Membrane electrolyte assembly (MEA) aging is a major concern for deployed proton exchange membrane (PEM) fuel cell stacks. Studies have shown that working conditions, such as the operating temperature, humidity, and open circuit voltage (OCV), have a major effect on degradation rates and also vary significantly from cell to cell. Individual cell health estimations would be very beneficial to maintenance and control schemes. Ideally, estimations would occur in response to the applied load to avoid service interruptions. To this end, this paper presents the use of an extended Kalman filter (EKF) to estimate the effective membrane surface area (EMSA) of each cell using cell voltage measurements taken during operation. The EKF method has a low computational cost and can be applied in real time to estimate the EMSA of each cell in the stack. This yields quantifiable data regarding cell degradation. The EKF algorithm was applied to experimental data taken on a 23-cell stack. The load profiles for the experiments were based on the FTP-75 and highway fuel economy test (HWFET) standard drive cycle tests to test the ability of the algorithm to perform in realistic load scenarios. To confirm the results of the EKF method, low performing cells and an additional “healthy” cell were selected for scanning electron microscope (SEM) analysis. The images taken of the cells confirm that the EKF accurately identified problematic cells in the stack. The results of this study could be used to formulate online sate of health estimators for each cell in the stack that can operate during normal operation.

## Introduction

In the search for alternative energy sources for a more sustainable future, proton exchange membrane (PEM) fuel cells have garnered extensive research efforts, both in academia and industry. PEM fuel cells are of particular interest for use in the transportation sector and for distributed power generation due to their unique combination of benefits [1]. For automotive applications, PEM fuel cells have advantages over both traditional internal combustion engines and battery power. While they can respond appropriately to fairly fast load changes [1,2], they have no direct harmful emissions. Also, they can provide a similar user experience to traditional automotive power sources. They can be refilled in a similar amount of time to current gasoline vehicles [3] and can operate with a similar driving range, which can eliminate the range anxiety concerns that have slowed the adoption of battery powered electric vehicles [4,5].

However, PEM fuel cell technology still has a number of hurdles to overcome to reach its full market potential. Particularly, the long-term durability of the membrane electrolyte assemblies (MEAs) is a major concern. This is exacerbated by the fact that the MEAs degrade differently depending on the operating conditions they are subjected to Refs. [6] and [7]. Studies have shown that the degradation rate is affected by the frequency and duration of open circuit voltage (OCV) instances [812], low humidity operation [1316], high humidity operation [17,18], and by the operating temperature [7]. In general, degradation tends to become worse with temperatures above 75 °C, the use of gases that are not fully humidified, and with load cycling, particularly if the OCV potential is included [7].

Given the inherent variability of the operating conditions, both with load variations and depending on the stack location, it is difficult to determine the rate at which individual cells will become unserviceable. While the concept of fuel cell prognostics has been broached, studies have generally assumed known and consistent load profiles, constant stack inputs, and only investigated stack level degradation of a general impedance parameter [19,20]. Though stack level health estimations are useful, often maintenance may be forced due to the poor performance of individual cells in a stack.

Ideally, it would be best to investigate MEA parameters on an individual cell basis as manufacturing variability and differences in the local operating conditions lead to different aging rates for each cell in the stack. Preferably, this would be done in real time during the natural operation of the stack, without the need for additional characterization tests. To this end, this paper presents the use of an extended Kalman filter (EKF) to estimate the effective membrane surface area (EMSA) of each cell in a fuel cell stack in real time.

Though there have been other applications of Kalman filters in PEM fuel cells, none have quite approached the issue of MEA health estimations in this manner. Many have used state estimation methods for water management and flooding fault diagnoses [2022]. These works could help to limit the need for high-quality humidity sensors, which can be a significant portion of the balance-of-plant costs, but do not address the issue of MEA degradation. One study by Zhang and Pisu [20] used an unscented Kalman filter implementation to estimate the degradation in the EMSA of a fuel cell stack. However, this work did not include experimental data and assumed that a consistent prescribed load profile was used. Furthermore, they did not consider differences in aging between cells in the stack.

In this study, the EKF is integrated with the distributed model developed by the authors [23] to estimate the EMSA of each cell in a 23-cell stack based on individual cell voltage measurements. This model captures the spatial distribution in the cathode using a series of six control volumes (CVs) to represent the channel [23]. Implementing this method with the multiple CV modeling approach for the cathode channel makes it possible to investigate the differences in the voltage parameters across the length of the stack. The EMSA estimations provide a useful addition to the multi-CV modeling approach and also yield quantifiable data regarding aging effects.

The EKF algorithm was tested using experimental data from the test fuel cell stack in our lab. To test the ability of the algorithm to perform during normal stack operation, the load profiles for the experiments were based on the FTP-75 and highway fuel economy test (HWFET) standard drive cycle tests, as will be described later in the paper. To confirm the effectiveness of the EKF method in estimating the health of each cell in the stack, key cells were selected for scanning electron microscope (SEM) analysis. The images taken of the cells confirm that EKF could accurately identify problematic cells in the stack. The results of this study could be used to formulate online sate of health estimators for each cell in the stack. This information could be used to monitor the health of individual cells and ultimately to inform prognostics models to more appropriately predict the end of life of the stack and schedule maintenance operations.

## Extended Kalman Filter for Fuel Cell Membrane Electrolyte Assembly Parameters

The decline in EMSAs as a result of agglomeration and platinum dissolution in the catalyst layer has been discussed by a number of studies [2426] and is considered to be the major contributor to the loss of performance or achievable voltage in fuel cell stacks. As such, we focused on this parameter for estimation in the study. The mechanisms of EMSA loss are extensive and varied, as there are many effects that lead to Pt particle growth and dissolution in MEAs during operation. A thorough review of the modes of EMSA loss, as well as other forms of degradation in fuel cell MEAs, can be found in Ref. [7]. Furthermore, many operational conditions, such as the fuel cell temperature, relative humidity, and open circuit voltage, have been shown to affect the rate of EMSA loss. This makes efforts to determine the EMSA degradation rate from functional forms extremely complex and necessitates empirical methods to determine this parameter.

However, measurement of the EMSA is not trivial. Ex situ measurement techniques such as SEM, TEM, and X-ray diffraction are the most common methods [7], but this is clearly not beneficial for characterizing MEAs in operation. Though in situ techniques such as cyclic voltammetry can also be used, these methods require specialized load profiles, environments, etc., to characterize the EMSA, making these methods impractical for characterization of deployed MEAs as well.

In this study, the EKF technique was chosen for the EMSA characterization as this method can be used in real time in during operation to estimate the state of health from the voltage response. As such, no destructive testing or system downtime is required. The EMSA is a particularly good candidate for estimation using this technique because it affects all of the major overpotential losses (activation, ohmic, and concentration losses) through the current density. This makes the EMSA readily observable with respect to the measured cell voltages. Also, the EMSA also gives a clear, physical definition of the state of health of the MEA, and a simple lower limit on could be defined to determine when a MEA needed to be replaced (e.g., 50% of the original value). Note that though other parameters may change with time as well, in this study we focus on the EMSA given the limited number of measurements (1 voltage/cell) and because it is the major contributor to voltage losses.

Finally, it should be noted explicitly that for the EMSA estimation technique outlined here, cell voltage measurements are required. While this could potentially be expensive for large stacks with hundreds of cells, commercial options do exist and cost-effective methods have been developed [27,28]. Furthermore, some resolution could be sacrificed, and sets of cells rather than individual cells could be monitored to reduce the number of required channels to limit costs. Also, the sampling rate could be much lower than what was used for this study, which would effectively only extend the convergence time of the EKF, again to limit the complexity of the voltage monitoring system. The EKF process used for this study is described below.

### General Extended Kalman Filtering Algorithm.

The general EKF algorithm can be described by two major processes, a state propagation in time followed by a state update based on the measurements. The state propagation process is used to determine how the state alters between measurements using rate equations based on the current state of the system and the system inputs. Subsequently, the measurement update process provides the optimal estimate of the state in question based on a related system measurement and the value of the propagated state. This process has the following general form:

State equations
$x˙=f(x(t),u(t))+G(t)w(t)$
(1)
Measurements
$z(t)=h(x(t))+v(t)$
(2)
State propagation process
$x(ti+1−)=x(ti)+x˙(ti)ΔtP(ti+1−)=P(ti)+P˙(ti)Δt$
(3)
where x is the state vector, u is the input vector, f is a function relating the rate of change of the state to the current state and inputs, w is the process noise, and G is known matrix relating the process noise to the state. In Eqs. (1)(3), the (−) indicates the time immediately before a measurement, Δt is the time between measurements, and P is the state covariance matrix whose rate of change is calculated as
$P˙(ti)=F(x(ti))P(ti)+P(ti)FT(ti)+G(ti)Q(ti)GT(ti)F(ti)=δf(x(ti),u(ti))δx$
(4)

where Q is the strength of the zero-mean white Gaussian process represented by matrix G.

Measurement update
$x(ti+)=x(ti−)+K(ti){zi−h[x(ti)]}P(ti+)=P(ti−)−K(ti)H[x(ti)]P(ti−)$
(5)
where the (+) indicates the time immediately after a measurement, and K is the Kalman gain defined as
$K(ti)=P(ti−)HT[x(ti−)]{H[x(ti−)]P(ti−)HT[x(ti−)]+R(ti)}−1$
(6)
where H is a partial derivative matrix defined as
$H[x(ti−)]=δh(x(ti))δx$
(7)

In Eq. (6), R is the strength of the Gaussian white noise process associated with the system measurements (i.e., measurement error or variance). Note that for this application, R was taken to be the average standard deviation of the cell voltage measurements during steady OCV operation.

### Extended Kalman Filtering Algorithm for MEA State Estimates.

A 10 Hz sampling rate was used for this study. As such, the health of the MEA changes slowly relative to the time between measurements as the time scale for degradation is generally hundreds to thousands of hours [7]. Therefore, any MEA state that is investigated for estimation can be considered to be constant for state propagation processes spanning short durations. This fact effectively eliminates the state propagation step. However, to account for the fact that the system parameters are known to slowly change [26,29], the covariance needs to propagate in time between measurements to account for the increasing uncertainty in the value of the parameters between measurements. The resulting system equations for the case in which the EMSA is estimated are as follows:

State equations
$x=[Afc,1⋮Afc,n]x˙≈[0]+wP˙=Q$
(8)
Since the rate of change of the states is essentially zero, matrix F in Eq. (4) is also zero. Note that as the noise is assumed to apply directly to the individual states, matrix G becomes an identity matrix and hence is not shown in Eq. (8). The strength of the white noise variance of the states was estimated from previous degradation studies of PEM membrane assemblies. A number of studies have investigated this issue [7,30] but often report degradation in terms of a voltage loss rate due to the number of possible contributors to this decay rather than directly citing the decline of individual cell parameters. To estimate the process noise strength, the value given by De Bruijn et al. [7] for a cell operated at 75 °C and near 100% humidity was used. They suggested that a 10% decline in voltage over 40,000 h was possible. As a conservative estimate of the process noise of the EMSA, this was assumed to relate to two standard deviations as follows:
$Q≈(Afc,o×0.1/2)240,000×60×60$
(9)

This ensures that the covariance would propagate in such a way that after 40,000 h, two standard deviations of the EMSA would encompass a 10% decline from the initial value with no updates from the measurements.

Measurements
$z=[Vcell,1...Vcell,n]$
(10)
The measurement update process proceeds according to Eq. (5), where matrix H is defined by the model of the connection between the measurement and the states. In this case, the measurements are the individual cell voltages, which are modeled as [31]
$Vcell=Videal(PH2,PO2,TFC)−Vact−Vohm−Vconc=Videal−[V0+Va(1−e−c1⋅IstAfc)+Ist⋅tmAfc(b11λm−b12)exp(b2(1303−1Tfc))+IstAfc(c2IstAfcimax)c3]$
(11)
where Ist is the stack voltage, Afc is the effective area, λm is the membrane water content, Tfc is the stack temperature, and V0, Va, c1, c2, b11, b12, and b2 are voltage parameters that were reported in Ref. [31]. Subsequently, for the case of tuning the EMSA, the H matrix is defined by differentiating Eq. (11) with respect to the EMSA (i.e., Afc) for each cell
$H=[HAfc,1000⋱000HAfc,n]$
(12)
where $HAfc,n$ is defined as
$HAfc,n=Va,nIstc1e−Istc1Afc,nAfc,n2+IstRohm,nAfc,n2+Ist(Istc2Afc,nimax)c3Afc,n2−c3c2(Istc2Afcimax)c3−1Afc,n3imax$
(13)

To complete the implementation, the initial conditions for the MEA states and covariance matrix needed to be defined. The initial EMSA for each cell was taken to be the nominal value for new MEAs used in our test station (EMSA = 27.85 cm2). For the covariance matrix, it was assumed that there were no cross-covariance relationships in this system (i.e., the EMSA of one cell does not affect that of another), so the matrix was diagonal, and all the off-diagonal terms were set to 0.

For the diagonal terms, the initial covariance value should equal the square of the standard deviation for each state based on the initial guess for the uncertainty in the nominal values. The selection of the initial covariance is important as it determines the size of the initial step in the measurement update. In this case, it was known that the MEAs had degraded significantly. Therefore, to allow for faster convergence of the EMSA from the initial value, the initial standard deviation was assumed to be 5% of the nominal value for the EMSA after a trial-and-error study of the EKF stability with different initial standard deviations.

## Standard Drive Cycle Tests

To test the ability of the model to predict the voltage outputs from individual cells, experiments were performed on a FCATS G100 (Greenlight Innovation, Burnaby, BC, Canada) test station in our lab that has been used for previous experiments. The test station can be used to control all the stack inputs (load, inlet temperatures, flow rates, etc.) and also measures the outputs of the stack, including individual cell voltages. For these tests, data were logged at a 10 Hz sampling rate on a 23-cell stack. A full description of the test station and cell configurations can be found in Ref. [23]. To ensure that the method would perform appropriately in realistic scenarios, the load profiles for these tests were based on standard drive cycle tests. Specifically, the FTP-75 and HWFET drive cycles were used. The FTP-75 drive cycle is an American driving cycle that was designed to simulate urban driving and includes frequent stops as well as time at highway speeds [32] and was chosen as a rigorous test of the fuel cell and voltage model during in-city driving situations. The HWFET was also selected as it is the standard test used for highway fuel economy estimates [32]. To correlate the velocity profiles to the required power in the fuel cell, simplified equations for the power needed to accelerate a standard, midsize vehicle to the speeds specified in the drive cycle tests were used. The power calculations were then scaled to the stack size of our test station. The required power can be calculated as
$Pstack(t)=Fstack(t)⋅v(t)$
(14)
where v is the velocity specified by the drive cycle, and Fstack is the required force to match the specified speeds. This force can be calculated as
$Fstack=mvehicleaDC+FRR+Fdrag$
(15)
where aDC is the acceleration calculated from the drive cycle specifications, and FRR and Fdrag are the rolling resistance and drag forces, respectively, that are estimated as follows:
$FRR=fr⋅mvehiclegFdrag=12ρairCdAfv2$
(16)

where fr is the rolling resistance coefficient, Cd is the drag coefficient of the vehicle, and Af is the frontal area. Note that Eq. (15) assumes zero wind speed and a level road grade for the drive tests. Additionally, effects such as those related to the height of the vehicle and distance of the tires from the center of gravity were neglected. All of the vehicle parameters were based on a 2015 Toyota Corolla and are listed in Table 1.

Finally, the required power was scaled to our test station using the ratio of the effective surface area of the MEAs in the Toyota Mirai to the effective surface area of our test MEAs. As the active area of the cells in the Mirai was unknown, this value was estimated from the maximum power output of the Mirai (114 kW). It was also assumed that the maximum power output of the Mirai was designed to occur with a current density of 800 mA/cm2 and cell voltage of ∼0.5 V, which is a conservative estimate based on the polarization curve published in Ref. [36]. As such, the scaling of the required power was as follows:
$Pscaled=Pstack⋅ncells,testAfc,testncells,MiraiAfc,MiraiAfc,Mirai≈Pmax,Mirai0.5 V⋅ncells,Mirai⋅800mAcm2$
(17)

The speed profiles and scaled experimental power for the FTP-75 and HWFET drive cycles used for the validation experiments are shown in Figs. 1 and 2.

Given the limitations of the inputs to the test station, these load profiles were simplified to capture their main features in a manner that could be easily translated to the test station.

## Extended Kalman Filter Effective Membrane Surface Area Tuning Results

The initial EMSA estimations were performed during the HWFET experiment. This test was used as it was less volatile than the FTP-75 approximation and contained more sections of steady current demand. Figure 3 shows how the EMSA estimates made by the EKF algorithm propagate over the course of the test for all 23 cells. Each line in the lower section of the plot represents the EMSA estimation for one of the 23 cells. As you can see, the estimated EMSAs all began at the new MEA value (27.85 cm2) but quickly declined for all of the cells. This is because the MEAs had aged significantly and no longer performed to the same level as new MEAs. As a result, the measured voltages were initially lower than the modeled voltages, which drove the decline in the EMSA estimations. Furthermore, the EKF predicted varying degrees of health for each cell. Note that the lowest line in Fig. 3 corresponds to cell 8 in the stack, which was the poorest performer during both tests. Additional cells of interest to this study, as will be described later in the paper, are also labeled in the figure.

As the EKF process progressed, the agreement with the model improved, and the estimated EMSAs converged to steady values for each cell. It should be noted that the EKF was able to fully tune the EMSA estimations for each cell within approximately 12 min of test time. Though all of the cells had the same initial condition, the process estimated varying levels of health, as is indicated by the different EMSA predictions.

Figure 4 shows the response of the state estimations with the EKF enabled during the FTP-75 test cycle. The initial state and covariance estimates for this process were set to the final values from the EKF process during the HWFET test cycle for the state estimation process.

Firstly, it can be seen that the prediction of the relative state of health is consistent for both tests despite the significantly different load dynamics. For both tests, cell 8 was found to be the least healthy MEA, and the ranking of the EMSA for each cell remained the same besides. This suggests that the EKF method gives a good indication of the MEA state of health. However, it can be seen that the EMSA state estimations tend to increase in response to swift load variations. When the load is held constant, the estimations decline and approach the values estimated by the EKF during the HWFET process. This could be due to a lag in the voltage measurements from the test station, which would lead the EKF to alter the states to compensate for the difference between the measurement and modeled voltage. The severity of the variation caused by the fast dynamics could be reduced by increasing the assumed signal noise strength, R, or reducing the process signal noise, Q. Both of these changes would reduce the Kalman gain, thereby limiting the step in the state estimates due to any single measurement.

Figure 5 shows the final estimated EMSA values for each cell in the stack during the HWFET and FTP-75 test cycles. In these plots, cells 1 and 23 correspond to the outlet and inlet of the stack, respectively. The trends in the estimated EMSA remained the same during both test cycles, despite the variations in the absolute value of the estimation. This suggests that the method reveals information about the MEA health and performance as the relative estimations are consistent over a wide range of variations in the load and conditions. A moving average of the EMSA estimation for each cell could be used to track long-term health degradation as well as to inform prognostics models to schedule preemptive maintenance operations. It should also be noted that the value of the estimated EMSA was fairly consistent for both cell 1 and cell 8, which were the two lowest performing cells in the stack. This indicates that this method effectively identifies particularly low performing MEAs that are in need of replacement, regardless of the load dynamics.

Excluding cells 1 and 8, there is a general trend of increasing health from the inlet (cell 23) to the outlet (cell 1). This is likely because the OCV decreases slightly along the length of the stack due to the drop in pressure associated with the flow of reactants through the channels. A number of studies have shown that Pt particle agglomeration and dissolution mechanisms are enhanced by high electrochemical potentials and load cycling [17,26,37,38]. The slightly lower OCVs and decreased ohmic resistance typical in the latter cells would reduce the magnitude of the changes in cell voltage and contribute to limiting the EMSA loss.

## Ex Situ Health Verification

To test the validity of the estimations made by the EKF algorithm, cells 1, 2, and 8 were removed from the stack for further investigation on a Hitachi S-5500 SEM to investigate the catalyst layers more closely. The MEAs from these cells were selected as they represented two poorly performing cells and one of the high performing cells in the stack. Samples from each MEA were taken from their center where they were in direct contact with the reactant gases during operation. In preparing the samples, the Nafion membrane was removed so that the catalyst layer could be observed directly. It should also be noted that though the anode and cathode catalyst layers were scanned independently, no significant differences between the electrodes were noted within the same MEA in this study. The following figure shows a representative image of the catalyst layers from cell 8.

Figure 6 shows the first signs of the source of poor performance in cell 8. There were clear signs of “pitting” or “pinholes” throughout the catalyst, which indicate the beginnings of membrane hotspot formations. Similar formations were noted in cell 1, but these formations were not seen in the MEA from cell 2. Though these pitting formations suggest degradation beyond just the EMSA of cells 1 and 8, there were indications of significant EMSA loss for these cells as well. The following figures show 90k magnification images of cells 1 and 8 with their corresponding backscattered emission images.

Figure 7 gives a good indication of the relative aging patterns for cells 1, 2, and 8, respectively. Cell 1 had a number of large agglomerations. Cell 8 also showed some large agglomerations and seemed to have less Pt present than the other cells in most areas, which could be a sign of larger agglomerations elsewhere in the catalyst. Conversely, cell 2 consistently had far more small Pt particles that were dispersed relatively evenly, though there were clearly some larger particles that formed in cell 2 as well. This is highlighted in the following figure, which compares images from cells 8 and 2 at 450k magnification (Fig. 8).

The SEM images collected from selected cells in the stack agree with the results of the EKF estimation, which predicted that cells 1 and 8 had degraded more significantly than cell 2. This is apparent from the Pt particles seen in the images, in addition to the pitting that was seen throughout both cells 1 and 8. Again, though the pitting phenomena may not directly correlate to a loss in the EMSA of the MEAs, they are further indications as to why cells 1 and 8 would perform more poorly than cell 2. As such, the EMSA estimations should be viewed as an indicator of the overall health of the MEA.

## Conclusions

The loss in voltage efficiency from PEM cells over the life of the system is a major issue still facing the advancement of this technology. Though the aging mechanisms in these systems are being actively researched, there is still a need to characterize the health of the system in real time to improve time-to-failure predictions and maintenance scheduling for deployed systems. To this end, the paper presented the development of an online membrane electrolyte assembly health estimation technique based on the EKF algorithm. This state estimator was combined with the control-oriented, distributed system model to estimate the effective surface area of each cell in the stack. The state-of-health estimation technique was tested by running a series of experiments based on the HWFET and FTP-75 standard drive cycles to ensure the viability of the EKF in realistic load situations.

The EKF algorithm flagged two cells as particularly low performers as compared to the rest of the stack. SEM analysis was performed on the two problem cells and one of the high performing cells in the stack. The analysis showed that the EKF accurately estimated the health of the cells. The two problem cells had clear signs of Pt agglomeration in addition to other damage in the catalyst layer. Though the healthy cell showed some agglomeration, the severity was much less than that of the low performing cells, giving a clear indication as to why this cell was estimated to have a higher effective surface area. The technique presented in this research could be used to estimate the health of each cell in the stack in real time in response to the load that is placed on the system during operation. This would be a major benefit to the areas of prognostics and maintenance scheduling procedures in PEM fuel cell applications.

## Acknowledgment

Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under Contract No. DE-NA0003525.

## Funding Data

• National Science Foundation (NSF) Materials Processing and Manufacturing GOALI Award (Grant No. CMMI-1201171).

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