Apparatus and computer-implemented method for determining the state of a fuel cell system

Abstract

To provide a device and a computer-implemented method for identifying a state of a fuel cell system having a fuel cell stack.SOLUTION: In a device and a computer-implemented method, data for mapping an input variable of a fuel cell system and a cell position of a fuel cell stack to cell voltage are provided (301); a training of a model for mapping the input variable of the fuel cell system and the cell position of the fuel cell stack to a probability distribution for predicting the cell voltage is performed on the basis of the data (302); a current input variable of the fuel cell system is determined (303): with respect to at least one cell of the fuel cell stack, at least one probability with respect to cell voltage and / or the total voltage of the fuel cell stack is determined on the basis of the current input variable, using the model, and on the basis of the probability distribution (304); and a state of the fuel cell system is identified on the basis of the probability (305).SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] Prior art The present invention relates to an apparatus and computer-implemented method for determining the state of a fuel cell system. [Background technology]

[0002] A fuel cell system represents an overall system that includes multiple subsystems: one or more fuel cell stacks and the subsystems that must be provided to power the fuel cell stack(s).

[0003] The fuel cell stack essentially does not have any actuators, i.e. the fuel cell stack itself is a passive component or assembly. Summary of the Invention [Problem to be solved by the invention]

[0004] To monitor the condition of the fuel cell stack, sensors can be installed to monitor fuel cell stack variables, such as cell voltage. These sensors are expensive and must be protected from failure or measurement errors. [Means for solving the problem]

[0005] Disclosure of the Invention A computer-implemented method for determining the state of a fuel cell system including a fuel cell stack includes providing data mapping fuel cell system input variables and fuel cell stack cell positions to cell voltages, training a model based on the data for mapping the fuel cell system input variables and fuel cell stack cell positions to probability distributions for predicting cell voltages, determining current input variables for the fuel cell system, determining at least one probability for the cell voltage and / or the total fuel cell stack voltage using the model based on the current input variables and the probability distributions for at least one cell of the fuel cell stack, and determining the state of the fuel cell system based on the probabilities. This allows for individual cell monitoring, operating strategy monitoring, and diagnosis during operation of the fuel cell system after training without requiring all of the sensors used to train the model.

[0006] In one aspect, the conditions characterize the safety of input variables for at least one cell voltage and / or total fuel cell stack voltage, and a probability is determined based on a probability distribution, and if the probability is satisfied, the operation of the fuel cell system is classified as safe, thereby enabling the recognition of safety-related aspects.

[0007] The probability that at least one cell voltage is less than a first threshold, or at least one cell voltage is greater than a second threshold, or the total fuel cell stack voltage is greater than a third threshold can be determined, thereby avoiding safety-related overshoots or undershoots during operation.

[0008] During training, at least one expectation and variance for the probability distribution can be determined based on the data. This allows for the creation of an objective function, particularly a likelihood function, that quantifies how well the parameterized model describes the data. The parameterized model is, for example, a Gaussian process model. The Gaussian process model parameterizes the optimization of the objective function.

[0009] From the probability distribution, a probability value for the cell's voltage can be determined and checked to see if the value meets a condition, effectively monitoring a single cell.

[0010] A probability value can be determined for each of the cells in the fuel cell stack, and the values ​​are used to determine a common probability for the cells, and the common probability is checked to see if it satisfies a condition, thereby effectively monitoring the total voltage based on the probabilities for the individual cells.

[0011] A solution to an optimization problem defined based on a common probability and a function for multiple cells of a fuel cell stack can be identified, the solution defining at least one control variable or at least one parameter for operating the fuel cell system, thereby ensuring reliable operation of the fuel cell system as appropriate.

[0012] A function can be defined based on the difference between the minimum and maximum voltage of the cell.

[0013] A function can be defined based on the variance of the cell voltages.

[0014] In one aspect, the model can be used to identify cells and / or cell locations in the fuel cell stack that have a higher probability of being in a safe operating state relative to other cells, or cells and / or cell locations in the fuel cell stack that have a lower probability of being in a safe operating state relative to other cells, thereby enabling operational strategy-related discrepancies between the respective voltages of multiple cells to be recognized and subsequently avoided.

[0015] A first probability distribution for the real part of the impedance of the cell and / or fuel cell stack and a second probability distribution for the imaginary part can be determined, and the state of the fuel cell system is identified based on the first probability distribution and the second probability distribution, allowing for more detailed monitoring.

[0016] Impedance measurements, when voltage is present, result in the real and imaginary parts of the impedance, which provides an additional characteristic variable. For example, the water content of the membrane can be inferred from the impedance.

[0017] This makes it even easier to operate a fuel cell system without continuous cell voltage monitoring (CVM) and a CVM sensor tailored for this purpose. To support the omission of the CVM sensor system, data from impedance measurements can additionally be used in machine learning methods, which significantly improves the persuasiveness of the model.

[0018] In one embodiment, during training, a first measurement of the fuel cell system can be detected and a first measure of information content, particularly a first entropy, can be determined for the first measurement. In this embodiment, a second measurement of the fuel cell system can be detected and a second measure of information content, particularly a second entropy, can be determined for the second measurement. If the first measure is greater than the second measure, data can be provided from the first measurement; otherwise, data can be provided from the second measurement. This allows training to occur more quickly.

[0019] In particular, training data can be provided that is limited by at least one barrier to the minimum or maximum allowed voltage of the cell, so that the model learns a probability distribution that takes into account the minimum or maximum allowed voltage of the cell during operation, thereby further improving monitoring.

[0020] An apparatus for determining the state of a fuel cell system is contemplated, wherein the apparatus is configured to perform the method.

[0021] Further advantageous embodiments will become apparent from the following description and drawings. [Brief explanation of the drawings]

[0022] [Figure 1] 1 is a schematic diagram of an apparatus for operating a fuel cell system. [Figure 2] FIG. 1 is a schematic diagram of model interactions for the operation of a fuel cell system. [Figure 3] 1 illustrates steps in a method for operating a fuel cell system. DETAILED DESCRIPTION OF THE INVENTION

[0023] The structures described below, and in particular the structure of Figure 2, are provided as examples to illustrate the method described below, which is correspondingly applicable to other model and controller structures.

[0024] 1 shows a schematic diagram of an apparatus 100 for determining the state of a fuel cell system having a fuel cell stack. The apparatus 100 is configured to implement the method described below. The apparatus 100 includes a forward model configured to determine power and voltage as a function of a regulation variable. For example, the forward model includes a first model 101, a second model 102, and at least one third model 103. The fuel cell system includes a fuel cell stack and a power supply system. The fuel cell system forms an overall system that is modeled, at least in part, by the at least one third model 103 in this example. The at least one third model 103 is, in particular, a chemical or physical model described by a differential equation.

[0025] In this example, four third models 103 are shown:

[0026] Model 103-1 for the portion of the overall system used for air supply and / or air exhaust.

[0027] Model 103-2 for the portion of the overall system used to meter hydrogen from the tank system, to vent purge gas from the anode path, to drain the anode path, and to circulate hydrogen within the fuel cell system.

[0028] Model 103-3 for the portion of the overall system used to cool the fuel cell system.

[0029] Model 103-4 relates to the portion of the overall system that transfers the fuel cell stack's power to the vehicle's onboard electrical system or other electrical system, for example, using DC / DC converters and other components, and for example, using devices for short-circuiting, current measurement, and voltage measurement of the fuel cell stack and / or cell packs and / or individual cells of the fuel cell stack.

[0030] The first model 101 is configured as a physical model that describes the physical relationships within the fuel cell system using, for example, differential equations.

[0031] The second model 102 is configured as a data-based model that models the difference between the physical model and the actual behavior of the fuel cell system.

[0032] So far, there is no accurate dynamic model that describes the behavior of the entire fuel cell system. Although it is possible to describe well the individual parts of the entire system using at least one third model 103, the dynamic interactions between the individual parts in the entire system are unknown or poorly known.

[0033] The forward model makes it possible to predict, at a certain time t, the power of a fuel cell system at the next time t+1, for example, based on possible control variables at that time t and within a short period of time T previously.

[0034] The modeling is based on a hybrid model having a chemical and / or physical division and a data-based division. The chemical and physical divisions consist of known parts of the overall system, for which a first model 101 and at least one third model 103 are defined in the form of differential equations. Examples of differential equations used, describing the dynamic behavior of the individual parts of the overall system, such as the air system, the cooling system, the hydrogen system and the electrical system, are known, for example, from the following documents:

[0035] [1]Control Analysis of an Ejector Based Fuel Cell Anode Recirculation System, Amey Y. Karnik, Jing Sun and Julia H. Buckland. [2]Model-based control of cathode pressure and oxygen excess ratio of a PEM fuel cell system, Michael A. Danzer, Joerg Wilhelm, Harald Aschemann, Eberhard P. Hofer. [3] Humidity and Pressure Regulation in a PEM Fuel Cell Using a Gain-Scheduled Static Feedback Controller, Amey Y. Karnik, Jing Sun, Fellow, IEEE, Anna G. Stefanopoulou, and Julia H. Buckland. [4]MODELING AND CONTROL OF AN EJECTOR BASED ANODE RECIRCULATION SYSTEM FOR FUEL CELLS, Amey Y. Karnik, Jing Sun. [5]Flatness-based design of multivariable control systems using the example of a fuel cell system, Daniel Zirkel. [6]Model predictive control of a PEM fuel cell system, Jens Niemeyer. [7]Regulation for the efficient operation of a PEM fuel cell system, Christian Haehnel.

[0036] All of these parts of the overall system have individual operating variables that affect their dynamics. Below are descriptions of fuel cell system operating variables that can or do affect the dynamics of exemplary parts of the overall system. These variables are particularly important with respect to the degradation or aging of individual components of the fuel cell stack, and also with respect to the energy consumption or power demand of the system that powers the fuel cell stack, particularly due to parasitic losses. For example, the air compressor of a fuel cell system may alone consume 15% of the fuel cell stack output. The fuel cell stack must collectively output more of this power to provide the desired net power output as useful power.

[0037] 1) Air system lambda_cath: The excess air ratio for the stoichiometry in the cathode path of the fuel cell system. mAir_cath: Air mass flow rate in the cathode path of the fuel cell system. p_cath: Pressure in the cathode path of the fuel cell system. T_cath: The temperature in the cathode path of the fuel cell system. fi_cath: Humidity in the cathode path of the fuel cell system.

[0038] This part of the fuel cell system is used for the air supply and / or air exhaust for the fuel cell stack.

[0039] The variables lambda_cath and mAir_cath can be used interchangeably in this example. If the fuel cell system is able to set the humidity of the supply air, the humidity can be used.

[0040] 2) Hydrogen System lambda_anod: The molecular hydrogen excess ratio relative to the stoichiometry in the anode pathway of the fuel cell system, i.e., the H2 excess ratio. mH2_anod: The molecular hydrogen mass flow rate in the anode path of the fuel cell system, i.e., the H2 mass flow rate. p_anod: The pressure in the anode path of the fuel cell system. dp_anod_cath: The pressure difference between the cathode and anode pathways in the fuel cell system. mN2_anod: Nitrogen mass flow rate, nitrogen concentration or nitrogen molecular flow rate in the anode. mH2_addfromtank: H2 mass or H2 mass flow rate metered into the anode path from the H2 tank or externally from the fuel cell system. Purge_actuation: Control for purging or removing anode gas from the anode path. Drain_actuation: Control for draining or removing liquid water from the anode path. Purge & Drain_actuation: Overall control of multiple valves or one common valve for Purge_actuation and Drain_actuation.

[0041] This portion of the fuel cell system is used for hydrogen circulation and other functions for the fuel cell system.

[0042] The variables lambda_anod and mH2_anod can be used interchangeably in this example. For example, if a hydrogen recirculation fan is provided in the fuel cell system, mH2_anod is related to the recirculation rate of the hydrogen recirculation fan.

[0043] The variable mH2_addfromtank may further include a temperature specification. The variable mH2_addfromtank may be used in addition to or in combination with lambda_anod or mH2_anod.

[0044] The variable mN2_anod can be derived from a model calculation or determined by a sensor. The variable mN2_anod can be used to trigger a purge action.

[0045] The variable Purge_actuation can specify the opening period and / or the opening interval of the valve to release or remove the anode gas in a time-discrete and intermittent manner. The opening period and / or the opening interval can both be variable.

[0046] The variable Drain_actuation can specify the opening period and / or the opening interval of the valve for releasing or removing liquid water in a time-discrete and intermittent manner. The opening period and / or the opening interval can both be variable.

[0047] 3) The cooling system T_Stack_op: The operating temperature of the coolant for the fuel cell system, i.e., approximately the operating temperature of the fuel cell stack. Fan_actuation: Fan control. dT_Stack: The temperature change of the coolant, e.g., heating across the fuel cell stack, or the temperature change of the fuel cell system. m_Cool: Coolant mass flow rate through the cooling path of the fuel cell stack or fuel cell system. dp_Cool: Pressure drop across the cooling path of the fuel cell stack or fuel cell system. Pump_actuation: Pump control for generating coolant mass flow rate. Valve_actuation: Valve control for generating coolant mass flow rate. p_Cool: Pressure in the coolant passages of the stack.

[0048] This portion of the fuel cell system is used to circulate coolant within the fuel cell system.

[0049] The variable T_Stack_op can be expanded, or more precisely, used for the membrane, a temperature-critical component of the fuel cell stack. For example, a model can be used to estimate membrane temperature from coolant temperature, stack exhaust temperature, stack voltage, and stack current. Operating temperature can be modeled based on fan load, ambient temperature, and control, i.e., Fan_actuation.

[0050] The variable dT_Stack can be determined based on the temperature difference between the output and input temperatures of the coolant and can be set by the coolant mass flow rate, for example, using a pump and a three-way valve in a cooling system for the fuel cell stack or fuel cell system.

[0051] Instead of the variable p_Cool, the pressure difference across the cathode and / or anode may be used.

[0052] 4) Electrical System Voltage: Current: Current density: Power: Shorting relays, shorting devices, and possibly other electrical actuators

[0053] The electrical variables of a fuel cell stack - voltage, current, current density and power - interact strongly with the current grid, the architecture of which can be very different.

[0054] For example, fuel cell stack power can be transferred from the fuel cell stack to a current grid by a direct current converter, such as a DC / DC converter, based on the voltage and / or current. For example, the DC / DC converter can set the current drawn from the fuel cell stack via a voltage gradient.

[0055] A short-circuit relay may be provided to short-circuit the fuel cell stack, i.e. both terminals, for example, for freeze starts, in which power is temporarily not output to the current grid but is instead converted into heat.

[0056] It is also possible to model variables derived from this, such as resistance or efficiency.

[0057] The electrical subsystem of the fuel cell system may also incorporate impedance measurements, such as impedance spectroscopy, that may be configured to determine and output the real and imaginary components of the impedance for one or more cells of the fuel cell stack for further calculation.

[0058] These variables are variables. This is not an exhaustive list of all possible variables. Some variables may be model-based and others may be measured. Differential variables or differences from reference values ​​may be used in addition to or instead of absolute variables. Only a subset of the possible variables may be used as parameters for modeling.

[0059] The device 100 comprises a control means 104 configured to control a subsystem for operating a fuel cell system or a fuel cell stack using respective manipulated variables. The device 100 may comprise measurement means 106, in particular sensors for detecting variables in the fuel cell system. The device comprises, in this example, at least one calculation means 108 configured to perform the steps of the methods described below and at least one memory 110 for a model. The at least one calculation means 108 may be a local calculation means in the vehicle, a calculation means on a server or in the cloud, or a calculation means distributed, in particular on multiple servers or on the vehicle and at least one server.

[0060] The fuel cell system includes a fuel cell stack, which in this example includes n cells 112, numbered according to their position i in the fuel cell stack, where i=1,...n, and shown schematically in Figure 1.

[0061] Based on FIG. 2, the interaction of the models for operating the fuel cell system will be explained.

[0062] For the fuel cell system, in this example, an operating variable y_req to be provided is defined as an input variable. Preferably, this operating variable is the power, voltage, efficiency or waste heat, in particular thermal output, of the fuel cell system. It is required to control the fuel cell system by means of at least one control variable u_req so that the fuel cell actually provides this operating variable. This at least one control variable u_req is a target value for controlling the fuel cell system by the control means 104. In this example, the operating variable y_req to be provided is mapped to the at least one control variable u_req by a control strategy. This strategy can be to map the operating variable y_req to be provided to the at least one control variable u_req by a predetermined linear or non-linear function or by a predetermined table.

[0063] Due to dead time, inertia, hysteresis, aging effects, or deviations of actuators from their setpoints, a controlled variable may be set that deviates from its setpoint. On the one hand, such a controlled variable can be detected as an actual set controlled variable u_act, for example by a sensor. On the other hand, at least one set controlled variable u_pred can be determined as a prediction using at least one third model 103. In this example, for at least one part of the fuel cell system, in particular for the fuel cell stack or for at least one subsystem for supplying the fuel cell stack, at least one prediction x[subsy]_pred for at least one set controlled variable u_pred of at least this part of the fuel cell system is determined based on a predetermined controlled variable x[subsy]_req for the at least one part of the fuel cell system, and at least one set controlled variable u_pred is defined based on this prediction x[subsy]_pred. In this example, these variables x[subsy]_req are combined into a vector that defines the controlled variable u_req. Each of the manipulated variables listed above can be used as a variable x[subsy]_req for a respective part of the fuel cell system. If multiple manipulated variables are provided for one part, the variable x[subsy]_req represents a vector containing these manipulated variables. Only selected variables are described below as examples.

[0064] In FIG. 2, the variables for model 103-1, i.e., the air system, are indicated by [subsy]=A, the variables for model 103-2, i.e., the hydrogen system, are indicated by [subsy]=H, the variables for model 103-3, i.e., the refrigeration system, are indicated by [subsy]=C, and the variables for model 103-4, i.e., the electrical system, are indicated by [subsy]=E.

[0065] All or only some of the actual control variables may be determined or measured by the model based on each predetermined control variable.

[0066] The set controlled variable, whether a measured controlled variable u_act or a modeled controlled variable u_pred, may be the pressure difference between the anode and the cathode of the fuel cell system, the temperature difference between a first temperature of the coolant when it enters the fuel cell stack and a second temperature of the coolant when it leaves the fuel cell stack, in particular the humidity of the air when it leaves the fuel cell stack, the pressure of the air, hydrogen and / or coolant, the operating temperature, the air mass flow rate, the hydrogen molecular mass flow rate, the coolant mass flow rate, or an electrical property variable in the fuel cell system, in particular the current, current density or voltage. The fuel cell system represents the entire system.

[0067] The control variable may define, for example, the pressure difference between the anode and cathode of the fuel cell system, the temperature difference between a first temperature of the coolant entering the fuel cell stack and a second temperature of the coolant exiting the fuel cell stack, in particular the humidity of the air exiting the fuel cell stack, the pressure of the air, hydrogen and / or coolant, the operating temperature or the air mass flow rate in the part of the fuel cell system used for air supply and / or air exhaust. The set control variable may define the hydrogen molecular mass flow rate in the part of the fuel cell system used to circulate hydrogen within the fuel cell system. The control variable may define the coolant mass flow rate in the part of the fuel cell system used to cool the fuel cell system. The set control variable may define the operating temperature, which is approximately the coolant temperature. The set control variable may define an electrical property variable of an electrical part of the fuel cell system, for example the current, current density or voltage of one of the fuel cells or of the fuel cell system.

[0068] Preferably, the at least one predetermined control variable u_req defines a target value for the pressure, operating temperature, air mass flow rate, molecular hydrogen mass flow rate, coolant mass flow rate, or an electrical characteristic variable, in particular the current or voltage of the fuel cell system. The control variable xA_req, in this example, defines a target value for the pressure or air mass flow rate in a part of the overall system used for air supply and / or air exhaust at a certain time t. The control variable xH_req, in this example, defines a target value for the molecular hydrogen mass flow rate in a part of the overall system used for circulating hydrogen in the fuel cell system at a certain time t. The control variable xC_req, in this example, defines a target value for the coolant mass flow rate in a part of the overall system used for cooling the fuel cell system at a certain time t. This control variable can also define an operating temperature, which is approximately the coolant temperature. The control variable xE_req, in this example, defines a target value for an electrical characteristic variable of an electrical part of the overall system, for example the current or voltage of the fuel cell or fuel cell system, at a certain time t. In this example, the predetermined control variable u_req is a vector u_req=(xA_req, xH_req, xC_req, xE_req) T Therefore, the controlled variables to be set are defined by a vector in this example. If all the controlled variables to be set are measurable, the controlled variables to be set are u_act=(xA_act, xH_act, xC_act, xE_act). T If all the specified controlled variables are modeled, the specified controlled variables are u_pred=(xA_pred, xH_pred, xC_pred, xE_pred). T Preferably, a mixed configuration is used, in which certain controlled variables are measured and other controlled variables are modeled, which are measurable anyway using sensors already present in the fuel cell system.

[0069] The first model 101 determines an operating variable y_act of the fuel cell system based on at least one set control variable. In this example, the set operating variable is a scalar; however, the first model 101 can also determine a vector having values ​​for multiple different operating variables. In this example, the Kulikovsky fuel cell model is used for the first model 101, which is a static model. The Kulikovsky model was analytically derived from an underlying system of differential equations to describe the electrokinetics of the cathode catalyst layer. The model uses the following input variables: cathode mass flow rate, cathode drum, cathode input pressure, cathode output pressure, air humidity at the cathode inlet, air humidity at the cathode outlet, current or current density, coolant inlet temperature, and coolant outlet temperature.

[0070] The second model 102 determines a prediction of the deviation dy_pred between the operating variable y_act determined by the first model 101 and the actual value of the operating variable in the fuel cell system based on at least one set control variable.

[0071] The second model 102 is a data-based model, in this example, that aims to predict, by a Gaussian process, the deviation dy_pred between the first model 101 and the actual measured behavior of the fuel cell system. During training, the second model 102 can be initially randomly initialized and trained over multiple iterations.

[0072] The second model 102 has already been trained in this example.

[0073] In the correction means 202, the motion variable y_pred is determined based on the motion variable y_act determined by the first model 101 and a prediction of the deviation dy_pred. This means that the prediction of the motion variable by the physical model is corrected by a prediction of the deviation using a data-based model.

[0074] Basically, the voltage u of the individual cells in the fuel cell stack i It is important that the distribution of u varies within a bandwidth dU, which is measured via the cell voltage. The bandwidth dU is due to, among other things, the distribution of the medium, the flow conditions, and the aging conditions. For n cells, the maximum voltage u at cell j of the n cells is max,j =max(u 1,···, u n ) and the minimum voltage u at cell k among n cells min,k =min(u 1,···, u n ) is the bandwidth between dU=u max,j -u min,k where j and k each represent a different cell.

[0075] The bandwidth dU is sought to be as small as possible in this example. The medium here denotes, for example, one or more of the above-mentioned fluids. The voltage u of a fuel cell stack having n cells ges is the voltage of each individual cell, u i from, u ges =u1+u2+····+u n It is synthesized as follows.

[0076] To protect the fuel cell system components, especially to avoid damage to the cells, the cell voltage u i of, u i >u min As shown, the minimum threshold u min can be larger than

[0077] Minimum threshold u mincan be positive, negative, or zero. The computer-implemented method for determining the state of a fuel cell system, described below with reference to Figure 3, contemplates placing additional sensors in the fuel cell system during the machine learning step. These sensors, or some, but not all, of these sensors are required to operate the fuel cell system after the machine learning.

[0078] Using sensors, we generate labeled data tuples (u act , i, u), where u act is the input variable, i is the cell position, and u is the cell voltage. act are, for example, the current density, the air mass flow rate, the air pressure, the hydrogen molecule mass flow rate, and the temperature of the fuel cell stack. If all the set control variables are measurable, u act =u_act=(xA_act,xH_act,xC_act,xE_act) T If all the control variables are modeled, then u act =u_pred=(xA_pred,xH_pred,xC_pred,xE_pred) T can be used. act For this purpose, partially measurable and partially modeled variables can be used. Data can be detected in a vehicle platoon or on a test bench. Data can be determined for many different environmental conditions, driving profiles, driving characteristics, or power distributions.

[0079] The calculation means 108 is configured to train a model based on the data during machine learning. The model is based on the input variables u of the fuel cell system. act and the position of cell i in the fuel cell system, the cell voltage u i It is trained to map a probability distribution for predicting

[0080] In this example, the probability distribution for cell i is defined by its expectation and variance. For a Gaussian process, e.g., μ u (u act , i) and σ u (u act ,i) is used.

[0081] The model is based on the input variables u act For example, the voltage of an individual cell, u i The operation of the fuel cell system is classified as safe if the probability that is less than a threshold c satisfies condition b. This condition can be, for example, P(u i >c)>b where c represents a threshold for the voltage at cell i. Condition b and threshold c can be specified by an expert. Condition b can be set to an appropriate value or can be defined as a function that depends, for example, on environmental or operating conditions. The same threshold c and the same condition b can be used for multiple cells.

[0082] cell-dependent threshold c i For example, the cells at the edges, i.e., cells i=1 and i=2 and cells i=n and i=n-1, have the most problem maintaining their voltages. For example, for n cells, c1, c2, c3,..., c n-2 ,c n-1 ,c n where c1, c2, c n-1 ,c n is c3,···,c n-2 The thresholds c1, c2, and c n-1 ,c n can have the same or different values. n-2 can have the same or different values. In this case, the thresholds c3,...,c n-2 are the thresholds c1, c2, c n-1 ,c n It is different from.

[0083] A bandwidth or variance can also be provided for the voltage at cell i.

[0084] The calculation means 108 is configured to determine, for example based on a model, one common probability P that the operation of the fuel cell system is safe. The common probability P can be, for example, for n cells: P(u1>c, ,u n >c) where u1, ,u n is the input variable u for each of the n cells. act , i. For example, the common probability P is an n-dimensional Gaussian process, i.e., an n-dimensional normal distribution.

[0085] The calculation means 108 is configured to, for example, determine, based on the model, the location of cell i and thus which of the n cells has a higher probability of being in a safe operating state compared to the other cells.

[0086] The calculation means 108 are configured, for example, based on a model, to identify the location of cell i and thus which of the n cells has a higher probability of being in an unsafe operating state compared to the other cells or to a threshold value s, which can be specified by an expert. In this example, threshold value s is determined in a similar manner to that described for threshold value c. The value of threshold value s is determined differently from the determination of threshold value c, and depends on the voltage u of the individual cells. i is defined for unsafe operating conditions where s is greater than the threshold s. i It is also possible to provide:

[0087] Therefore, the probability that a cell is in an unsafe operating state is P(u i <s)> The condition b may be expert-defined as above, or may have other values.

[0088] It is important that the entire stack, i.e., all cells, are operationally safe. This applies if each individual cell is operated within its safe operational range. Furthermore, the bandwidth of the cell voltage across all cells, dU, is required to be less than a limit value.

[0089] A distribution over the bandwidth or bandwidth dU can also be provided.

[0090] For additional supplementary limiting values, the fuel cell stack voltage u ges can be used.

[0091] As an additional criterion, the impedance value can be used. It can be used in addition to other variables in the model to calculate the voltage. P(u i <s)> An alternative to saying that b applies individually to all i is, for example, P(for all i:u i <s)> b.

[0092] The secondary condition is, for example, for a threshold d for a bandwidth dU, P(u max,j -u min,k <d)> b is.

[0093] In this example, the voltage u of each cell i i From the probabilities where P is greater than a threshold c, it is checked whether the common probability satisfies the condition b. In this example, this condition b is defined by a parameter δ that characterizes the acceptable risk. The parameter δ is defined, for example, by an expert. In this example, for the common probability P for n cells, P(u1>c, ,u n >c)>b=1-δ is true, a safe operating condition is recognized.

[0094] The calculation means 108 calculates, based on the common probability P for the n cells,

number

[0095] F(u) is referred to as the quality index in the following. The quality index F(u) represents an objective function, e.g., as the difference between the minimum and maximum voltages dropped across n cells: F(u)=u min -u max It can be defined as follows.

[0096] The quality index F(u) can be expressed as, for example, the variance of the voltage, F(u)=σ(U) It can be defined as follows.

[0097] Alternatively, the individual voltages u1, . . . , u of the n cells in the fuel cell stack n The objective function for F(u1, ,u n )=det σ(u1, ,u n ) where σ(u1, ,u n ) is the predictive n×n covariance matrix for the n voltages, and det is the determinant.

[0098] Alternatively, F(u1, ,u n )=λ {max} σ(u1, ,u n ) The largest eigenvalue can also be used instead of the determinant, as in

[0099] Alternatively, the trace of the covariance matrix may be used.

[0100] For example, the individual voltages u1, u n Expected values ​​μ1, ,μ n The individual voltages u1, u2, u3 of the n cells of the fuel cell stackn The objective function for F(u1, ,u n )=trace σ(μ1,...,μ n ) It is defined as follows:

[0101] It is also possible to use the Pareto front as a combination of options for solving an optimization problem.

[0102] The real and imaginary parts of the impedance of one or more cells of the fuel cell stack can be evaluated. For example, these real and imaginary parts can be determined by impedance spectroscopy of one or more cells of the fuel cell stack. The impedance values ​​of the cells can be used as input variables for the model. Individual impedance values ​​of individual cells of the fuel cell stack can also be used as input variables for the model. Separate thresholds can be defined for the real and imaginary parts.

[0103] In one aspect, different models can be trained and / or used for different operating states of the fuel cell system, which can be defined in terms of, for example, start-up, normal operation, end-of-operation, or cold start.

[0104] During data detection, measurements can be detected in multiple iterations to select the data that provides more, and in particular the most, information. This speeds up detection, since fewer measurements are needed for the same training quality. For example, in the case of a Gaussian process as a model, the entropy can be determined for each measurement and used as a measure for information about the uncertainty of the model.

[0105] During training, safety barriers can be used, which can be specified, for example, by physical models or other models from the field of machine learning. For example, one or more models are trained with a minimum allowable voltage for the cell to avoid destroying the cell by falling below the minimum allowable voltage.

[0106] For example, dynamic effects can be considered by using the history of the input variables. For example, the input variables u act A model with a Nonlinear Autoregressive Exogeneous (NARX) structure is used to consider the input space for

[0107] Input variable u act The data can be flagged so that important combinations of can be recognized. Once recognized, these combinations can be output for inspection by the user.

[0108] To optimize the quality metric F(u), Bayesian optimization can be used instead of the active learning described above. In this case, instead of learning the complete mapping from the input variables to the quality metric F(u), only the optimal operating point is sought. This allows for a faster determination of the optimal operating point for F(u).

[0109] It is also possible to learn one common model for both the machine learning of the states and the corresponding quality indicator F(u), for example, a Gaussian process for the multidimensional output variable can be used for this purpose.

[0110] Total voltage of the fuel cell stack u ges is available, and the voltage of each individual cell, u i may not be available. In this case, the total voltage of the fuel cell stack, u ges or the total voltage u of the fuel cell stack gesThe deviation between the calculated value and the value predicted by the model can be used for evaluation.

[0111] The method described below with reference to Figure 3 can be performed in a vehicle or on a test bench. After training, the method can be performed in a vehicle, in which case the method steps for training may no longer be performed.

[0112] In step 301, the method calculates the input variables u of the fuel cell system. act The present invention contemplates providing data comprising multiple tuples that map the voltage, u, of a cell in a fuel cell stack and the position, i, of the cell in the fuel cell stack.

[0113] In one embodiment, data is provided through multiple iterations. In a first iteration, a first measurement of the fuel cell system can be detected. A first measure of information content, particularly a first entropy, can be determined for the first measurement. In a second iteration, a second measurement of the fuel cell system can be detected. A second measure of information content, particularly a second entropy, can be determined for the second measurement. If the first measure is greater than the second measure, data can be provided from the first measurement; otherwise, data can be provided from the second measurement. The measurement with the greatest information content is then selected.

[0114] In one embodiment, the data is provided as being limited by at least one barrier, in particular a safety barrier, that defines a minimum or maximum allowable voltage in the cell.

[0115] In one embodiment, the data is provided to enable the use of bandwidth dU.

[0116] In a subsequent step 302, the input variables u of the fuel cell system are act and the position of the cell in the fuel cell stack i, the cell voltage u iA model is trained based on the data to map the probability distribution for predicting

[0117] In this example, the expectation and variance for the probability distribution are learned based on the data. In the case of a Gaussian process, for example, for cell i, the expectation μ u (u act , i) and variance σ u (u act , i) are determined. The trained model represents a probability distribution over multiple cells in the fuel cell stack, in this example n cells.

[0118] The model trained in this way can then be used to identify the state of the fuel cell system, for which reason steps 301 and 302 may no longer be performed.

[0119] In step 303, the current input variables u of the fuel cell system are act The input variables u used during training are determined. act Only a portion of the

[0120] In step 304, for at least one cell i of the fuel cell system, the current input variable u act Based on this, a probability is determined using a model based on the probability distribution.

[0121] In one embodiment, the voltage u of at least one cell i The probability that is less than a threshold c is determined.

[0122] In one embodiment, the voltage u of at least one cell i The probability that is greater than a threshold s is determined.

[0123] For a number of cells, preferably n cells, of the fuel cell system, a probability can be determined for each based on the probability distribution.

[0124] A single common probability may be determined.

[0125] In step 305, the state of the fuel cell system is determined based on at least one probability determined for cell i and / or based on the common probability.

[0126] The state is determined by the voltage u of at least one cell. i The input variable u act The safety of the

[0127] The state is the total voltage of the fuel cell system, u ges The input variable u act The safety of the

[0128] For example, if the probability and / or the common probability meets condition b, the operation of the fuel cell system is classified as safe.

[0129] The voltage of at least one cell, u i We can check whether the probability P that is smaller than a threshold c satisfies the condition b.

[0130] The voltage of at least one cell, u i We can check whether the probability P that is greater than a threshold s satisfies the condition b.

[0131] We can check whether the common probability P satisfies condition b.

[0132] It can be checked whether the probability P that the bandwidth dU for a voltage is smaller than the threshold d satisfies the condition b.

[0133] In this example, a safe operating condition is recognized if each of the checked conditions is met.

[0134] A solution to an optimization problem defined based on the probabilities P for n cells can be identified.

[0135] In this example, with a threshold c, the following optimization problem:

number

[0136] The optimization problem can be defined correspondingly for other thresholds. For a threshold s, the optimization problem can be, for example,

number

[0137] For a threshold d, the optimization problem becomes, e.g.,

number

[0138] In optional step 306, the fuel cell system may be operated using at least one control variable or at least one parameter defined by the solution.

[0139] Step 303 can then be performed, whereby the method calculates the new current input variable u act The process continues using

[0140] The method can be implemented for a first probability distribution for the real part of the impedance of a cell of a fuel cell system and a second probability distribution for the imaginary part of the impedance. In this case, the state of the fuel cell system is identified based on the first probability distribution and the second probability distribution. For example, the above conditions must be met for safe operation of both parts; otherwise, operation is classified as unsafe.

[0141] The method may be implemented using different models for different operating conditions of the fuel cell system.

Claims

1. 1. A computer-implemented method for determining safety of a fuel cell system including a fuel cell stack, comprising: respectively, the input variables (u ａｃｔ 301, data is provided that maps the voltage of the cell to the voltage of the cell and the position of the cell in the fuel cell stack; The input variables (u ａｃｔ a model is trained (302) based on the data to map the voltage of the fuel cell and the position of the cell in the fuel cell stack to a probability distribution for predicting the voltage of the cell; The current input variable (u ａｃｔ ) is determined (303), For at least one cell of the fuel cell stack, the current input variable (u ａｃｔ ), using the model to determine (304) at least one probability for the cell voltage and / or the total voltage of the fuel cell stack based on the probability distribution, without requiring all sensors used in training the model; Based on the probability, the safety of the fuel cell system is determined (305). In the method, a first probability distribution for the real part and a second probability distribution for the imaginary part of the impedance of the cell and / or the fuel cell stack are determined; The safety of the fuel cell system is determined based on the first probability distribution and the second probability distribution. A method characterized by:

2. The safety of the fuel cell system is determined by the input variable (u) for the voltage of the at least one cell and / or the total voltage of the fuel cell stack. ａｃｔ ) characterize the safety of determining a probability based on the probability distribution; If the probability is satisfied, the operation of the fuel cell system is classified as safe (305). The method of claim 1.

3. determining at least one of an expectation and a variance for the probability distribution based on the data; 3. The method according to claim 1 or 2.

4. determining a probability value for the voltage of the cell from the probability distribution; The value is checked to see if it satisfies a condition (305); The method of claim 3.

5. determining a respective probability value for a plurality of cells of the fuel cell stack; using said values ​​to determine a common probability for said plurality of cells; It is checked whether the common probability satisfies a condition (305); The method according to claim 3 or 4.

6. A solution to an optimization problem defined based on a common probability and function for the plurality of cells is identified; the solution defines at least one control variable or at least one parameter for operating the fuel cell system; The method of claim 5.

7. the function is defined based on the difference between the minimum and maximum voltages of the cells; The method of claim 6.

8. The function is defined based on the variance of the cell voltage. The method of claim 6.

9. Based on the model, Cells and / or cell positions in the fuel cell stack that have a higher probability of being in a safe operating state compared to other cells, or A cell and / or a cell position in the fuel cell stack that has a lower probability of being in a safe operating state compared to other cells. is identified, 9. The method according to any one of claims 1 to 8.

10. a first measurement value in the fuel cell system is detected; a first entropy for information content is determined for the first measurement; a second measurement value in the fuel cell system is detected; a second entropy related to information content is determined for the second measurement; If the first entropy is greater than the second entropy, the data is provided from the first measurement, otherwise the data is provided from the second measurement (301); 10. The method according to any one of claims 1 to 9.

11. The method of claim 10, wherein data is provided that is limited by at least one barrier to a minimum or maximum allowable voltage of the cell (301).

11. The method according to any one of claims 1 to 10.

12. 1. An apparatus for determining the safety of a fuel cell system, comprising:

12. Apparatus, characterized in that the apparatus is configured to carry out the method according to any one of claims 1 to 11.

13. A computer program comprising machine-readable instructions for carrying out a method according to any one of claims 1 to 11 when executed by a computer.

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