Method and system for determining a degradation indicator of a fuel cell

Description

[0001] The invention relates to the field of fuel cells, in particular fuel cells for powering electric vehicles, including electric or hybrid cars. The invention addresses the general problem of detecting, monitoring and tracking the health of a fuel cell in operational conditions. More specifically, the invention relates to a method and a system for determining a degradation indicator of the fuel cell or more generally of a cell of the fuel cell. The degradation indicator is developed by estimating a loss of active surface area of ​​one or more cells of the cell. The invention also proposes to provide indicators of the origin of the degradation, including flooding, drying out or corrosion phenomena.

[0002] Several reversible and irreversible degradation mechanisms occur in a fuel cell. These degradations affect most of the cell's components. In particular, the degradation phenomenon impacts the active layer of a cell so that the active surface area can decrease over time, impacting the overall efficiency of the device.

[0003] The active layer of a cell encompasses several elements. An active layer of a cell is organized into a microporous network consisting of an ionomer, a catalyst support, and a catalyst. The ionomer provides proton conductivity. The catalyst support can be carbon black or, more commonly, porous graphite. It provides electronic conductivity and provides a porous medium for the transport of gases and liquid water. The catalyst is most often platinum-based. It is deposited in the form of nanoparticles and increases the kinetics of the electrochemical reaction.

[0004] There are two active layers on either side of a cell's membrane, one being the anode and the other the cathode.

[0005] During the lifetime of the fuel cell, various degradation phenomena can impact the active surface of a cell.

[0006] The concept of active surface area is distinguished from geometric surface area in that it defines the total developed surface area which participates in chemical reactions.

[0007] Thus, degradation of the active surface of the catalyst occurs when there is a loss of active platinum surface or an alteration of the properties of the catalyst. Degradation of the active surface of the catalyst can be reversible, for example when it is an oxidation of platinum, or irreversible, for example when it is a dissolution-redeposition of platinum phenomena.

[0008] The carbon support of the catalyst can also be affected by corrosion.

[0009] The geometric surface area of ​​a cell membrane can decrease in the presence of liquid water in the channels or during nitrogen stratification at the anode.

[0010] Generally speaking, the active surface of a cell refers to all the elements involved in chemical reactions and which may be subject to the degradations listed above.

[0011] Detecting fuel cell damage and identifying the causes of damage often requires completely dismantling the cell to analyze the condition of the cell membranes. This requires vehicle maintenance to remove the cell and analyze it, which has its drawbacks.

[0012] There is a need for indicators that can reflect the evolution of the state of the fuel cell without having to disassemble it. In particular, it is desirable to have indicators of the degradation of the state of each cell in the cell in order to improve the efficiency of maintenance and failure prevention.

[0013] Furthermore, there is a need to detect certain key defects directly impacting the performance of the cell such as a water management fault which can cause drying or flooding, or even degradation of the catalyst.

[0014] It is possible to obtain a first indication of the presence of degradation from a measurement of pressure or tension, however this indication is not sufficient to characterize the problem.

[0015] A first type of solution for monitoring the evolution of the health of a fuel cell consists of introducing in-situ sensors in order to carry out local measurements. This solution has the disadvantage of being intrusive and therefore sensitive to the risks of hydrogen leaks inside the cell. Furthermore, it is difficult to implement due to the very small dimensions of the different components, for example the active layers have a thickness of a few micrometers. Furthermore, the measurements must be as non-invasive as possible so as not to disturb either the measurement or the operation of the cell. Finally, to obtain a sufficiently precise diagnosis, the measurement device must be complete to allow access to measurements of different physical quantities, which can lead to an additional cost of over-instrumentation.

[0016] There are three main types of measurement systems suitable for embedding in a fuel cell. The first type of device is a segmented cell, which most often consists of modifying a bipolar plate to include sensors on its surface according to a predefined mesh. A disadvantage of this technology is that it is invasive and not easily implemented.

[0017] A second type of solution involves magneto-tomography measurement methods. This type of method requires a large space around the stack for positioning the sensors. It has the disadvantage of being impossible to implement for fuel cells in operation on board a vehicle. Furthermore, the method presents significant computational complexity.

[0018] A third solution is to insert a dedicated electronic card for measurements into the battery. This solution also has drawbacks.

[0019] The current density and temperature measured by the device are actually the result of an average of the values ​​for each "AME" (Membrane Electrode Assembly) assembly on either side of the cell integrating the card. The placement of the latter at the ends of the stack (first or last cell) must therefore be avoided to not take into account edge effects. In addition, despite the electrical conductivity of the card supposed to be higher in the thickness than in the plane, as well as an effort made to electrically isolate each of the segments, a study has shown that lateral currents can be created on the surface of the card. The image of the measured current density will then be affected and the information concerning heterogeneities can be degraded. On the other hand, the measurement of the current density is dependent on the electrical contact between the distributor plates and the neighboring cells.Since the bipolar plates are traversed by channels, the contact between the flat surface of the electronic board and these plates takes place only on the teeth. It should be noted that other effects may appear on the measured maps that are not directly related to the measuring tool. The solder points existing between the two half-plates allowing to form a bipolar plate are also problematic in the sense that their electrical conductivity is higher than that of the plates. They therefore constitute a preferential point for the passage of current. Similarly, during the assembly of the battery, it is pressed then held by tie rods on its periphery. The electrical contact is therefore better on the edges, which can constitute another preferential point for the passage of current and appear on the contours of the measured current maps.Despite a complicated setup, the use of this card can be considered at the laboratory scale for understanding and experimental validation. However, too many modifications in the stack are required if we want to have individualized monitoring of each cell (more than 70 in general) and therefore too many parasitic phenomena will be created.

[0020] Another type of solution, less intrusive than those based solely on on-board sensors, consists of modeling the physical behavior of the fuel cell in order to detect deviations from the model.

[0021] Modeling is an alternative to experimental testing, which can be lengthy, costly, and not necessarily comprehensive. It provides access to the internal behavior of the fuel cell (local conditions of the cell core) and helps understand the heterogeneities that exist on the cell surface.

[0022] Many models have been developed in the literature attempting to account for heat and mass exchanges, relative humidity distributions, current densities along incoming gas flow directions, and other physical parameters.

[0023] The documents “An Unscented Kalman Filter based approach for the health monitoring and prognostics of a polymer electrolyte membrane fuel cell, Xian Zhang et al” and “Extended Kalman Filter for prognostic of proton exchange membrane fuel cell, Bressel Mathieu et al” disclose examples of such models.

[0024] The models proposed in the literature are most often multi-input physical models that must take into account the geometry of the cell. They are often very detailed, aim to recreate as best as possible the physical phenomena that occur at the heart of the battery and are based on differential equations in order to account for the exchanges. These models are often long in computation time to have a quality resolution. The necessary input variables are obtained for the most part from characterizations carried out on a test bench under given conditions. Once the local conditions are obtained via these models, the active surface loss of a cell can be estimated.

[0025] To estimate a loss of active surface, the authors of reference [1] rely on a semi-empirical law, which derives from the Butler-Volmer law, making it possible to express the overvoltage per mesh as a function of the local conditions of the anodic and cathodic active layers.

[0026] To calculate the model parameters, several test bench characterizations are required for different values ​​of current, pressure, humidity and temperature.

[0027] This method makes it possible to obtain an estimate of the evolution of the active surface in a very specific manner and especially outside of operational conditions (the measurements must be carried out on a test bench).

[0028] The invention proposes a method for determining a degradation indicator which is based on a simplified model and which makes it possible to dispense with measurements carried out on a test bench. Thus, the invention is based on an electrochemical model of the operation of the battery which is used to determine an indicator of loss of active surface, over time, from a Kalman filter. The invention uses measurements which can be carried out via on-board sensors and thus does not require the extraction of the battery from the vehicle. The method is therefore not very intrusive.

[0029] The proposed method allows real-time monitoring of the evolution of the active surface area of ​​one or more cells in the battery. It also provides an indicator of the origin of the degradation of the active surface area, which improves the diagnostic assistance for battery maintenance.

[0030] The subject of the invention is a method, implemented by computer, for determining a degradation indicator of at least one cell of a fuel cell comprising a plurality of cells each having an active surface, the method comprising the recursive steps of, at each new time t: Receive a set of measurements of physical quantities characteristic of the operation of the fuel cell, Apply a Kalman filter to said measurements, the Kalman filter being defined from an electrochemical model of the operation of the fuel cell linking said physical quantities to a state variable representative of a loss of the active surface between an initial instant and instant t, Determine the degradation indicator from the state variable estimated by the Kalman filter.

[0031] According to an alternative embodiment, the method according to the invention comprises a step of linearizing the electrochemical model to model the operation of the fuel cell in the form of a dynamic system whose states can be estimated by a Kalman filter.

[0032] According to a particular aspect of the invention, said set of measurements comprises a measurement of the voltage across a group of cells of the fuel cell comprising at least one cell, a measurement of the current or current density passing through the fuel cell, a measurement of the temperature, a measurement of the oxygen pressure in the fuel cell, a measurement of the resistance of the membrane of at least one cell.

[0033] According to a particular aspect of the invention, the electrochemical model of the operation of the fuel cell is a model of the overvoltage at the terminals of said group of cells.

[0034] According to an alternative embodiment, the method according to the invention comprises the determination of an estimate of the overvoltage at the terminals of said group of cells from the measurement of the voltage at the terminals of said group of cells, the measurement of the current and the measurement of the resistance of the membrane of at least one cell.

[0035] According to a particular aspect of the invention, the voltage measurement is carried out at the terminals of the fuel cell and is averaged to produce an estimate of the average voltage at the terminals of one or more cells of the cell.

[0036] According to an alternative embodiment, the method according to the invention comprises, for a group of at least one cell, the determination of a first reference indicator calculated from the estimate of the average voltage and a second individualized indicator calculated from a measurement of the voltage at the terminals of said group, the method further comprising a step of determining, for at least one physical quantity of said electrochemical model, a correction coefficient of the associated measurement, the correction coefficient being determined so as to take into account the influence of the physical quantity on the differences observed between the first reference indicator and the second individualized indicator.

[0037] According to an alternative embodiment, the method according to the invention comprises the steps of: Express the first reference indicator and the second individual indicator in a base defined by the physical quantities from said electrochemical model, Convert the first reference indicator and the second individual indicator into an orthogonal base, Identify the coefficients of the first reference indicator in the orthogonal base with the coefficients of the second individual indicator in the orthogonal base, Deduce a correction coefficient for the measurement of each physical quantity.

[0038] According to an alternative embodiment, the method according to the invention further comprises a step of determining an indicator of the origin of the degradation, including an indicator of degradation by flooding, an indicator of degradation by drying, and an indicator of degradation by corrosion.

[0039] According to an alternative embodiment, the method according to the invention comprises a step of generating, for at least one physical quantity characteristic of the operation of the fuel cell, an intermediate indicator of degradation linked to the influence of this physical quantity, from the correction coefficient determined for this physical quantity.

[0040] According to an alternative embodiment, the method according to the invention comprises determining the indicator of the origin of the degradation from a combination of several intermediate indicators of degradation linked to the influence of different physical quantities.

[0041] The invention also relates to a computer program comprising instructions for executing the method for determining a degradation indicator of at least one cell of a fuel cell according to the invention, when the program is executed by a processor.

[0042] The invention also relates to a recording medium readable by a processor on which is recorded a program comprising instructions for executing the method for determining a degradation indicator of at least one cell of a fuel cell according to the invention, when the program is executed by a processor.

[0043] The invention also relates to a system for determining a degradation indicator of at least one cell of a fuel cell comprising a plurality of cells, the system comprising several sensors for measuring different physical quantities characteristic of the operation of the fuel cell and a computer for executing the method for determining a degradation indicator according to the invention.

[0044] According to an alternative embodiment, the system according to the invention further comprises a visual interface for displaying at least one graphical representation generated by the calculator.

[0045] According to a particular aspect of the invention, the system and the fuel cell are embedded in a vehicle in operation.

[0046] Other features and advantages of the present invention will become more apparent upon reading the following description in relation to the following appended drawings: [ Fig. 1 ] there figure 1 represents a diagram of a fuel cell, [ Fig. 2 ] there figure 2 represents a diagram of a fuel cell equipped with sensors to carry out measurements, [ Fig. 3 ] there figure 3 represents a flowchart detailing the steps of implementing a method for determining a degradation indicator of at least one cell of a fuel cell according to a first embodiment of the invention, [ Fig. 4 ] there figure 4 represents a diagram of a Kalman filter applied to an electrochemical model of the operation of the battery, [ Fig. 5 ] there figure 5 represents a flowchart detailing the steps of implementing a method for determining a local degradation indicator for one or more cells, according to a second embodiment of the invention, [ Fig. 6 ] there figure 6 represents a flowchart detailing the steps of implementing a method for determining an indicator of the source of the degradation according to a third embodiment of the invention, [ Fig. 7 ] there figure 7 represents two probability curves used to determine intermediate indicators, [ Fig. 8 ] there figure 8 represents two other probability curves used to determine an intermediate indicator.

[0047] There figure 1 represents, in a diagram, a fuel cell PAC composed of several C cells connected in series. Each cell comprises a MEM membrane arranged between two bipolar plates PB1, PB2. At each opposite end of the fuel cell, a monopolar plate PM1, PM2 is provided with CD channels for distributing hydrogen and oxygen to supply the cell.

[0048] On the right of the figure 1 , a single elementary cell C of the fuel cell PAC is shown. A cell C comprises the following elements arranged in series: a first bipolar plate PB1, a first support S1, a first catalyst CAT1, a membrane MEM, a second catalyst CAT2, a second support S2, a second bipolar plate PB2.

[0049] A PAC fuel cell is subject to degradation over time mainly due to the degradation of the MEM membranes.

[0050] All the cells of the PAC fuel cell are crossed by the same current, however the local current density may not be uniform in a cell and may have a different spatial distribution from one cell to another due to the potential degradation of the MEM membranes over time.

[0051] There figure 2 schematizes a device 200 comprising a fuel cell equipped with sensors and associated with a transmitter, to implement the invention.

[0052] The device 200 comprises a fuel cell PAC, of ​​the type described in figure 1 The PAC fuel cell is supplied on the one hand with hydrogen by a tank 201 and on the other hand with air by a distribution channel 202. The air passes through a compressor and a humidifier (not shown in the figure 2 ) to supply oxygen, at the required pressure and humidity, to the PAC stack.

[0053] The device 200 is provided with several sensors for measuring several physical quantities characteristic of the operation of the fuel cell PAC. Thus, a current measuring instrument 210, for example an ammeter, is arranged at the output of the fuel cell PAC to measure the current I passing through the cell or the average current density. A voltage measuring instrument 211 is arranged at the terminals of the fuel cell PAC to measure the voltage U at the terminals of the cell. In a particular embodiment of the invention, the voltage can also be measured at the terminals of one or more cell(s) of the cell by means of one or more voltmeters 212, 213, 214, 21n.

[0054] The device 200 further comprises a sensor 220 for measuring the temperature T arranged near the PAC battery or a cell of the battery. It also comprises a sensor 230 for measuring the gas pressure, arranged at the oxygen inlet of the battery.

[0055] The device 200 also comprises means for processing the measurements provided by the various sensors to implement the invention in order to produce one or more indicators of degradation of the battery or of a cell of the battery. These means (not shown in the figure 2 ) take the form, for example, of an on-board processor and a memory or even a wireless transmitter capable of transmitting the measurements taken by the various sensors to a remote control unit configured to carry out the invention.

[0056] There figure 3 represents, on a flowchart, the steps of implementing a method for determining a degradation indicator of at least one cell of a fuel cell according to a first embodiment of the invention.

[0057] The method aims to determine, at different successive times t, a degradation rate of the fuel cell or of a cell in the cell or of a group of cells in the cell.

[0058] The method begins with a step 301 of acquiring measurements using the different sensors of the device 200. The measurements are carried out for different successive instants t. An electrochemical model of the operation of the battery is then used to determine 302, using a Kalman filter, an estimate of the loss of active surface area at each instant t. A degradation indicator is finally determined 303 from the state variable of the Kalman filter. The steps of the method are iterated over time in order to provide, for each new set of measurements, a new indicator.

[0059] The invention is based on the electrochemical model described in reference [1]. [Math. 1] η = β 0 + β 1 T + β 2 Tln j t + β 3 Tln P O 2 P 0 + β 4 Tln P H P 0 η is an overvoltage, T is the temperature, P O 2 is the air pressure, P H is the pressure of hydrogen, P 0 is atmospheric pressure

[0060] In an alternative embodiment of the invention, the electrochemical model is not pressure regulated, in this case, the term P H P 0 is equal to 1. jt is the local current density defined by the following relation: [Math. 2] j t = i t S t = i t ∗ S 0 S 0 ∗ S t = j t 0 S 0 S t it is the current measured at time t, S t is the active surface at time t and S 0 is the initial active surface. jt 0< is the average current density.

[0061] The coefficients β 0 , β 1 , β 2 , β 3 , β 4 are parameters of the model.

[0062] Temperature T, current density j t 0 and air pressure P O 2 , are measured using the sensors of the device 200.

[0063] The overvoltage is obtained using the following relation: [Math. 3] η = U − E rev + R Tot I

[0064] U is the voltage measured across the terminals of the battery or a cell or group of cells.

[0065] E rev is a reversible voltage which can be determined from a thermochemical balance as described for example in reference [2].

[0066] R tot = R m + R c , is a total resistance determined from a resistance R m of the membrane and a fixed value, for example equal to R c = 3 * 10 -7< Ω .

[0067] The membrane resistance R m can be obtained using different methods. Examples of measurement methods are described in reference [3].

[0068] The ratio S 0 S t gives the ratio between the initial active surface area and the active surface area at time t. This ratio gives an indication of the loss of active surface area over time and therefore of the degradation of the battery or cell.

[0069] To determine this ratio, we use a Kalman filter defined using a model whose state variable is the ratio S 0 S t , this model arising from relation (1).

[0070] To be able to apply a Kalman filter, it is first necessary to linearize the model given by relation (1). This linearization is obtained by differentiating equation (1) with respect to the temperature.

[0071] We then obtain the model expressed in equation (4) then equation (5). [Math. 4] η t T t = β 1 + β 0 1 T t + β 2 ln j t + β 3 ln P O 2 t P 0 [Math. 5] η t T t = β 1 + β 0 1 T t + β 2 ln j t 0 + β 3 ln P O 2 t P 0 + + β 2 ln S 0 S t

[0072] The subscripts t in equation (5) indicate that the different measurements are made at time t.

[0073] From this equation, we can define the following state model: [Math. 6] Y t = A t X t + ε t ∼ N 0 H t [Math. 7] X t + 1 = B t X t + ω t ∼ N 0 Q t

[0074] H t And Q t are the noise covariance matrices ε t And ω t following a normal law. [Math. 8] Y t = η t T t A t = γ 1 T t ln j t 0 ln P O 2 t P 0 0 0 0 0 B t = λ 0 0 0 0 1 1 T t ln j t 0 ln P O 2 t P 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 X t <mprescripts / > <none / > T = ln S 0 S t α 0 α 1 α 2 α 3 C 1 C 2 C 3 C 4

[0075] In an alternative embodiment of the invention, when a measurement of the hydrogen pressure is available, equations (4) and (5) as well as the Kalman filter model can be adapted taking into account this additional measurement.

[0076] An advantage to the above modeling is that the parameters α i And ln S 0 S t are estimated via the Kalman filter and not by maximum likelihood.

[0077] The parameter λ is, for example, estimated by an EM (Expectation Maximization) type algorithm.

[0078] At each time step by applying this filter, the active surface is estimated. We then obtain: S t = S 0 exp − X t 1

[0079] We can define a degradation rate as follows: τ t = 1 − S t S 0 ou τ t = S t S 0 according to the chosen convention

[0080] There figure 4 represents on a diagram the application of the Kalman filter to the model determined from the measurements provided by the different sensors.

[0081] At each instant t, the Kalman filter KAL receives as input the temperature measurements T t , average current density j t 0 and air pressure P O2 as well as voltage U t and membrane resistance R m . The observation variable Y t is calculated from equations (8) and (3) and the state variable X t is calculated via the Kalman filter KAL (equations (6) and (7))

[0082] From the state variable X t , we deduce the loss of active surface then the degradation rate.

[0083] A second embodiment of the invention is now described which aims to take into account the phenomena of heterogeneity between cells of a battery.

[0084] The first embodiment described above takes as input data the measurement of a voltage U at the terminals either of the battery, or of a group of cells, or of a specific cell (see equation (3)).

[0085] However, in an operational application case, measurements are generally carried out on the entire cell, and it is often difficult to access the local conditions at the heart of a fuel cell and we know that by nature the cells of a cell are non-homogeneous. However, it remains industrially feasible to provide for the addition of a voltage measurement (but not of other quantities) at the level of the different cells.

[0086] The second embodiment of the invention therefore aims to compare the overall degradation rate of the battery, calculated from a voltage measurement at the terminals of the battery, with a local degradation rate for a cell (or a group of cells) and to deduce correction coefficients for the measurements (other than the voltage) in order to be able to correct the local degradation rate.

[0087] There figure 5 describes, on a flowchart, the steps of implementing the method according to the second embodiment of the invention.

[0088] The first two steps 501,502 consist of applying the first embodiment of the invention (described in figure 3 ) to obtain on the one hand a first reference indicator of average degradation of a cell of the battery and on the other hand a second individualized degradation indicator for a cell. Alternatively, the method can be applied to a group of cells instead of an individual cell. Subsequently, the principle of this method is described by considering an individual cell.

[0089] The first reference indicator τ t REF is obtained by applying the method of figure 3 from an overall voltage measurement at the terminals of the battery divided by the number of cells to obtain an average voltage at the terminals of the cell. This first reference indicator is therefore identical for each cell of the battery since the measurements used to determine the degradation indicator are the same for each cell.

[0090] The second individualized indicator τ t i is determined, for each cell identified by the index i, from a local voltage measurement at the terminals of this cell.

[0091] The second individualized degradation indicator is closer to reality because it takes into account the local voltage at the cell terminals instead of an average voltage. However, the other measurements, i.e., temperature, pressure and current density, are still considered identical for each cell.

[0092] An objective of the second embodiment of the invention is to determine the contribution of each measurement to the differences observed between the reference degradation indicator and the individualized degradation indicator.

[0093] Starting from relation (5), it is possible to express the two degradation indicators τ t REF And τ t i in the following way [Math. 12] ln τ t REF = π 0 REF + π 1 REF η 0 REF T t + π 2 REF ln j t 0 + π 3 REF 1 T t + π 4 REF ln P O 2 t P 0 [Math. 13] ln τ t i = π 0 i + π 1 REF η 0 i T t + π 2 i ln j t 0 + π 3 i 1 T t + π 4 i ln P O 2 t P 0

[0094] In an alternative embodiment of the invention, when a measurement of the hydrogen pressure is available, equations (12) and (13) can be adapted to take into account this additional measurement, by adding a term dependent on the hydrogen pressure in these equations.

[0095] Relations (12) and (13) allow us to express the natural logarithm of each indicator in a base B defined by the following vector: B = 1 , U t REF , ln j t 0 , 1 T t , ln P O 2 t P 0

[0096] The tension U t REF measured at the battery terminals is used to calculate overvoltages η 0 REF And η 0 i .

[0097] Thus, each indicator is defined in base B by a set of coefficients.

[0098] To be able to compare the two indicators by identifying the coefficients term by term, it is necessary, first, to orthogonalize 503 the base B.

[0099] The orthogonalization of the basis B is, for example, carried out by means of a Graham Schmidt method as described for example in reference [4].

[0100] The basis B is denoted B = (1,Z 1 , Z 2 , Z 3 , Z 4 ), where the variables Z i designate the different physical quantities defining the basis B, these variables being ordered according to a chosen ordering. The choice of ordering is, for example, achieved by imposing certain hypotheses on the measured quantities.

[0101] After orthogonalization, the new basis B orth becomes B orth = (u 0 , u 1 , u 2 , u 3 , u 4 ).

[0102] Equations (12) and (13) are then rewritten in the new basis B orth . [Math. 14] ln τ t REF = ∏ 0 REF u 0 + π 1 REF u 1 + π 2 REF u 2 + π 3 REF u 3 + π 4 REF u 4 [Math. 15] ln τ t i = ∏ 0 i u 0 + ∏ 1 i u 1 + ∏ 2 i u 2 + ∏ 3 i u 3 + ∏ 4 i u 4

[0103] In the new orthogonal basis B orth , it is then possible, in a step 504, to identify the coefficients of the two equations (14) and (15). Thus, if term-by-term differences exist between the coefficients of the two relations, they are due to a difference in the operating conditions.

[0104] We then seek to correct the operating conditions in which the individualized degradation indicator is obtained, that is to say, correct the measurements taken to produce this indicator.

[0105] Step 504 of identifying the coefficients of the two equations (14) and (15) consists of carrying out the following calculations.

[0106] We define a new basis B i< orth with modified operating conditions. B i< orth = (u' 0 , u' 1 , u' 2 , u' 3 , u' 4 ). In this new basis B i< orth , we identify the terms of the two equations (14) and (15): [Math. 16] ∏ k i u ′ k = ∏ k REF u k 16 pour k variant de 0 à 4

[0107] We then fix u' k = λ k . uk , with λ k a coefficient allowing us to move from the basis B orth to the basis B i< orth . We deduce λ k = Π k REF Π k i .

[0108] The basis B i< orth is an orthogonal basis which corresponds to a non-orthogonal operating basis B i< defined as B i< = (1,Z i< 1 , Z i< 2 , Z i< 3 , Z i< 4 ) with Z i< k = µ k * Z k for k varying from 0 to 4.

[0109] We can then demonstrate that µ k = 1 / λ k for k varying from 0 to 4.

[0110] Finally, we determine, via step 505, the correction coefficients µ k to be applied to the operating conditions Z k: [Math. 17] μ k = Π k i Π k REF

[0111] Thus, at the end of step 505, we obtain the correction coefficients µ k to be applied to the components Z k of the base B in which the individualized indicator is expressed. τ t i in order to produce a corrected individualized indicator.

[0112] The second embodiment of the invention makes it possible to provide a local degradation indicator for each cell, which takes into account the heterogeneity between cells. This indicator is, for example, used, in comparison with an alert threshold to trigger battery maintenance when a significant number of cells are degraded. It also allows a local diagnosis of the operation of each cell, which has the advantage of being able to more precisely prevent the evolution of degradations impacting each cell individually.

[0113] A third embodiment of the invention is now described which concerns the determination of indicators of the origin of the degradation observed on a cell. In other words, we seek to characterize the type of degradation undergone by a cell from intermediate indicators obtained which depend on the correction coefficients µ k .

[0114] The method proposed according to this third embodiment is represented by the flowchart of the figure 6 . It consists mainly of three main steps. The method is applied following that described in figure 5 and begins with the determination 505 of correction coefficients for each measurement associated with each physical quantity among temperature, current density, air or oxygen pressure.

[0115] In a second step 506, an intermediate indicator of degradation linked to the influence of each physical quantity is determined for at least certain physical quantities. Steps 505, 506 are carried out for several different physical quantities.

[0116] In a third step 507, at least one indicator of the origin of the degradation is determined, from a combination of several intermediate indicators. The origin of the degradation concerns degradation by flooding, by drying or even by corrosion.

[0117] Step 506 of determining an intermediate indicator can take several embodiments.

[0118] A first embodiment consists of determining, from a correction coefficient µ k , a probability of degradation linked to the associated physical quantity. This applies in particular to temperature, air pressure and current density.

[0119] The probability of degradation is, for example, modeled using basic probabilistic functions such as sigmoid functions or Weibull-type distributions. The probability of degradation is determined by considering that it is higher or lower depending on the value of the correction coefficient µ k relative to 1. A probability value is chosen to correspond to the value µ k = 1, for example a probability value equal to 0.4, then the evolution of the probability as a function of the value of µ k is plotted as a function of the type of degradation.

[0120] There figure 7 illustrates two examples of probability curves 701,702 as a function of the value of a correction coefficient. The direction of evolution of the function (and therefore the choice of curve 701 or 702) depends on the origin of the degradation. For example, it is known that the temperature decreases during degradation by flooding. To estimate an indicator of degradation by flooding, the intermediate indicator linked to the temperature will be constructed using a decreasing function of the type of curve 701. Conversely, to estimate an indicator of degradation via a cause generated by an increase in temperature, an increasing function of the type of curve 702 is chosen for the intermediate indicator linked to the temperature.

[0121] Concerning air pressure and current density, these two quantities are involved in the electrochemical model via natural logarithms. The evolution of the quantity therefore depends on the sign of the natural logarithm of its value. If it is negative, this means that the value has decreased after correction by a factor µ k greater than 1, if it is positive, this means that the value has increased after correction by a factor µ k greater than 1.

[0122] As with temperature, depending on the origin of the degradation that we are trying to estimate (flooding or drying out for example), we choose an increasing function 702 or a decreasing function 701 to estimate the probability of degradation linked to the influence of the physical quantity considered (air pressure or current density).

[0123] In an alternative embodiment of step 506, a humidity rate calculation is carried out, for example by means of the following relationships: [Math. 18] λ m = e m R m S e 1268 T t + 21.41 1 33.75 [Math. 19] λ m = 0.043 + 17.81 ∗ HR m − 38.85 HR m 2 + 36 ∗ HR m 3

[0124] HR m is the humidity rate, λ m is an intermediate parameter, R m is the resistance of the membrane of a cell which is part of the measured quantities, em is the thickness of the membrane.

[0125] The humidity level measurement HR m is converted into a humidity-related degradation probability using straight lines as shown in figure 8 . When the origin of the desired degradation is drying out, we consider a decreasing straight line 801 with the increase in humidity level. When the origin of the desired degradation is flooding, we consider an increasing straight line 802.

[0126] The same principle can be applied by replacing the humidity level with the membrane resistance R m .

[0127] Regarding the tension the corrective factor is directly calculated by the ratio μ = U REF U i obtained by measurement, with u REF< the reference voltage and u i< the voltage across cell i.

[0128] We note P HRm, PP, P j, PT, PR, PU, ​​the probabilities of degradation linked to the respective influence of the humidity rate, air pressure, current density, temperature, membrane resistance and voltage.

[0129] In step 507, an indicator of the origin of the degradation is determined by combining several of these probabilities.

[0130] According to a first exemplary embodiment, a degradation indicator linked to flooding of a cell is determined. Flooding is considered to result from three joint conditions: an increase in the humidity level, a decrease in air pressure and a decrease in current density. The probability of degradation by flooding P noy is then equal to P noy = P HRm * PP * P j . In a variant, the influence of a decrease in temperature can also be considered by calculating the probability of degradation by flooding in two stages: P int = P HRm * PP * P j , then P noy =1-(1-P int )*(1-PT ).

[0131] According to a second exemplary embodiment, a degradation indicator linked to drying out of a cell is determined. Drying out is considered to result from the combination of four joint conditions: an increase in the humidity level, an increase in resistance, an increase in air pressure and a decrease in voltage. The probability of degradation by drying out P ass is equal to P ass = P HRm * PP * PR * PU .

[0132] According to a third exemplary embodiment, a degradation indicator linked to corrosion is determined which results from an increase in the humidity level, an increase in voltage and an increase in temperature. The probability of degradation by corrosion is equal to P cor =P HRm *PU *PT .

[0133] The invention may be implemented as a computer program having instructions for its execution. The computer program may be recorded on a recording medium readable by a processor. Reference to a computer program that, when executed, performs any of the functions described above, is not limited to an application program running on a single host computer. Rather, the terms computer program and software are used herein in a general sense to refer to any type of computer code (e.g., application software, firmware, microcode, or any other form of computer instruction) that can be used to program one or more processors to implement aspects of the techniques described herein. The computing means or resources may notably be distributed ( "Cloud computing" ) ,possibly using peer-to-peer technologies. The software code may be executed on any suitable processor (e.g., a microprocessor) or processor core or a set of processors, whether provided in a single computing device or distributed among several computing devices (e.g., as may be accessible in the device environment). The executable code of each program enabling the programmable device to implement the processes according to the invention may be stored, for example, in the hard disk or in read-only memory. Generally, the program(s) may be loaded into one of the storage means of the device before being executed.The central unit can control and direct the execution of the instructions or portions of software code of the program(s) according to the invention, instructions which are stored in the hard disk or in the read-only memory or in the other aforementioned storage elements. The executable code can also be downloaded from a remote server.

[0134] The computer program may comprise source code, object code, intermediate source code or partially compiled object code or any other form of program code instructions suitable for implementing the invention in the form of a computer program.

[0135] Such a program may have various functional architectures. For example, a computer program according to the invention may be decomposed into one or more routines that may be adapted to execute one or more functions of the invention as described above. The routines may be recorded together in a single executable file but may also be saved in one or more external files in the form of libraries that are associated with a main program statically or dynamically. The routines may be called from the main program but may also include calls to other routines or subroutines.

[0136] All methods or method steps, programs or subroutines described in flowchart form are to be interpreted as corresponding to modules, segments or portions of program code which include one or more code instructions for implementing the logical functions and steps of the invention described.

[0137] Alternatively, the invention can also be implemented using a processor that can be a generic processor, a specific processor, an application-specific integrated circuit (also known as an ASIC for "Application-Specific Integrated Circuit") or an in situ programmable gate network (also known as an FPGA for "Field-Programmable Gate Array"). The technique of the invention can be carried out on a reprogrammable computing machine (a processor or a microcontroller for example) executing a program comprising a sequence of instructions, or on a dedicated computing machine (for example a set of logic gates such as an FPGA or an ASIC, or any other hardware module).

[0138] The various indicators calculated over time can be returned to a user via a display screen or any other graphical interface.

[0139] When a maintenance alert is triggered by the method according to the invention, the alert may be visual or audible.

[0140] The invention can be implemented in a maintenance assistance device and corresponds to a tool for automating the maintenance of a fuel cell on board a vehicle. [Références]

[0141] [1] C. Robin, M. Gerard, M. Quinaud, J. d Arbigny, and Y. Bultel, "Proton exchange membrane fuel cell model for aging predictions: Simulated equivalent active surface area loss and comparisons with durability tests," Journal of Power Sources, vol. 326, pp. 417-427, 2016. [2] J. C. Amphlett, R. M. Baumert, R. F. Mann, B. A. Peppley, P. R. Roberge, and T. J. Harris, "Performance modeling of the Ballard Mark IV solid polymer electrolyte fuel cell I. Mechanistic model development," Journal of the Electrochemical Society, vol. 142, no. 1, pp. 1-8, 1995. [3] Cooper, KR and Smith, M ,Electrical test methods for on-line fuel cell ohmic resistance measurement, Journal of Power Sources 160 (2006) 1088-1095 [4] Hazewinkel, Michiel, ed. (2001)

[1994] , "Orthogonalization", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4.

Claims

1. A computer-implemented method for determining a degradation indicator of at least one cell of a fuel cell (PAC) comprising a plurality of cells (C1, C2, Cn) each having an active surface, the method comprising, for each new instant t, the recursive steps of: - receiving (301) a set of measurements of physical quantities characteristic of the operation of the fuel cell; - applying (302) a linear Kalman filter to said measurements, with the Kalman filter being defined based on an electrochemical model of the operation of the fuel cell connecting said physical quantities to a state variable representing a loss of the active surface between an initial instant and the instant t; - said electrochemical model being linearised to model the operation of the fuel cell in the form of a dynamic system, the states of which can be estimated by a Kalman filter; - determining (303) the degradation indicator based on the state variable estimated by the Kalman filter.

2. The method for determining a degradation indicator according to claim 1, wherein said set of measurements comprises a measurement of the voltage across the terminals of a group of cells of the fuel cell comprising at least one cell, a measurement of the current or of the current density passing through the fuel cell, a measurement of the temperature, a measurement of the oxygen pressure in the fuel cell, a measurement of the resistance of the membrane of at least one cell.

3. The method for determining a degradation indicator according to claim 2, wherein the electrochemical model of the operation of the fuel cell is a model of the overvoltage across the terminals of said group of cells.

4. The method for determining a degradation indicator according to claim 3, comprising determining an estimate of the overvoltage across the terminals of said group of cells based on the voltage measurement across the terminals of said group of cells, measuring the current and measuring the resistance of the membrane of at least one cell.

5. The method for determining a degradation indicator according to any of claims 2 to 4, wherein the voltage measurement is carried out across the terminals of the fuel cell and is averaged to produce an estimate of the average voltage across the terminals of one or more cells of the fuel cell.

6. The method for determining a degradation indicator according to claim 5, comprising, for a group of at least one cell, determining a first reference indicator (501) computed based on the estimate of the average voltage and a second individualised indicator (502) computed based on a measurement of the voltage across the terminals of said group, the method further comprising a step of determining (505), for at least one physical quantity of said electrochemical model, a correction coefficient of the associated measurement, with the correction coefficient being determined so as to take into account the influence of the physical quantity on the differences observed between the first reference indicator and the second individualised indicator.

7. The method for determining a degradation indicator according to claim 6, comprising the steps of: - expressing the first reference indicator and the second individualised indicator in a base defined by the physical quantities based on said electrochemical model; - converting (503) the first reference indicator and the second individualised indicator into an orthogonalised base; - identifying (504) the coefficients of the first reference indicator in the orthogonalised base with the coefficients of the second individualised indicator in the orthogonalised base; - deducing (505) a correction coefficient of the measurement of each physical quantity therefrom.

8. The method for determining a degradation indicator according to any of claims 6 to 7, further comprising a step of determining (507) a provenance indicator for the degradation, including a flooding degradation indicator, a dewatering degradation indicator, a corrosion degradation indicator.

9. The method for determining a degradation indicator according to claim 8, comprising a step of generating (506), for at least one physical quantity characteristic of the operation of the fuel cell, an intermediate degradation indicator related to the influence of this physical quantity based on the correction coefficient determined for this physical quantity.

10. The method for determining a degradation indicator according to claim 9, comprising determining (507) the provenance indicator for the degradation based on a combination of several intermediate degradation indicators related to the influence of various physical quantities.

11. A computer program containing instructions for executing the method for determining a degradation indicator of at least one cell of a fuel cell according to any one of the preceding claims, when the program is executed by a processor.

12. A processor-readable storage medium storing a program comprising instructions for executing the method for determining a degradation indicator of at least one cell of a fuel cell according to any one of claims 1 to 10, when the program is executed by a processor.

13. A system for determining a degradation indicator of at least one cell of a fuel cell comprising a plurality of cells, the system comprising several sensors for measuring various physical quantities characteristic of the operation of the fuel cell and a computer for executing the method for determining a degradation indicator according to any one of claims 1 to 10.

14. The system according to claim 13, further comprising a visual interface for displaying at least one graphical representation generated by the computer.

15. The system according to any one of claims 13 or 14, wherein the system and the fuel cell are intended to be placed on board a running vehicle.