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Model-based diagnosis for proton exchange membrane fuel cells
Available online at www.sciencedirect.com
Mathematics and Computers in Simulation 81 (2010) 158–170
Model-based diagnosis for proton exchange membrane fuel cells N. Yousfi Steiner a,b,∗ , D. Candusso c , D. Hissel b , P. Moc¸oteguy a a EIFER, European Institute for Energy Research, Emmy-Noether Str., 11, Karlsruhe, Germany FEMTO-ST/ENISYS/FCLAB, UMR CNRS 6174, University of Franche-Comté, rue Mieg, 90010 Belfort Cedex, France INRETS/FCLAB, The French National Institute for Transport and Safety Research, rue Mieg, 90010 Belfort Cedex, France b
c
Received 3 October 2008; accepted 26 February 2010 Available online 6 March 2010
Abstract Proton Exchange Membrane Fuel Cell (PEMFC) systems are more and more presented as a good alternative to current energy converters such as internal combustion engines. They suffer however from insufficient reliability and durability for stationary and transport applications. Reliability and lifetime may be improved by suitable fault detection and localization. Traditionally, fault diagnosis in fuel cell systems needs the knowledge of number of parameters, which might require a special inner parameter monitoring setup. This is difficult, even impossible with respect to fuel cell stacks geometry. Moreover, with respect to the transportation application that aims at minimizing the embedded instrumentation, simple diagnosis methods involving non-intrusive and easy-to-monitor parameters are highly desired in PEMFC systems. We present in this paper a flooding diagnosis procedure based on black-box model. This diagnosis method allows automating the flooding diagnosis and the parameters used are minimal, low-cost and simple to monitor. The model inputs are some variables that are critical for water management in the PEMFC and consequently for fuel cell performances while the output is a variable that can be monitored in a non-intrusive way and can be used to detect flooding (namely pressure drop through the cathode). The flooding diagnosis procedure is based on the analysis of a residual obtained from the comparison between an experimental and an estimated pressure drop. The estimation of this latter is ensured by an artificial Neural Network that has been trained with flooding-free data. Fault detection is obtained by means of a residual analysis. It has been successfully tested under different experimental conditions including non-flooding and deliberately induced flooding as well as a succession of the two states of health. A proposition to include drying out problems is given as perspective to this work. © 2010 Published by Elsevier B.V. on behalf of IMACS. Keywords: PEM fuel cell; Water management; Diagnosis; Flooding; Elman neural network
1. Introduction Proton Exchange Membrane Fuel Cell (PEMFC) systems are more and more presented as a potential substitute to existing technologies such as internal combustion engines. The growing interest for these energy converters can be seen in the growing number of publications and projects dealing with the subject.
∗
Corresponding author at: EIFER, European Institute for Energy Research, Emmy-Noether Str., 11, Karlsruhe, Germany. Tel.: +49 72161051338; fax: +49 72161051332. E-mail addresses: [email protected] (N.Y. Steiner), [email protected] (D. Candusso), [email protected] (D. Hissel), [email protected] (P. Moc¸oteguy). 0378-4754/$36.00 © 2010 Published by Elsevier B.V. on behalf of IMACS. doi:10.1016/j.matcom.2010.02.006
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PEM fuel cells are energy systems that convert directly the chemical energy of hydrogen into electrical energy with high efficiency, without CO2 emission (when the fuel is cleanly produced), releasing only heat and water. However, the PEMFC is still suffering from a low reliability and a short lifetime, which make it not fully adapted to applications like transportation and stationary cogeneration for which reliability and lifetime are key considerations. These aspects must be improved by suitable fault detection and localization which explains why the last few years have seen a lot of studies investigating durability and diagnosis issues in PEMFC [1,6,11]. It is necessary to have a good knowledge of the influent parameters in the cell operation, but the lack of adequate tools for monitoring the fuel cell’s inner parameters is a hurdle to the cell active control. Moreover, with respect to transportation application, which aims at minimizing the embedded instrumentation, minimal monitoring system is highly desirable. An efficient control and supervision of such systems depend on the proper understanding and behavioral representation of the processes occurring both at stack level and at system level (between the stack and its peripheral ancillaries). Therefore, modeling and experimentation are efficient tools for the diagnosis of such systems. Fuel cells diagnosis can be considered under different approaches, going from heuristic knowledge to mathematical models. There are many different approaches to model the PEMFC stack operations. These approaches have generally different purposes and different ways of implementation. The first approach includes mechanistic models, which aim at simulating for instance the heat and mass transfers together with the electrochemical phenomena encountered in fuel cells [2]. This class of models is based on the “knowledge” of cell inner phenomena and describes their physical behavior using mathematical equations. It requires therefore complete and accurate parameter identification, which is not easy to obtain in fuel cell systems. The second class of models is “behavioral models”, which resort to a “black box” representation, admitting some input variables and evaluating the output values. This kind of model is fast to implement and overcomes the strong limitation that is the need of identifying accurately the PEMFC inner parameters. Among those “black box” models applied to PEMFC, many are based on Neural Networks (NNs) [5,8] for applications such as functional approximation of behavior, diagnosis, prediction and pattern recognition. The application of NN method for fault diagnosis in a fuel cell is rather easy to develop. It permits the use of the available information for training and detecting the faulty operation mode as the data is monitored. We first present in this paper a flooding diagnosis based on black-box model, then we propose a solution to integrate also drying out problems. The parameters are minimal, low-cost, simple to monitor and usually controlled/regulated by the system. The diagnosis method allows automating the flooding diagnosis. The model inputs are some variables that are critical for water management in the PEMFC, and consequently for fuel cell performance, while the output is a variable that can be monitored in a non-intrusive way and can be used to detect flooding (namely pressure drop through the cathode). The NN achieves a nonlinear model of the pressure drop as a function of current, flow rate, stack and dew point temperature in case of safe operation (flooding-free) and compares it to the actual pressure drop (measured from the system). The residual obtained will detect a flooding according to a given threshold. The data used for the NNs training are results of experimentations conducted on a PEMFC under different operating conditions. Section 2 of this paper gives a description of fuel cell operation and performance degradation. The model based flooding diagnosis is discussed in the following section, which also describes the Elman neural network used for the model. Experiments and simulations description as well as results are respectively given in Sections 4 and 5. A proposition to include drying out problems is given as perspective to this work in Section 6. Some conclusions and final remarks are given in Section 7. 2. Fault diagnosis in fuel cells 2.1. Fuel cell operation PEMFC is an electrochemical energy converter that transforms the “chemical” energy contained in many hydrogenous fuels into electrical and thermal energies. It is composed of two electrodes (anode, cathode) in contact with a membrane separating gas compartments (cf. Fig. 1). The fuel cell is fed by reactive gases (humidified hydrogen and oxygen or air) through bipolar plates containing channels. The two oxido-reduction couples involved in the fuel cell electrochemical energy production are H+ /H2 at the anode and O2 /H2 O at the cathode.
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Fig. 1. Fuel cell operation.
At the anode, the hydrogen is oxidized into protons and electrons according to: H2 → 2H+ + 2e−
(1)
At the cathode, the oxygen is reduced into water according to: O2 + 4H+ + 4e− → 2H2 O
(2)
The global reaction is therefore: 2H2 + O2 → 2H2 O
(3)
Thus, during its operation, the fuel cell delivers some current and produces water inside the Membrane Electrode Assembly (MEA). The reactions release also some heat. 2.2. Fault analysis in a PEM fuel cell Degradation in fuel cell can be classified into two rough categories: degradation due to long-term operation (degradation of materials due natural ageing) and degradation due to operation incidents such as MEA contamination or reactant starvation. All “fault” incidents have a common consequence, which is a voltage drop. This could be considered as the main and first indicator of a degraded state but can also drive to fast irreversible failure. Operation incidents linked to water management (cells flooding and membrane drying out) are of particular interest because they may occur frequently during fuel cell operation and they cause rapid power decay. They can even lead to irreversible chemical and mechanical degradation [11]. Flooding events occur when vapor partial pressure is above the saturation pressure and, among others, when the stack temperature is below the gas dew point temperature. It is therefore necessary to understand the causes and characterize flooding, as a first step to the fault diagnosis. The operating conditions and parameters that have a large impact in the flooding phenomenon as well as the contribution of each factor are discussed in a previous paper [12]. Fig. 2 represents a fault tree that provides a better insight into the PEM flooding. This fault tree is built in order to reveal the connections between causes and symptoms. We consider in the present study, four influent operating parameters in the flooding phenomenon (the operating parameters that are in the final “leaves” of the tree): air inlet flow rate, fuel cell temperature, dew point temperature
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Fig. 2. Fault tree concerning the flooding [12].
(or relative humidity at the cathode) and current. Any change in one of these parameters leads to flooding occurrence, mitigation or intensity modification. 2.3. Pertinent parameter for flooding diagnosis: pressure drop In this work, we consider the pressure drop as the difference between the pressure at the inlet and at the outlet of the channels. It is caused by the mechanical, non-conservative interactions on gas particles. Several studies have pointed out this parameter’s relevance to reflect the liquid water accumulation and removal [1,4]. The pressure drop is given by the Darcy’s law that can be used for any flow field, as long as the flow is laminar. ∇P = μ
Q L AK
(4)
where ∇P is the pressure gradient through the porous medium [Pa], Q is the volumetric flow rate [m3 s−1 ], K is the permeability coefficient of the flow field [m2 ], A is the cross-sectional area [m2 ], L the channel length [m] and μ the cinematic viscosity [Pa s]. This assumption is valid near an operating point. Eq. (4) shows that for a given gas flow rate, the presence of liquid water reduces the cross-sectional area available for gas diffusion which in turn reduces the gas permeability K, and then, leads to a pressure drop increase. Thereby, the pressure drop in the flow fields can indicate the presence of liquid water and varies as a function of flooding level. It increases as temperature decreases (condensation rate increases) and as current increases (increase in the amount of produced water). When pressure modeling is needed for a long-range variation of flow, temperature and humidity conditions, the relation (Eq. (4)) between the pressure drop and the flow rate is no longer linear [5]. Thus, a non-linear estimator such as a NN is needed. We choose to build our flooding-diagnosis system on pressure drop because this parameter is low cost, non-intrusive and easy to monitor. 3. Model presentation 3.1. Flooding diagnosis system The flooding diagnosis methodology is a model-based one described in Fig. 3. The model is built using a NN trained to fit the strongly non-linear relation between a set of input parameters and the cathode pressure drop, as output parameters.
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Fig. 3. Scheme of the diagnosis methodology.
The choice of input/output data is crucial for the results of the Neural Network training. The most influent variables (operating parameters) in the flooding process must be included and the less influent data should be discarded. A high number of inputs imply a complex and slow-to-run model. For the inlet parameters, we based our choice on the failure tree represented in Fig. 2. The variables chosen to predict the NN outlet are the following ones: stack current I, and, dew point temperature Tdwpt that reflects the inlet relative humidity, stack temperature T and air inlet flow rate Q. Other methods like “the design of experiments methodology” are adapted [10] to assess the relevance of the chosen input values. Note that these physical parameters can easily be estimated even in one autonomous or embedded fuel cell system. The stack current I can be measured by a LEM sensor, its temperature T can be measured by a thermocouple (placed for instance at the cooling circuit outlet), the air flow rate Q can be determined from the compressor speed. Therefore, the diagnosis method proposed can easily be adapted to an on-board system. The outlet parameters are the pressure drop, a relevant parameter to describe a flooding in an electrode, and the voltage which is the first parameter indicating a degradation. The neural network is trained with different experimental data under “no flooding” conditions and thus serves as a reference basis to the diagnosis procedure. Since the neural network has been trained to recognize the flooding-free operation, each deviation from the predicted value will be interpreted as a flooding state since the flooding impacts the pressure drop through the cathode [1]. Finally, the residual obtained is classified into flooded and non-flooded according to a threshold value. 3.2. Elman Neural Networks A NN consists of a number of processing units (neurons) that communicate by sending information to each other. The link between two neurons is done via weighted connections. Each neuron receives an input from others and uses it to calculate an output signal which will also be sent to other units. The state of a neuron is given by the following function. sj (x) = f (bj + wj,i xi ) (5) i∈I
where xi is the value input to the neuron, wj,i are the weights of the connections between neurons j and i, bj the bias, sj (x) is the neuron’s output value and f the activation or transfer function. The neurons are organized in a set of layers. The number of input and output parameters is specified thanks to the external problem specifications while the model parameters (values of weights and bias) are set by training the NN. This latter consists in minimizing the difference between the output calculated by the NN and the expected one. In feed-forward networks, all input signals flow in one direction, from input to output. These networks can only perform static mapping between an input space and an output space. In recurrent networks, the outputs of some neurons are fed back either to the same neurons or to neurons in the preceding layers. This implies that signals can flow in both forward and backward directions and that the outputs at a given instant reflect the input at that instant as well as previous inputs and outputs. This makes this kind of NN particularly suitable for dynamic systems. First introduced by Elman [3], the Elman’s NN (ENN) is a recurrent NN with three layers: input, hidden and output layers. The feedback connections in ENN go from the outputs of neurons in the hidden layer to a special copy layer called “context” that constitutes a kind of “storage” of previous state of the hidden layer. This recurrent connection allows the ENN to detect and generate time-varying patterns.
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Fig. 4. Example of Elman neural network architecture.
The Elman network has “tansig” neurons in its hidden layer, and “purelin” neurons in its output layer. Mathematical description of ENN can be given as follows: A general architecture of ENN is shown in Fig. 4. U, H, O and C are the vectors input to each layer, Z−1 is the delay element, Y the NN output, W1 = (w1 ) the weight matrix between input and hidden layers, W2 = (w2 ) the weight matrix between hidden and output layers and Wc = (wc ) is the weight matrix between layer and hidden layers. The following vectors at the kth iteration are defined: (k)
i = 1, . . . , n
(6)
(k)
j = 1, . . . , m
(7)
(k)
l = 1, . . . , r
(8)
(k)
j = 1, . . . , m
(9)
ui ∈ U, hj ∈ H, ol ∈ O, and cj ∈ C,
The number of input neurons, hidden neurons and output neurons which are respectively n, m and r. The context layer has the same number of neurons as the hidden layer. With respect to the weight matrices at the kth iteration, the context input is calculated as: (k)
(k−1)
cj = hj
the input of the hidden layer is calculated as: (k) (k−1) (k) hj = f , W1,ij × uj + Wc,ij × hj
(10)
i = 1, . . . , n and
j = 1, . . . , m
(11)
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and the input of the output layer is: (k) (k) ol = f W2,jl × hj ,
j = 1, . . . , m
(12)
Training an ENN is adapting its parameters, namely the weight matrices and the bias (these are not considered in this section for commodity purpose), by back propagation of the error. This means that during the training, at each iteration, the matrices coefficients will be updated by minimizing the error between the value calculated by the NN and the expected value according to the training set. In this work, the training set is defined as: Tr = {[U t (t), Y t (t)],
t = 1, . . . , p}
(13)
p is the number of points used in the training set and U t (t) is a 4xp matrix defined as: U t (t) = [I(t), Qair (t), Tcell (t), Tdwpt (t)]
(14)
and Y t (t) a 1xp vector defined by: Y t (t) = Pexp (t)
(15)
Note that this set of collected data must include information about the system’s global behavior. If Tr presents lack of information within a given range of operating conditions, the model will predict the expected output with difficulties while it will predict with accuracy the output in case of redundancy in a given operating conditions data. Note that redundancy can also lead to problems like the fact that the NN looses its ability to generalize to other sets of data. In this work, four vectors composed of 3900 points (p = 3900) are considered. The model parameters (weights) that constitute the model that will be able to give the best prediction of the system’s real outputs are determined during the training. The model that satisfies the minimal value of the following criterion is chosen: 2 1 (k) E(w) = [Yl (t) − Yˆ lk (t)] , k = 1, . . . , p and l = 1, . . . , r (16) 2 k
l
(k) Yl (t)
where is the vector of measured outputs in the training set, Yˆ lk (t) is the target value at kth iteration and p the length of the training sequence. Weight coefficients of the matrices W1 and W2 are adjusted using the Standard Backpropagation algorithm [7] because this part of the NN has a feed forward character. Wc , is calculated using the following equation [9]: wc,ij = −
∂E ∂hj ∂hj ∂wc,ij
(17)
where the first term at the kth iteration is calculated as: ∂E (k)
∂hj
=
∂E ∂o(k) (k) l = − [Yl (t) − Yˆ lk (t)]w2,jl (k) ∂o ∂hj l
(18)
l
and the second term is calculated as: (k)
∂hj
(k)
∂wc,ij
= f (hj )hj (k)
(k−1)
where f is the derivate of the activation function. Finally, combining the last two equations, we obtain: (k) (k) (k−1) wc,ij = [Yl (t) − Yˆ lk (t)] · w2,jl f hj hj
(19)
(20)
l
This value is finally used to update the weight coefficients between context and hidden layers for the ENN training procedure. In this study, the pressure drop has a dynamical behavior depending on the dynamical evolution of the four above mentioned operating parameters. Therefore, an ENN has been used to predict the pressure drop evolution from the evolution of current, fuel cell temperature and dew point temperature as well as the air flow rate.
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3.3. Performance of the NN The NN performances are usually evaluated by the Mean of squared errors that quantifies the deviation of the result calculated by the NN from the expected value according to the relation: 1 ˆ 2 (Pexp − P) N N
er =
(21)
Another way to analyze the network performance is to perform a simple linear regression between the network response Yˆ and the corresponding target Y. The results of this fitting are subject to statistical analysis in order to explain the relationship between the two data sets. The linear regression model postulates that: Yˆ = aY + b + e
(22)
where the coefficients a and b are determined by minimizing the sum of the square residuals and e is a random variable with average equal to zero. As a consequence, the linear model between Yˆ and Y will fit some values better than others. The well-adapted values are attributed to the “useful” signal and the others to noise. The quality of the regression done by the NN can be assessed using the value of the linear regression parameter r (the Pearson correlation coefficient): ρ ˆ r = YY , − 1 ≤ r ≤ 1 (23) ρYˆ ρY and 1 (xk − μyˆ )(yk − μy ) N −1 N
ρY Yˆ = E[(X − μyˆ )(Y − μy )] =
(24)
k=1
where μyˆ and μy are the mean values of the variables Yˆ and Y. The parameter r measures the correlation (strength and direction) of a linear relationship between Yˆ and Y. The closer is r to 1, the better is the correlation between Yˆ and Y, r = 0 means that the correlation between Yˆ and Y is unpredictable. 4. Experimental and simulation 4.1. Fuel cell stack specifications and data collection The data used in the simulation are collected from a 20 cells PEMFC stack that has been assembled with commercial MEAs (Gore MESGA Primea Series 5510) and graphite distribution plates. Table 1 summarizes some characteristics of the fuel cell stack investigated in the tests. In order to simulate flooding states experimentally, we increased progressively the inlet gases dew point temperature or decreased progressively the stack temperature, so that the water condensation was favored inside the cell. The correlation between dew point increase, stack temperature decrease and fuel cell voltage decrease indicates the presence of flooding, since the power decay is quite fast and no other parameter is changed. Fig. 5 shows the stack temperature and inlet gases dew point temperatures (a). The corresponding voltage and pressure drop signals are given respectively Table 1 Technical specifications of the fuel cell. Number of cells Cell area [cm2 ] Operating temperature [◦ C] Operating pressure [bar abs] Nominal output power [W] Experiments are done under different operating conditions (cf. Table 2).
20 100 20–65 Maximum 1.5 500
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Fig. 5. Experiment showing intentional flooding.
Notice that in a safe operation without flooding, the fuel cell performance is quite stable.
in (b) and (c). The decay of voltage indicates degradation while the increase of pressure drop indicates a potential flooding. From the experiments under the different operating conditions which ranges are related in Table 2, three data sets have been collected to build the NN model and assess its performance (training, validation and test): the ENN was first trained with the first data set in order to learn the non-linear function existing between the pressure drop on one hand and the current, the stack temperature, the dew point temperature and air inlet flow rate as a four dimensional variable (Tdwpt, T, I, Q) on the other hand. A pre-processing is performed in order to normalize the data sets between −1 and 1 (coded values) so as to facilitate the network training. Normalization ensures homogenized ranges and allows comparing the various weights related with different factors. Therefore, neglecting critical data with small absolute value is avoided. The other data sets (validation and test) are used to assess the performance of the training. The neural networks toolbox of the Matlab® software has been used in the present work. 4.2. Training of the NN Fig. 6 shows a result from the training of the ENN, for the following operating conditions (I = 0 A, Q = 52 N l min−1 , Tstack = 40 ◦ C and Tdwpt = 35 ◦ C). Fig. 6(a) corresponds to voltage and Fig. 6(b) corresponds to pressure drop (calculated and measured) as well as the corresponding residual. Concerning the ENN performance, the linear regression parameter related to the previously simulated Pˆ and the corresponding target Pexp is r = 0.94173. This means that the NN predicted a signal that is quite well correlated to the expected one. The pressure drop predicted by the ENN is compared to the expected one (experimental measurement) with a data set that has not been previously introduced into the ENN (the validation set). 4.3. Determination of threshold value, s With respect to the whole training and test set, a threshold value has been defined. This choice has been after several error-trials, so that the residual obtained after training and test data is always lower than the threshold value. In the present study, s is chosen equal to 0.02. Table 2 Variation ranges of the ENN input parameters. T [◦ C] Tdwpt [◦ C] I [A] Q [N l min−1 ]
35–50 25–50 0–35 30–55
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Fig. 6. Model results for an excerpt of the training data set (normal operation). Table 3 List of the different tests and the corresponding operating conditions. Test
Operating conditions
Flooding-free Flooding Flooding + recovery
I = 0 A, Q = 52 N l min−1 , Tstack = 40 ◦ C and Tdwpt = 35 ◦ C (Fig. 7) I = 20 A, Q = 32 N l min−1 , Tstack = 50 ◦ C and Tdwpt = 50 ◦ C (Fig. 8) I = 20 A, Q = 32 N l min−1 , Tstack = 50 ◦ C and Tdwpt = 50 → 20 ◦ C (Fig. 9)
5. Results: diagnosis test Several data sets were collected in order to test the flooding diagnosis procedure (Table 3). The corresponding results are shown in Figs. 7–9.
Fig. 7. Simulated and experimental pressures in case of “non-flooded” cell as well as the corresponding residual under operating conditions: I = 30 A, Q = 52 N l min−1 , Tstack = 50 ◦ C and Tdwpt = 40 ◦ C.
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Fig. 8. Flooding. (a) Fuel cell voltage, calculated and experimental pressure drop (b), residual (c), under the following operating conditions: I = 20 A, Q = 32 N l min−1 , Tstack = 50 ◦ C and Tdwpt = 50 ◦ C.
5.1. Flooding-free The first test refers to a case where the fuel cell is not flooded. The flooding-free experiment (case A) is represented in Fig. 7. In this case, the residual is lower than the threshold value s = 0.02. The diagnostic system does not detect any flooding, except for some points that we call “punctual false detection”. This point is discussed further.
5.2. Flooding The experiment is performed in operating conditions where the fuel cell is deliberately flooded (case B) by setting a gas dew point temperature lower than cell temperature. Fig. 8 presents the evolution of cell voltage, both simulated and measured pressure drops as well as the residual. In this case, the diagnosis method detects the flooding, since the residual is higher than threshold value s.
Fig. 9. Flooding followed by a recovery. Evolution of fuel cell temperature (T) and air dew point temperature (Tdwpt ), stack voltage (U), simulated and experimental pressure drops (dp) and residual (I = 20 A, Q = 32 N l min−1 , Tstack = 50 ◦ C and Tdwpt = 50 → 20 ◦ C).
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5.3. Flooding recovery Fig. 9 shows the evolution of operating parameters, stack voltage, both simulated and experimental pressure drops as well as the residual obtained in case of successive flooding and recovery. Inlet air humidification was used as controlling parameter. At the beginning of the simulation, the pressure drops calculated by the model and measured in the system diverge. The residual is increased and the ENN detects a flooding. The voltage decrease confirms the flooding state induced by a relative humidity of 100% (T = Tdwpt ) until t around 15 min. Since then, the dew point temperature is decreased, favoring water evaporation and therefore mitigating the flooding. After the transition state around t = 15 min, the cell recovers from flooding and the voltage begins to increase. In the same time, the pressure drop estimated by the ENN matches the experimental one which leads to a lower residual. These latter decreases below the fixed threshold, leading to a non-flooding diagnosis. In this case, the diagnosis system detects correctly the transition of the cell’s state of health from flooding to recovery. Few points where the system gives false detections are still observed in this case. They are probably linked to the choice of the threshold value or to the noise that has not been considered in this study. However, since the flooding or recovery processes are quite slow, some conditions such as “An alarm could not be sent unless the residual is above the threshold value for a given time” could be added before the diagnosis system’s decision in order to avoid false flooding diagnosis. On the other hand, some false detection due to noisy data could be also avoided using an adapted filtering process. 6. Perspectives and conclusion 6.1. Drying out problem in fuel cells Inside a fuel cell, water balance is critical and very subtle to reach. On the one hand, the presence and accumulation of liquid water in the fuel cell electrodes causes flooding problems as seen above, and on the other hand, low water content leads to membrane drying out problems. In fact, protonic conductivity is maximal in wet conditions because protons move in the hydrated parts of the ionomer [12]. The protons cannot migrate in a dry ionomer phase. Therefore, the conductivity is reduced and a low ionic conductivity hinders the access of protons to the catalyst surface. This leads to a decrease of the actual number of possible reacting sites in the three-phase boundary layer, thus increasing the activation losses. The operating parameters behind flooding and drying out problems are the same [12]. The first consequence of a fuel cell drying out is performance degradation (power decrease). Unlike flooding problems, the pressure drop is not affected by drying out phenomena. The model improvement that we propose includes drying out problems in the fuel cell and will be published in a forthcoming paper. This procedure is adapted to a fuel cell that experienced water management problems (flooding and drying out): it compares the experimental values of pressure drop and voltage with the outputs of a recurrent neural network. In this procedure, fault detection is done first by analyzing the residual on voltage (comparison with a threshold value) and by classifying the state into “degraded operation” and “non-degraded operation”. In case of the a degraded state, the second residual on pressure drop is used in order to make a decision between “flooding” and “drying out” states. 7. Conclusion This paper aims at presenting a model-based diagnosis procedure using the comparison between measured and calculated pressure drops. The model based on Elman Neural Network is trained with data recorded in flooding-free conditions and the difference between calculated and experimental pressure drop is the residual. The analysis of the residual permits detection of flooding: it is in fact used as an input of a “sigmoid” function which classifies the fuel cell state of health into two classes as follows {flooded, non-flooded} according to a threshold value named s. The model-based diagnosis procedure presented uses physical parameters that can be easily estimated in an autonomous or embedded fuel cell system, which makes this method suitable for an on-board system. It is however still limited to flooding problems.
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Therefore, an improvement of our model is presented. The aim is to include other causes of fuel cell performance degradation as “membrane drying out”. Acknowledgments The authors would like to thank the French National Research Agency (ANR), in the scope of its national action plan for hydrogen (PAN-H) for financially supporting this work. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
[11] [12]
W. He, G. Lin, T.V. Ngyen, AIChE Journal 49 (2003) 3221. D.M. Bernardi, M.W. Verbrugge, Journal of the Electrochemical Society 139 (1992) 2477–2491. J.L. Elman, Cognitive Science 14 (1990) 179–211. A. Hernandez, D. Hissel, R. Outbib, Electric equivalent model of PEMFC, in: 8th Internal Conference on Modelling and Simulation of Electric Machines, Converters and Systems (ELECTRIMACS), Hammamet, Tunisia, April, 2005. S. Jemeï, D. Hissel, M.C. Péra, J.M. Kauffmann, J. Power Sources 124 (2003) 479–486. S. Knights, D. Colbow, M. Kevin, J. St-Pierre, D.P. Wilkinson, Journal of Power Sources 127 (2004) 127–134. Matlab Neural Network toolbox, www.mathworks.com. A. Saengrung, A. Abtahi, A. Zilouchian, Journal of Power Sources 172 (2007) 749–759. S. Seker, E. Ayaz, E. Turcan, Engineering Applications of Artificial Intelligence 16 (2003) 647–656. B. Wahdame, D. Candusso, F. Harel, X. Franc¸ois, M.C. Péra, D. Hissel, J.-M. Kauffmann, Analysis of a PEMFC durability test under low humidity conditions and stack behaviour modelling using experimental design techniques, Journal of Power Sources 182 (2) (August 2008) 429–440. D.P. Wilkinson, J. St-Pierre, Durability, in: W. Wielstich, H.A. Gasteiger, A. Lamm (Eds.), Handbook of Fuel Cells—Fundamentals, Technology, Applications, John Wiley, Wiley, England, 2003, pp. 611–626 (Chapter 47). N. Yousfi-Steiner, P. Mocoteguy, D. Candusso, D. Hissel, A. Aslanides, A review on PEM voltage degradation associated with water management: impacts, influent factors and characterization, Journal of Power Sources 183 (1) (2008) 260–274.
Mathematics and Computers in Simulation 81 (2010) 158–170
Model-based diagnosis for proton exchange membrane fuel cells N. Yousfi Steiner a,b,∗ , D. Candusso c , D. Hissel b , P. Moc¸oteguy a a EIFER, European Institute for Energy Research, Emmy-Noether Str., 11, Karlsruhe, Germany FEMTO-ST/ENISYS/FCLAB, UMR CNRS 6174, University of Franche-Comté, rue Mieg, 90010 Belfort Cedex, France INRETS/FCLAB, The French National Institute for Transport and Safety Research, rue Mieg, 90010 Belfort Cedex, France b
c
Received 3 October 2008; accepted 26 February 2010 Available online 6 March 2010
Abstract Proton Exchange Membrane Fuel Cell (PEMFC) systems are more and more presented as a good alternative to current energy converters such as internal combustion engines. They suffer however from insufficient reliability and durability for stationary and transport applications. Reliability and lifetime may be improved by suitable fault detection and localization. Traditionally, fault diagnosis in fuel cell systems needs the knowledge of number of parameters, which might require a special inner parameter monitoring setup. This is difficult, even impossible with respect to fuel cell stacks geometry. Moreover, with respect to the transportation application that aims at minimizing the embedded instrumentation, simple diagnosis methods involving non-intrusive and easy-to-monitor parameters are highly desired in PEMFC systems. We present in this paper a flooding diagnosis procedure based on black-box model. This diagnosis method allows automating the flooding diagnosis and the parameters used are minimal, low-cost and simple to monitor. The model inputs are some variables that are critical for water management in the PEMFC and consequently for fuel cell performances while the output is a variable that can be monitored in a non-intrusive way and can be used to detect flooding (namely pressure drop through the cathode). The flooding diagnosis procedure is based on the analysis of a residual obtained from the comparison between an experimental and an estimated pressure drop. The estimation of this latter is ensured by an artificial Neural Network that has been trained with flooding-free data. Fault detection is obtained by means of a residual analysis. It has been successfully tested under different experimental conditions including non-flooding and deliberately induced flooding as well as a succession of the two states of health. A proposition to include drying out problems is given as perspective to this work. © 2010 Published by Elsevier B.V. on behalf of IMACS. Keywords: PEM fuel cell; Water management; Diagnosis; Flooding; Elman neural network
1. Introduction Proton Exchange Membrane Fuel Cell (PEMFC) systems are more and more presented as a potential substitute to existing technologies such as internal combustion engines. The growing interest for these energy converters can be seen in the growing number of publications and projects dealing with the subject.
∗
Corresponding author at: EIFER, European Institute for Energy Research, Emmy-Noether Str., 11, Karlsruhe, Germany. Tel.: +49 72161051338; fax: +49 72161051332. E-mail addresses: [email protected] (N.Y. Steiner), [email protected] (D. Candusso), [email protected] (D. Hissel), [email protected] (P. Moc¸oteguy). 0378-4754/$36.00 © 2010 Published by Elsevier B.V. on behalf of IMACS. doi:10.1016/j.matcom.2010.02.006
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PEM fuel cells are energy systems that convert directly the chemical energy of hydrogen into electrical energy with high efficiency, without CO2 emission (when the fuel is cleanly produced), releasing only heat and water. However, the PEMFC is still suffering from a low reliability and a short lifetime, which make it not fully adapted to applications like transportation and stationary cogeneration for which reliability and lifetime are key considerations. These aspects must be improved by suitable fault detection and localization which explains why the last few years have seen a lot of studies investigating durability and diagnosis issues in PEMFC [1,6,11]. It is necessary to have a good knowledge of the influent parameters in the cell operation, but the lack of adequate tools for monitoring the fuel cell’s inner parameters is a hurdle to the cell active control. Moreover, with respect to transportation application, which aims at minimizing the embedded instrumentation, minimal monitoring system is highly desirable. An efficient control and supervision of such systems depend on the proper understanding and behavioral representation of the processes occurring both at stack level and at system level (between the stack and its peripheral ancillaries). Therefore, modeling and experimentation are efficient tools for the diagnosis of such systems. Fuel cells diagnosis can be considered under different approaches, going from heuristic knowledge to mathematical models. There are many different approaches to model the PEMFC stack operations. These approaches have generally different purposes and different ways of implementation. The first approach includes mechanistic models, which aim at simulating for instance the heat and mass transfers together with the electrochemical phenomena encountered in fuel cells [2]. This class of models is based on the “knowledge” of cell inner phenomena and describes their physical behavior using mathematical equations. It requires therefore complete and accurate parameter identification, which is not easy to obtain in fuel cell systems. The second class of models is “behavioral models”, which resort to a “black box” representation, admitting some input variables and evaluating the output values. This kind of model is fast to implement and overcomes the strong limitation that is the need of identifying accurately the PEMFC inner parameters. Among those “black box” models applied to PEMFC, many are based on Neural Networks (NNs) [5,8] for applications such as functional approximation of behavior, diagnosis, prediction and pattern recognition. The application of NN method for fault diagnosis in a fuel cell is rather easy to develop. It permits the use of the available information for training and detecting the faulty operation mode as the data is monitored. We first present in this paper a flooding diagnosis based on black-box model, then we propose a solution to integrate also drying out problems. The parameters are minimal, low-cost, simple to monitor and usually controlled/regulated by the system. The diagnosis method allows automating the flooding diagnosis. The model inputs are some variables that are critical for water management in the PEMFC, and consequently for fuel cell performance, while the output is a variable that can be monitored in a non-intrusive way and can be used to detect flooding (namely pressure drop through the cathode). The NN achieves a nonlinear model of the pressure drop as a function of current, flow rate, stack and dew point temperature in case of safe operation (flooding-free) and compares it to the actual pressure drop (measured from the system). The residual obtained will detect a flooding according to a given threshold. The data used for the NNs training are results of experimentations conducted on a PEMFC under different operating conditions. Section 2 of this paper gives a description of fuel cell operation and performance degradation. The model based flooding diagnosis is discussed in the following section, which also describes the Elman neural network used for the model. Experiments and simulations description as well as results are respectively given in Sections 4 and 5. A proposition to include drying out problems is given as perspective to this work in Section 6. Some conclusions and final remarks are given in Section 7. 2. Fault diagnosis in fuel cells 2.1. Fuel cell operation PEMFC is an electrochemical energy converter that transforms the “chemical” energy contained in many hydrogenous fuels into electrical and thermal energies. It is composed of two electrodes (anode, cathode) in contact with a membrane separating gas compartments (cf. Fig. 1). The fuel cell is fed by reactive gases (humidified hydrogen and oxygen or air) through bipolar plates containing channels. The two oxido-reduction couples involved in the fuel cell electrochemical energy production are H+ /H2 at the anode and O2 /H2 O at the cathode.
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Fig. 1. Fuel cell operation.
At the anode, the hydrogen is oxidized into protons and electrons according to: H2 → 2H+ + 2e−
(1)
At the cathode, the oxygen is reduced into water according to: O2 + 4H+ + 4e− → 2H2 O
(2)
The global reaction is therefore: 2H2 + O2 → 2H2 O
(3)
Thus, during its operation, the fuel cell delivers some current and produces water inside the Membrane Electrode Assembly (MEA). The reactions release also some heat. 2.2. Fault analysis in a PEM fuel cell Degradation in fuel cell can be classified into two rough categories: degradation due to long-term operation (degradation of materials due natural ageing) and degradation due to operation incidents such as MEA contamination or reactant starvation. All “fault” incidents have a common consequence, which is a voltage drop. This could be considered as the main and first indicator of a degraded state but can also drive to fast irreversible failure. Operation incidents linked to water management (cells flooding and membrane drying out) are of particular interest because they may occur frequently during fuel cell operation and they cause rapid power decay. They can even lead to irreversible chemical and mechanical degradation [11]. Flooding events occur when vapor partial pressure is above the saturation pressure and, among others, when the stack temperature is below the gas dew point temperature. It is therefore necessary to understand the causes and characterize flooding, as a first step to the fault diagnosis. The operating conditions and parameters that have a large impact in the flooding phenomenon as well as the contribution of each factor are discussed in a previous paper [12]. Fig. 2 represents a fault tree that provides a better insight into the PEM flooding. This fault tree is built in order to reveal the connections between causes and symptoms. We consider in the present study, four influent operating parameters in the flooding phenomenon (the operating parameters that are in the final “leaves” of the tree): air inlet flow rate, fuel cell temperature, dew point temperature
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Fig. 2. Fault tree concerning the flooding [12].
(or relative humidity at the cathode) and current. Any change in one of these parameters leads to flooding occurrence, mitigation or intensity modification. 2.3. Pertinent parameter for flooding diagnosis: pressure drop In this work, we consider the pressure drop as the difference between the pressure at the inlet and at the outlet of the channels. It is caused by the mechanical, non-conservative interactions on gas particles. Several studies have pointed out this parameter’s relevance to reflect the liquid water accumulation and removal [1,4]. The pressure drop is given by the Darcy’s law that can be used for any flow field, as long as the flow is laminar. ∇P = μ
Q L AK
(4)
where ∇P is the pressure gradient through the porous medium [Pa], Q is the volumetric flow rate [m3 s−1 ], K is the permeability coefficient of the flow field [m2 ], A is the cross-sectional area [m2 ], L the channel length [m] and μ the cinematic viscosity [Pa s]. This assumption is valid near an operating point. Eq. (4) shows that for a given gas flow rate, the presence of liquid water reduces the cross-sectional area available for gas diffusion which in turn reduces the gas permeability K, and then, leads to a pressure drop increase. Thereby, the pressure drop in the flow fields can indicate the presence of liquid water and varies as a function of flooding level. It increases as temperature decreases (condensation rate increases) and as current increases (increase in the amount of produced water). When pressure modeling is needed for a long-range variation of flow, temperature and humidity conditions, the relation (Eq. (4)) between the pressure drop and the flow rate is no longer linear [5]. Thus, a non-linear estimator such as a NN is needed. We choose to build our flooding-diagnosis system on pressure drop because this parameter is low cost, non-intrusive and easy to monitor. 3. Model presentation 3.1. Flooding diagnosis system The flooding diagnosis methodology is a model-based one described in Fig. 3. The model is built using a NN trained to fit the strongly non-linear relation between a set of input parameters and the cathode pressure drop, as output parameters.
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Fig. 3. Scheme of the diagnosis methodology.
The choice of input/output data is crucial for the results of the Neural Network training. The most influent variables (operating parameters) in the flooding process must be included and the less influent data should be discarded. A high number of inputs imply a complex and slow-to-run model. For the inlet parameters, we based our choice on the failure tree represented in Fig. 2. The variables chosen to predict the NN outlet are the following ones: stack current I, and, dew point temperature Tdwpt that reflects the inlet relative humidity, stack temperature T and air inlet flow rate Q. Other methods like “the design of experiments methodology” are adapted [10] to assess the relevance of the chosen input values. Note that these physical parameters can easily be estimated even in one autonomous or embedded fuel cell system. The stack current I can be measured by a LEM sensor, its temperature T can be measured by a thermocouple (placed for instance at the cooling circuit outlet), the air flow rate Q can be determined from the compressor speed. Therefore, the diagnosis method proposed can easily be adapted to an on-board system. The outlet parameters are the pressure drop, a relevant parameter to describe a flooding in an electrode, and the voltage which is the first parameter indicating a degradation. The neural network is trained with different experimental data under “no flooding” conditions and thus serves as a reference basis to the diagnosis procedure. Since the neural network has been trained to recognize the flooding-free operation, each deviation from the predicted value will be interpreted as a flooding state since the flooding impacts the pressure drop through the cathode [1]. Finally, the residual obtained is classified into flooded and non-flooded according to a threshold value. 3.2. Elman Neural Networks A NN consists of a number of processing units (neurons) that communicate by sending information to each other. The link between two neurons is done via weighted connections. Each neuron receives an input from others and uses it to calculate an output signal which will also be sent to other units. The state of a neuron is given by the following function. sj (x) = f (bj + wj,i xi ) (5) i∈I
where xi is the value input to the neuron, wj,i are the weights of the connections between neurons j and i, bj the bias, sj (x) is the neuron’s output value and f the activation or transfer function. The neurons are organized in a set of layers. The number of input and output parameters is specified thanks to the external problem specifications while the model parameters (values of weights and bias) are set by training the NN. This latter consists in minimizing the difference between the output calculated by the NN and the expected one. In feed-forward networks, all input signals flow in one direction, from input to output. These networks can only perform static mapping between an input space and an output space. In recurrent networks, the outputs of some neurons are fed back either to the same neurons or to neurons in the preceding layers. This implies that signals can flow in both forward and backward directions and that the outputs at a given instant reflect the input at that instant as well as previous inputs and outputs. This makes this kind of NN particularly suitable for dynamic systems. First introduced by Elman [3], the Elman’s NN (ENN) is a recurrent NN with three layers: input, hidden and output layers. The feedback connections in ENN go from the outputs of neurons in the hidden layer to a special copy layer called “context” that constitutes a kind of “storage” of previous state of the hidden layer. This recurrent connection allows the ENN to detect and generate time-varying patterns.
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Fig. 4. Example of Elman neural network architecture.
The Elman network has “tansig” neurons in its hidden layer, and “purelin” neurons in its output layer. Mathematical description of ENN can be given as follows: A general architecture of ENN is shown in Fig. 4. U, H, O and C are the vectors input to each layer, Z−1 is the delay element, Y the NN output, W1 = (w1 ) the weight matrix between input and hidden layers, W2 = (w2 ) the weight matrix between hidden and output layers and Wc = (wc ) is the weight matrix between layer and hidden layers. The following vectors at the kth iteration are defined: (k)
i = 1, . . . , n
(6)
(k)
j = 1, . . . , m
(7)
(k)
l = 1, . . . , r
(8)
(k)
j = 1, . . . , m
(9)
ui ∈ U, hj ∈ H, ol ∈ O, and cj ∈ C,
The number of input neurons, hidden neurons and output neurons which are respectively n, m and r. The context layer has the same number of neurons as the hidden layer. With respect to the weight matrices at the kth iteration, the context input is calculated as: (k)
(k−1)
cj = hj
the input of the hidden layer is calculated as: (k) (k−1) (k) hj = f , W1,ij × uj + Wc,ij × hj
(10)
i = 1, . . . , n and
j = 1, . . . , m
(11)
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and the input of the output layer is: (k) (k) ol = f W2,jl × hj ,
j = 1, . . . , m
(12)
Training an ENN is adapting its parameters, namely the weight matrices and the bias (these are not considered in this section for commodity purpose), by back propagation of the error. This means that during the training, at each iteration, the matrices coefficients will be updated by minimizing the error between the value calculated by the NN and the expected value according to the training set. In this work, the training set is defined as: Tr = {[U t (t), Y t (t)],
t = 1, . . . , p}
(13)
p is the number of points used in the training set and U t (t) is a 4xp matrix defined as: U t (t) = [I(t), Qair (t), Tcell (t), Tdwpt (t)]
(14)
and Y t (t) a 1xp vector defined by: Y t (t) = Pexp (t)
(15)
Note that this set of collected data must include information about the system’s global behavior. If Tr presents lack of information within a given range of operating conditions, the model will predict the expected output with difficulties while it will predict with accuracy the output in case of redundancy in a given operating conditions data. Note that redundancy can also lead to problems like the fact that the NN looses its ability to generalize to other sets of data. In this work, four vectors composed of 3900 points (p = 3900) are considered. The model parameters (weights) that constitute the model that will be able to give the best prediction of the system’s real outputs are determined during the training. The model that satisfies the minimal value of the following criterion is chosen: 2 1 (k) E(w) = [Yl (t) − Yˆ lk (t)] , k = 1, . . . , p and l = 1, . . . , r (16) 2 k
l
(k) Yl (t)
where is the vector of measured outputs in the training set, Yˆ lk (t) is the target value at kth iteration and p the length of the training sequence. Weight coefficients of the matrices W1 and W2 are adjusted using the Standard Backpropagation algorithm [7] because this part of the NN has a feed forward character. Wc , is calculated using the following equation [9]: wc,ij = −
∂E ∂hj ∂hj ∂wc,ij
(17)
where the first term at the kth iteration is calculated as: ∂E (k)
∂hj
=
∂E ∂o(k) (k) l = − [Yl (t) − Yˆ lk (t)]w2,jl (k) ∂o ∂hj l
(18)
l
and the second term is calculated as: (k)
∂hj
(k)
∂wc,ij
= f (hj )hj (k)
(k−1)
where f is the derivate of the activation function. Finally, combining the last two equations, we obtain: (k) (k) (k−1) wc,ij = [Yl (t) − Yˆ lk (t)] · w2,jl f hj hj
(19)
(20)
l
This value is finally used to update the weight coefficients between context and hidden layers for the ENN training procedure. In this study, the pressure drop has a dynamical behavior depending on the dynamical evolution of the four above mentioned operating parameters. Therefore, an ENN has been used to predict the pressure drop evolution from the evolution of current, fuel cell temperature and dew point temperature as well as the air flow rate.
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3.3. Performance of the NN The NN performances are usually evaluated by the Mean of squared errors that quantifies the deviation of the result calculated by the NN from the expected value according to the relation: 1 ˆ 2 (Pexp − P) N N
er =
(21)
Another way to analyze the network performance is to perform a simple linear regression between the network response Yˆ and the corresponding target Y. The results of this fitting are subject to statistical analysis in order to explain the relationship between the two data sets. The linear regression model postulates that: Yˆ = aY + b + e
(22)
where the coefficients a and b are determined by minimizing the sum of the square residuals and e is a random variable with average equal to zero. As a consequence, the linear model between Yˆ and Y will fit some values better than others. The well-adapted values are attributed to the “useful” signal and the others to noise. The quality of the regression done by the NN can be assessed using the value of the linear regression parameter r (the Pearson correlation coefficient): ρ ˆ r = YY , − 1 ≤ r ≤ 1 (23) ρYˆ ρY and 1 (xk − μyˆ )(yk − μy ) N −1 N
ρY Yˆ = E[(X − μyˆ )(Y − μy )] =
(24)
k=1
where μyˆ and μy are the mean values of the variables Yˆ and Y. The parameter r measures the correlation (strength and direction) of a linear relationship between Yˆ and Y. The closer is r to 1, the better is the correlation between Yˆ and Y, r = 0 means that the correlation between Yˆ and Y is unpredictable. 4. Experimental and simulation 4.1. Fuel cell stack specifications and data collection The data used in the simulation are collected from a 20 cells PEMFC stack that has been assembled with commercial MEAs (Gore MESGA Primea Series 5510) and graphite distribution plates. Table 1 summarizes some characteristics of the fuel cell stack investigated in the tests. In order to simulate flooding states experimentally, we increased progressively the inlet gases dew point temperature or decreased progressively the stack temperature, so that the water condensation was favored inside the cell. The correlation between dew point increase, stack temperature decrease and fuel cell voltage decrease indicates the presence of flooding, since the power decay is quite fast and no other parameter is changed. Fig. 5 shows the stack temperature and inlet gases dew point temperatures (a). The corresponding voltage and pressure drop signals are given respectively Table 1 Technical specifications of the fuel cell. Number of cells Cell area [cm2 ] Operating temperature [◦ C] Operating pressure [bar abs] Nominal output power [W] Experiments are done under different operating conditions (cf. Table 2).
20 100 20–65 Maximum 1.5 500
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Fig. 5. Experiment showing intentional flooding.
Notice that in a safe operation without flooding, the fuel cell performance is quite stable.
in (b) and (c). The decay of voltage indicates degradation while the increase of pressure drop indicates a potential flooding. From the experiments under the different operating conditions which ranges are related in Table 2, three data sets have been collected to build the NN model and assess its performance (training, validation and test): the ENN was first trained with the first data set in order to learn the non-linear function existing between the pressure drop on one hand and the current, the stack temperature, the dew point temperature and air inlet flow rate as a four dimensional variable (Tdwpt, T, I, Q) on the other hand. A pre-processing is performed in order to normalize the data sets between −1 and 1 (coded values) so as to facilitate the network training. Normalization ensures homogenized ranges and allows comparing the various weights related with different factors. Therefore, neglecting critical data with small absolute value is avoided. The other data sets (validation and test) are used to assess the performance of the training. The neural networks toolbox of the Matlab® software has been used in the present work. 4.2. Training of the NN Fig. 6 shows a result from the training of the ENN, for the following operating conditions (I = 0 A, Q = 52 N l min−1 , Tstack = 40 ◦ C and Tdwpt = 35 ◦ C). Fig. 6(a) corresponds to voltage and Fig. 6(b) corresponds to pressure drop (calculated and measured) as well as the corresponding residual. Concerning the ENN performance, the linear regression parameter related to the previously simulated Pˆ and the corresponding target Pexp is r = 0.94173. This means that the NN predicted a signal that is quite well correlated to the expected one. The pressure drop predicted by the ENN is compared to the expected one (experimental measurement) with a data set that has not been previously introduced into the ENN (the validation set). 4.3. Determination of threshold value, s With respect to the whole training and test set, a threshold value has been defined. This choice has been after several error-trials, so that the residual obtained after training and test data is always lower than the threshold value. In the present study, s is chosen equal to 0.02. Table 2 Variation ranges of the ENN input parameters. T [◦ C] Tdwpt [◦ C] I [A] Q [N l min−1 ]
35–50 25–50 0–35 30–55
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Fig. 6. Model results for an excerpt of the training data set (normal operation). Table 3 List of the different tests and the corresponding operating conditions. Test
Operating conditions
Flooding-free Flooding Flooding + recovery
I = 0 A, Q = 52 N l min−1 , Tstack = 40 ◦ C and Tdwpt = 35 ◦ C (Fig. 7) I = 20 A, Q = 32 N l min−1 , Tstack = 50 ◦ C and Tdwpt = 50 ◦ C (Fig. 8) I = 20 A, Q = 32 N l min−1 , Tstack = 50 ◦ C and Tdwpt = 50 → 20 ◦ C (Fig. 9)
5. Results: diagnosis test Several data sets were collected in order to test the flooding diagnosis procedure (Table 3). The corresponding results are shown in Figs. 7–9.
Fig. 7. Simulated and experimental pressures in case of “non-flooded” cell as well as the corresponding residual under operating conditions: I = 30 A, Q = 52 N l min−1 , Tstack = 50 ◦ C and Tdwpt = 40 ◦ C.
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Fig. 8. Flooding. (a) Fuel cell voltage, calculated and experimental pressure drop (b), residual (c), under the following operating conditions: I = 20 A, Q = 32 N l min−1 , Tstack = 50 ◦ C and Tdwpt = 50 ◦ C.
5.1. Flooding-free The first test refers to a case where the fuel cell is not flooded. The flooding-free experiment (case A) is represented in Fig. 7. In this case, the residual is lower than the threshold value s = 0.02. The diagnostic system does not detect any flooding, except for some points that we call “punctual false detection”. This point is discussed further.
5.2. Flooding The experiment is performed in operating conditions where the fuel cell is deliberately flooded (case B) by setting a gas dew point temperature lower than cell temperature. Fig. 8 presents the evolution of cell voltage, both simulated and measured pressure drops as well as the residual. In this case, the diagnosis method detects the flooding, since the residual is higher than threshold value s.
Fig. 9. Flooding followed by a recovery. Evolution of fuel cell temperature (T) and air dew point temperature (Tdwpt ), stack voltage (U), simulated and experimental pressure drops (dp) and residual (I = 20 A, Q = 32 N l min−1 , Tstack = 50 ◦ C and Tdwpt = 50 → 20 ◦ C).
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5.3. Flooding recovery Fig. 9 shows the evolution of operating parameters, stack voltage, both simulated and experimental pressure drops as well as the residual obtained in case of successive flooding and recovery. Inlet air humidification was used as controlling parameter. At the beginning of the simulation, the pressure drops calculated by the model and measured in the system diverge. The residual is increased and the ENN detects a flooding. The voltage decrease confirms the flooding state induced by a relative humidity of 100% (T = Tdwpt ) until t around 15 min. Since then, the dew point temperature is decreased, favoring water evaporation and therefore mitigating the flooding. After the transition state around t = 15 min, the cell recovers from flooding and the voltage begins to increase. In the same time, the pressure drop estimated by the ENN matches the experimental one which leads to a lower residual. These latter decreases below the fixed threshold, leading to a non-flooding diagnosis. In this case, the diagnosis system detects correctly the transition of the cell’s state of health from flooding to recovery. Few points where the system gives false detections are still observed in this case. They are probably linked to the choice of the threshold value or to the noise that has not been considered in this study. However, since the flooding or recovery processes are quite slow, some conditions such as “An alarm could not be sent unless the residual is above the threshold value for a given time” could be added before the diagnosis system’s decision in order to avoid false flooding diagnosis. On the other hand, some false detection due to noisy data could be also avoided using an adapted filtering process. 6. Perspectives and conclusion 6.1. Drying out problem in fuel cells Inside a fuel cell, water balance is critical and very subtle to reach. On the one hand, the presence and accumulation of liquid water in the fuel cell electrodes causes flooding problems as seen above, and on the other hand, low water content leads to membrane drying out problems. In fact, protonic conductivity is maximal in wet conditions because protons move in the hydrated parts of the ionomer [12]. The protons cannot migrate in a dry ionomer phase. Therefore, the conductivity is reduced and a low ionic conductivity hinders the access of protons to the catalyst surface. This leads to a decrease of the actual number of possible reacting sites in the three-phase boundary layer, thus increasing the activation losses. The operating parameters behind flooding and drying out problems are the same [12]. The first consequence of a fuel cell drying out is performance degradation (power decrease). Unlike flooding problems, the pressure drop is not affected by drying out phenomena. The model improvement that we propose includes drying out problems in the fuel cell and will be published in a forthcoming paper. This procedure is adapted to a fuel cell that experienced water management problems (flooding and drying out): it compares the experimental values of pressure drop and voltage with the outputs of a recurrent neural network. In this procedure, fault detection is done first by analyzing the residual on voltage (comparison with a threshold value) and by classifying the state into “degraded operation” and “non-degraded operation”. In case of the a degraded state, the second residual on pressure drop is used in order to make a decision between “flooding” and “drying out” states. 7. Conclusion This paper aims at presenting a model-based diagnosis procedure using the comparison between measured and calculated pressure drops. The model based on Elman Neural Network is trained with data recorded in flooding-free conditions and the difference between calculated and experimental pressure drop is the residual. The analysis of the residual permits detection of flooding: it is in fact used as an input of a “sigmoid” function which classifies the fuel cell state of health into two classes as follows {flooded, non-flooded} according to a threshold value named s. The model-based diagnosis procedure presented uses physical parameters that can be easily estimated in an autonomous or embedded fuel cell system, which makes this method suitable for an on-board system. It is however still limited to flooding problems.
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Therefore, an improvement of our model is presented. The aim is to include other causes of fuel cell performance degradation as “membrane drying out”. Acknowledgments The authors would like to thank the French National Research Agency (ANR), in the scope of its national action plan for hydrogen (PAN-H) for financially supporting this work. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
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