESN uses 36 a "reservoir pool" to build the structure of nonlinear systems, 37 which achieves high prediction speed and competitive predic-38 tion performance.The implementation of the ESN is shown in 39 Figure 10 and explained in what follows.

40
The state update model of ESN is written as: where x(t) ∈ R N x and y(t) ∈ R N y are the input and output, which, in this study, are the sequences of the degradation in-2 dicator α, u(t) ∈ R N u is the internal state in the reservoir and is the input weight matrix, w res ∈ R N u ×N u is the recurrent weight 5 matrix in the reservoir, and w out ∈ R N y ×(1+N x +N u ) is the out-6 put weight matrix.k is the leaking rate with a range of (0, 1].

7
The tanh function is generally adopted as the activation func- where I is N u order unit matrix, λ is the regulation parameter and The general working procedure is as following: 1. Choose the size of the reservoir N u and other parameters concerning the level of sparsity of connection, as well as the leakage; 2. Generate the input weights w in by sampling from a random binomial distribution; 3. Generate the reservoir weights w res by sampling from a uniform distribution; 4. Calculate the update of the state in the reservoir as the activation function f (•) of the input at the current time step multiplied by the weights plus the previous state multiplied by the the reservoir weights, as written in (5); 5. Create input sequences and connect them to the desired outputs using linear regression and obtain the trained ESN.
Based on the procedure of training an ESN, a input window and a prediction window need to be defined, which are used to formulate the input sequences and the output sequences of the ESN, respectively.The input window length is the length of the input sequence and the prediction window length is how many steps are going to be predicted following the input sequence.
The input window length and the prediction window length are selected according to the volume of available input data.Supposing the number of available measurements s is up to N, a window length of p is used for the input sequence, written as: For simplicity, it is written x(i) = [s(i + 1) : s(i + p)] in the following text.Then, the corresponding output with a prediction window length of q is written as: Similarly, it is written with the form of y(i) = [ ŝ(i + p + 1) : ŝ(i + p + q)] in the following text.

Adapt ESN for prognostics purpose
The prognostics process can be summarized as a process of estimating a system's remaining useful life and the uncertainties.The international organization for standardization (ISO) committee has defined prognostics as [35]: Standard ISO 13381 (2004).The aim of prognostics is the "estimation of time to failure and risk for one or more existing and future failure modes".
Therefore, to perform prognostics, we need to predict the system performance until the system failure.Based on the time series forecasting process described in Section 4.1, the last plength sequence in the training phase is used to predict a sequence with the length of q.Then, the prognostics starts, in which we cannot predict the subsequent states because the input sequences run out, the prediction cannot continue.As we need to continue to predict the time series until the end of life of the system, new input sequences should be formulated to successively move the input window.Thus, to retain the degradation tendency and to manage the prediction uncertainty, the predicted values of the last step with a sliding window of length m are reinjected to the input sequence of the next step, as shown in Figure 11.Therefore, the last m values of the input sequence are indeed the predicted values.This process allows the continuous formulation of the input even without measurements so that the prognostics can be realised.This process is repeated until reaching the end-of-life (EOL) threshold, which, in this paper, is supposed to be the value of 0.423, 97% of the maximum degradation of the tested fuel cell regarding the length of the experiment.1400 hours for the tested fuel cell.
The pseudo-code of implementing ESN adapted for prognostics purpose is shown as Algorithm 2, where N train is the number of training steps equal to N − p and N predict is the prediction steps until the system's EOL.The ESN is trained in the training phase using the prepared in-55 put and output sequences and then, the following 400 hours are 56 regarded as the evaluation phase.During the evaluation phase, 57 the measurement is supposed to be unavailable so that the out-58 put sequence is reformulated by the predicted values of the last 59 step.The trained ESN model is used to output the predictions of 60 α and the real values of α is used to evaluate the performance of 61 the prognostics.and determine optimal parameters of the ESN.62 Here, the result of prognostics is evaluated by calculating the 63 root mean square error (RMSE), written as (12).In order to find 64 the optimal settings of the ESN, an optimization method, i.e., 65 the genetic algorithm (GA), is applied to generate different pa-66 rameter combinations and run the prognostics algorithm repeat-67 edly until find the optimal settings.optimize the configuration 68 of the ESN.The idea is to code the unknown parameters into bi-69 nary digits, known as a chromosome, then, calculate the RMSE 70 on the evaluation phase by selecting, crossover and mutating 71 the chromosomes repeatedly until finding the optimal solution 72 [36].The advantage of GA is its ability to locate the global 73 optimum or near-global optimum solution without exhausting 74 search of the solution space.Besides, the processing time only 75 increased as the square of the project size and not exponentially.76 Some configured parameters of the proposed ESN-based prog-77 nostics method and the adopted GA are listed in Table 2, where 78 the length of the sliding window of m and the number of reser-79 voir neurons N are optimized by the GA.The influence of other 80 ESN parameters in prognostics results is not so critical and the 81 configuration method in [37] has been adopted. 82 Finally, in the prediction phase, no measurement is available 83 while the ESN has already been optimized and validated by the 84 evaluation phase, therefore, the data of both the training phase 85 and the evaluation phase are used to train the ESN and output 86 the prognostics results on the prediction phase are entered into 87 Prepare input and output x  that the output sequence is reformulated by the predicted values of the last step, as described in Section 4.2.The optimal result is plotted in red dashed line.However, when it comes to the prediction phase, the RMSEs get worse.This is because there is only one predicted value being considered in the next step, which could be accidental and cannot transfer enough information.Moreover, the implementation time of GA is less than 1 minute, while the implementation time of ESN-based prognostics is less than 1 second.Figure 14 shows the prognostics results with different training data lengths, in which both m and N are optimized.The GA optimization results of the two parameters and the RMSEs of both the evaluation phase and the prediction phase, together with the improvements compared with Table 3 are shown in Table 4.By optimizing the number of values that are reinjected into the input sequence of the next step, prognostics results in the prediction phase have been improved up to 90.8%.

Comparison with different methods
The proposed prognostics method is compared with different methods in the literature.The comparison methods include particle filter [9] and stacked long short-term memory (LSTM) [38].The training phase considers the same generated samples.In the compared particle filter method, a second order exponential model is used, and the details of model parameters of particle filter prognostics method is listed in Table 5.The stacked LSTM used for comparison is with two hidden layers  diction accuracy.Besides, the performance of stacked LSTM prognostics method is the worst due to the non-optimized configurations.When comparing the implementation time, the proposed ESN runs the fastest, which is more competitive for online applications.

Conclusion
A degradation identification and prognostics method for realtime operating PEM fuel cells was proposed in this paper.The degradation indicator was derived based on the polarization model and could be extracted from the stack voltage measurements with random system dynamics.To perform prognostics, an enhanced multi-step ESN was adapted for the prediction purpose and the parameters of the ESN were optimized through an  The proposed method of degradation identification and prog-8 nostics allows one to estimate and predict the PEM fuel cell 9 health state under variable and dynamic operating conditions.

10
The degradation identification can be realized in real time with-11 out using supplementary measurements and the prognostics strategy is model-free.This method is control-oriented and can facilitate the development of degradation tolerant control strategies as well as advanced predictive maintenance solutions. 71

Figure 1 :
Figure 1: Two-fuel-cell-module structureTable1: Parameters of the studied fuel cell stack module Parameter Value Active surface 33.625 cm 2 Number of cells 15 Nominal pressure at hydrogen inlet 0.35 bar Nominal output power 73.5 W Maximum operating temperature 75 • C Maximum current 13.45A (0.4 A/cm 2 ) Lowest permitted stack voltage 7.5 V Pressure interval at hydrogen inlet 0.1 to 0.4 bar

Figure 2 :Figure 3 :Figure 4 :
Figure 2: Test profile of a hydrogen bike

23. 1 .
Fuel cell polarization model 3 The polarization test is a common method to characterize a 4 fuel cell.Polarization curve displays the stack voltage output 5 V f c against its operating current i.The polarization curve model 6 of a n-cell fuel cell can be built as the reversible cell voltage 7 V 0 subtracting several irreversible losses including the activa-8 tion losses and the crossover losses V act+cross , the ohmic losses 9

13
to be assimilated to the hydrogen crossover current alone and 14 there is no current caused by membrane shorting, i 0 is the ex-15 change current at the electrodes, R eq is the equivalent ohmic 16 resistance, B c is an empirical parameter considering the water 17 and gas accumulation effects and i L is the limiting current at the 18 cathode[27].

19 3.2. Degradation description 20 To
find an adequate degradation indicator for the PEM fuel 21 cell operating under dynamic current, it is important to know 22 that which component degradation will cause which parameter 23 varies in (2).Some parameters, like R and F, are constant.T is 24 controlled in the experiment so that it is also regarded as con-25 stant, so as V 0 .Some parameters are difficult to know whether 26 they vary with time or not, therefore, they are set to fit the model 27 with the measurements, namely a and B c .i loss is not considered 28 as it is assumed to be assimilated to the hydrogen crossover 29 current.Thus, the variations of the left three parameters, R eq , i 0 30 and i L , should be considered as the source of degradation.31Req : The resistance increase can be caused by various phenom-32 ena.It includes the electronic and contact resistance in-33 crease, as well as the ionic resistance increase related to 34 the membrane degradation[27].The increase of the elec-35 tronic and contact resistance can be observed at the sur-36 face layer of the bipolar plates, the electrode/electrolyte 37 interface, etc, while the increase of the ionic resistance is 38 dominant by the electrolyte materials and influenced by 39

40 i 0 :
The effective exchange current is a function of the electrode catalyst loading and the catalyst specific surface area 42[29].For the fuel cell operated under dynamic load, the 43 cycling will lead to the major degradation of the elec-44 trodes: the catalyst layer degradation and the carbon sup-45 port degradation, especially, the catalyst loss is aggravated 46

Figure 6 :
Figure 6: Evolution of degradation parameters R eq , i 0 and i L

Algorithm 2
ESN for prognostics purpose Load training dataset s Load data Smooth the training data Smoothing Normalize the training data Normalization Define: Input window length = p Prediction window length = q Sliding window length = m Number of training steps = N train Number of prediction steps = N predict Time step i = 0 while x i < x EOL do for i = 0, ..., N train , do Training phase y train [i, :] = s[i + p + 1 : i + p + q]

4Figure 12 :
Figure 12: Procedure of ESN-based prognostics method Figure 13: Implementation of prognostics with different training data lengths (optimizing N) Figure 14: Implementation of prognostics with different training data lengths (optimizing m and N) 7 1.A real-time degradation indicator of PEM fuel cells is 57proposed that can be extracted in both static and dy-58 namic/random operation conditions; 63 4. The proposed prognostics strategy is validated by the long-64 term experimental PEM fuel cell degradation data.

Table 2 :
train [i, :] = s[i : i + p] end for Fit the ESN with prepared input x train and output y train Initialize x predict [0, :] by connecting x[N train + m : N train + p] and y train [−1, 0 : m] for i = 0, ..., N predict , do Start prognostics Predict y predict [i] using the fitted ESN and x predict [i, :] Reformulate x predict [i, :] by connecting x predict [i − 1, m : p] and y predict [i, 0 : m] Configuration of ESN-based prognostics method

Table 4 :
GA optimization and ESN-based prognostics results (optimizing m)The performance of the three different prognostics method is 4 compared in Table7.As it can be seen from Table7, the pro- 3 6 the best prediction accuracy at 600-hour, 700-hour and 800-7 hour training data length, while the accuracy is worse than the 8 particle filter method at 500-hour training data length.This is 9 because when more information is fed to the model, the model 10 can leverage more trend information, thus improving the pre-11

Table 5 :
Model parameters of particle filter prognostics method