Method and virtual sensor for determining a degradation parameter of an electrochemical system, in particular a fuel cell system, corrected with field data.

Abstract

The invention relates to a method (600) for determining a field-data corrected degradation value of an electrochemical system (10), in particular a fuel cell system (10), using a data-based correction model, and to a method (500) for training such a correction model. The invention further relates to a device (100), in particular a virtual sensor, and a digital process twin for determining the corrected degradation value and for quality monitoring of one or more electrochemical systems.

Description

State of the art

[0001] During the operation of electrochemical cells (both high-temperature systems such as SOFC and SOEC or low-temperature systems such as PEMFC or PEM-ELY) or cell arrays comprising such cells - so-called stacks - a continuous degradation takes place, which can manifest itself, for example, in an increase in the effective surface resistance of the active areas or a reduction in the active area, and thereby continuously reduces the performance and efficiency of the systems over time.

[0002] Under constant operating conditions, this continuous degradation can be observed in the system's performance, specifically in the voltage for fuel cells (PEMFC and SOFC) and the H2 volume flow rate for electrolysis (PEM-ELY, alkaline electrolysis, AEM-ELY, and SOEC). However, in practice, operating conditions (hereinafter also referred to as operating state) vary almost constantly, whether due to varying power requirements in mobile or stationary fuel cell applications or due to varying input power in electrolysis. Therefore, the degradation can no longer be directly determined from the power output.

[0003] To be able to draw conclusions about the progression of continuous degradation even under varying operating conditions, methods are needed to calculate a reference value from the combination of power and operating conditions. This reference value should describe the progression of continuous degradation independently of the changing operating conditions. While the evolution of the reference value (i.e., the degradation rate) can depend on the operating conditions, the current value should be independent of the current operating state to allow for comparisons between different points in time and between different units. This reference value can be a physically motivated, operating-condition-independent degradation parameter, such as the percentage increase in surface resistance, or it can be a conversion of values ​​that may have been obtained in the field.The power measured under varying operating conditions can be converted into a power value under defined reference operating conditions. The resulting reference value allows for the comparison of the degradation progress between different points in time and different systems.

[0004] Methodologically, there are basically two approaches here, both of which allow the calculation of the reference quantity, i.e. the degradation quantity, as a function of the power and the operating state present.

[0005] Firstly, a data-based model can be used to calculate the degradation magnitude, for example as an operating-condition-independent reference voltage of the systems.

[0006] Alternatively, physical models can be used that link power output and the current operating state using an internal, operating-condition-independent degradation parameter as a reference value. These models must be inverted (possibly with the aid of machine learning for real-time capability) to determine the reference value for a given combination of power output and operating conditions, thus enabling monitoring of the degradation progress. Using the model, the determined reference value can then be converted back into power output under given reference operating conditions.

[0007] The quality of both approaches depends primarily on the accurate representation of the combined impact of degradation and operating conditions on performance by either physically based or data-driven models. If these models are used to evaluate operating conditions or degradation states that are incorrectly parameterized in the physically based model or are not represented, or not sufficiently represented, in the training data of the data-driven model, an inaccurate prediction is to be expected. This may manifest as jumps in the calculated degradation value that do not originate from degradation itself, but rather from changes in operating conditions. Such jumps occur because the models typically, and due to practical limitations, only use individual (depending on the method, stationary) operating points from the field or limited intervals. Fig. Figure 1 shows exemplary values ​​of the degradation quantity 50 calculated using an inverted physical model for the degradation quantity (y). degradation ) for different operating states 70 (X operation ) and depending on an aging-relevant parameter ζ 70, for example the cumulative operating time of the system in question, as well as jumps described above that occur 55. Disclosure of the inventionAdvantages of the invention

[0008] Against this background, the invention relates to a method for determining a field-corrected degradation value of an electrochemical system. The value of the corrected degradation value, hereinafter also referred to as the corrected value, is determined as the sum of a value determined with a model for the degradation value and a correction value determined with a correction model. The model for the degradation value is hereinafter also referred to as the degradation model.

[0009] The electrochemical system may be, in particular, a fuel cell system or an electrolyzer system comprising one or more fuel cells or electrolyzer cells, especially a high-temperature system comprising, for example, one or more solid oxide electrolyzer cells (SOEC) and / or solid oxide fuel cells (SOFC), or a low-temperature system comprising, for example, one or more proton exchange membrane electrolyzer cells (PEM-ELY), proton exchange membrane fuel cells (PEMFC), anion exchange membrane electrolyzer cells (AEM-ELY), or anion exchange membrane fuel cells (AEMFC).Furthermore, the electrochemical system can be a battery, i.e., an electrochemical energy storage system, such as a lithium-ion battery, a sodium-ion battery, or a solid-state battery.

[0010] The correction model is a data-based model, preferably a regression model, which was trained using field data and based on values ​​determined by the degradation model (especially with respect to this field data). Field data refers to recorded data on operating parameters of at least one, preferably several (hereinafter also referred to as a fleet) electrochemical systems in use, in particular measured values ​​for the system's power output(s) and recorded, in particular measured, values ​​for operating conditions, especially at these measured power outputs, i.e., the operating state of the system(s).In the context of the invention, the term "performance of the system" can generally be understood as a measure of the system's performance during operation, for example, an electrical voltage or electrical power provided by the system, particularly in the case of a fuel cell, or an H2 volume flow rate in the case of electrolysis.

[0011] The method according to the invention advantageously enables the measurement of a degradation state of the electrochemical system by determining the corrected degradation quantity, wherein the determination or indirect measurement exhibits particularly high accuracy and reliability due to the correction by the field data. The method according to the invention can thus advantageously be used as a virtual sensor for degradation. In particular, when using field data from several electrochemical systems, a particularly reliable correction is achieved, since a wider variation of operating conditions is then covered and the distribution of differences, especially those resulting from manufacturing, is better represented.The invention particularly solves the problem that such degradation parameters cannot usually be measured directly due to the superposition of the influences of operating conditions and degradation on performance. This prevents the direct quantification of errors and the derivation of trivial correction approaches for the degradation models used. In other words, this problem lacks a "ground truth" for the degradation parameter that would allow for a directly determinable correction of the degradation model. The invention advantageously circumvents this problem effectively, resulting in the most accurate possible knowledge of the degradation state, which brings further useful advantages for the operation of electrochemical systems, in particular the following: • The most accurate possible knowledge of the degradation quantity allows for the detection of unusual or critical conditions, e.g., when the rate of change of the degradation quantity changes abruptly, especially when it increases. • The most accurate possible knowledge of the degradation magnitude allows for a more accurate prediction of the behavior of the systems in the near future, e.g. for the rapid control of operating conditions to achieve a desired performance. • The most accurate possible knowledge of the degradation magnitude allows for optimal distribution of the load in a network of cells or stacks, or systems with multiple stacks. • The most accurate possible knowledge of the degradation magnitude allows the derivation of limit values ​​or models with further parameters for targeted and degradation-dependent planning of maintenance interventions ("Smart / Predictive Maintenance"). • The most accurate possible knowledge of the degradation magnitude is the necessary basis for the development of algorithms that predict the evolution of degradation for the future. • The most accurate possible knowledge of the degradation magnitude allows for the calculation of degradation rates and the correlation of these rates with operating conditions and production data to identify key degradation drivers. This can serve as a basis for optimizing production and operating conditions.

[0012] Preferably, the trained correction model is further trained, in particular retrained, with additional field data not yet used for training the correction model. This advantageously leads to a continuously better and more robust determination of the correction values ​​and thus to a correspondingly improved determination of the corrected degradation values. The additional field data can be generated and measured, in particular, by further operation of the preferably multiple electrochemical systems, for example, by continued, in particular continuous, field test or series operation of the systems. Alternatively or additionally, the fleet can also be extended to include further, in particular similar, systems that provide additional field data.For example, further training with additional field data can be performed at regular intervals or when a minimum amount of additional field data not previously used for training is available. Alternatively, the correction model can be retrained with all, if any, of the collected field data. This means that all trainable parameters are reset to their initial values, and then the correction model is trained with a training dataset that includes both previously used training data and data not yet used for training—in particular, all usable training data. This has the advantage that all training data used is treated equally for training purposes, and, in particular, the training is not subsequently influenced by later-used training data.

[0013] In a specific configuration, only field data from a selected group of electrochemical systems is used as further field data. This is particularly advantageous when field data from some or more electrochemical systems are not to be used for training, for example, because these systems have been modified in their hardware or software and are therefore no longer sufficiently similar to the other systems. Preferably, in such a case, two different instances of the correction model and / or the degradation model are used separately for further training and the further determination of the correction and degradation values.In particular, the previously used trained correction model, and if necessary also the previously used degradation model, can be split into two instances, with the first instance being further trained with additional field data from a first group of electrochemical systems and the second instance with additional field data from a second group of electrochemical systems. The two groups of systems preferably each comprise only systems that are technically sufficiently similar.

[0014] Both the degradation model and the correction model are preferably designed to determine the value or the correction value as a function of operating values ​​of the electrochemical system, preferably as a function of power, in particular an electrical voltage in the case of fuel cells or a H₂ volume flow rate in the case of electrolysis, and an operating state of the electrochemical system at that power. The correction model is thus preferably designed as an additive correction function for the degradation quantity determined via the degradation model, or preferably includes such an additive correction function. Since the operating values ​​can be easily queried from the system in question as input values ​​for the degradation model and the correction model without complex calculations, i.e., measured directly, the determination and thus indirect measurement of the corrected degradation quantity can be performed directly in real time.This approach advantageously exploits the fact that aging, and thus degradation, typically has a negative impact on performance. In other words, the potential power output for a given operating state usually decreases with progressive aging / degradation due to wear and tear of the electrochemical system's components. As mentioned above, the operating values, particularly the power output and the operating state, can be incorporated as measured values ​​into the degradation model and / or the correction model, which is especially advantageous when using the method as a virtual sensor, as described above.

[0015] The degradation model can, in particular, be a model based on the two approaches described above, i.e., specifically a data-based and / or physically based model for determining the degradation quantity as a function of the power output and the operating state present at that power output. Preferably, a model is chosen that has at least one reference operating state or that can be parameterized for at least one such reference operating state, for which the value of the degradation quantity determined by the model can be considered sufficiently accurate so that no correction by a correction value of the correction model is necessary.

[0016] The degradation rate of a given electrochemical system is preferably a continuous function of an aging-relevant parameter, where an aging-relevant parameter is understood to be a quantity of the electrochemical system that increases monotonically with time. For example, the aging-relevant parameter corresponds to the cumulative operating time of the electrochemical system or the accumulated current density or hydrogen production density in the case of fuel cells or electrolyzers. Preferably, the same parameter is chosen for all electrochemical systems, in particular for all systems used in a considered fleet.

[0017] The invention also relates to a method for training such a correction model, i.e., a method for training a correction model to determine a correction value for a value of a degradation parameter of an electrochemical system, in particular a fuel cell system. The correction model is preferably a regression model, i.e., a model with parameters determined by a regression algorithm. For the training method, training data is used which includes data tuples with measured field data from at least one, preferably several, electrochemical systems. Each data tuple comprises a measured value of the power output of an electrochemical system and values ​​of a recorded operating state at this power output.In other words, each data tuple comprises an operating point of an electrochemical system, where the operating point is characterized by the measured power at the recorded operating state. When using field data from multiple electrochemical systems, the training data thus includes operating points of different electrochemical systems, with each operating point being assignable to exactly one electrochemical system. Furthermore, each data tuple includes a unique correction value for the degradation parameter associated with the power and the operating state. The unique correction value was determined by including at least some of the recorded field data as well as values ​​obtained with a model for the degradation parameter, whereby the determined values ​​for the degradation parameter were calculated by the model as a function of, in particular, the at least some of the recorded field data.Preferably, field data from exactly one electrochemical system were used to determine the individual correction value, so that each individual correction value and thus each data tuple can be uniquely assigned to exactly one electrochemical system.

[0018] The inventive method for training the correction model thus advantageously comprises a two-step training process. In a first step, individual correction values ​​for individual electrochemical systems are determined as a function of acquired field data of the respective system and combined with the values ​​of the associated operating points to form a data tuple for training the correction model. In a second step, the correction model is trained with this training data, wherein the training data now comprises field data of several, in particular all, electrochemical systems used, as well as the individual correction values ​​determined in the first step.

[0019] According to a preferred embodiment, the individual correction values ​​are calculated as differences between a value for the degradation quantity determined by the model and a function value of a fitted degradation function for the recorded values ​​of the operating states and the measured powers, wherein the model determines the value of the degradation quantity as a function of a power and an operating state of the electrochemical system present at the power, and wherein the degradation function is determined as a fit of a continuous function by values ​​of the degradation quantity determined by the model for the recorded values ​​of the operating states and the measured powers, i.e. for the recorded field data of the electrochemical system in question.The degradation function is chosen as a function of an aging-relevant parameter of the system in question, for example, as a function of the cumulative operating time or the accumulated current density of the system, as described above. For the fit, a value of the degradation quantity determined by the model is plotted against the corresponding value of the aging-relevant parameter, and the fit is then performed for the value pairs (determined value of the system's degradation quantity at operating point X, determined value of the system's aging-relevant parameter at operating point X). The required values ​​of the aging-relevant parameter can be transmitted with the field data, particularly as part of the recorded operating states, or determined from a recorded usage history of the system in question.

[0020] Preferably, the pairs of values ​​used for fitting the degradation function are weighted differently in the fit. This advantageously allows the pairs of values, and thus different operating states, to be weighted differently in the fit, particularly depending on the distance between the operating state of the respective pair of values ​​and one or more (explained above) reference operating states. For this purpose, a function of the distance can preferably be defined, which determines how strongly a pair of values ​​should be weighted in the fit. In particular, the function, which is used especially as a weighting function, can be a monotonically decreasing function, for example, a linearly, polynomially, or exponentially decreasing function. Furthermore, a metric for the distance is preferably defined to determine the influence of the pairs of values ​​depending on the distance, and the function is designed as a function of this metric.Depending on the number of operating conditions that define an operating state, and thus the number of values ​​per operating state, the metric for the distance between the operating state and the reference operating state can be chosen, for example, as a simple, weighted, or normalized Cartesian distance, or a maximum of the normalized distances. This advantageously allows not only the operating states as a whole, but also the various operating conditions and their expected influences to be considered to varying degrees in the fit. As described above, the degradation function determined in this way can be used to determine the individual correction values, which then form part of the training data for training the correction model.

[0021] As described above, the procedure for training the correction model can be applied again, preferably any number of times, to the already trained correction model, especially if further field data not yet used for training the correction model are available, in particular, as described above, further training with further field data from only certain electrochemical systems.

[0022] The methods according to the invention, namely the method for determining a degradation parameter of an electrochemical system corrected with field data and the method for training a correction model, can in particular be designed as computer-implemented methods. Accordingly, the invention also includes a computer program comprising instructions which, when executed by a computer, cause the computer to perform the respective method according to the invention, and a computer-readable data carrier on which this computer program is stored. Finally, the invention also includes a computer comprising such a computer-readable data carrier, as well as an evaluation and control unit comprising such a computer-readable data carrier and further comprising means for carrying out the method steps according to the invention.In particular, the methods according to the invention can also be used as part of a digital process twin and implemented as part, in particular as a virtual sensor, of such a process twin, especially for process and / or quality monitoring of one or more electrochemical systems. Brief description of the drawings

[0023] Exemplary embodiments of the invention are shown schematically in the drawings and explained in more detail in the following description.

[0024] They show Fig. 1. The problem of unphysical jumps in models for determining the degradation quantity, as described at the beginning. Fig. 2 a fleet of electrochemical systems with an embodiment of the device according to the invention and Fig. 3 & 4 Flowcharts for exemplary embodiments of the methods according to the invention as well as Fig. 5 a fit to determine a degradation function for a single electrochemical system for determining the individual correction value for the degradation value for that system. Embodiments of the invention

[0025] Fig. Figure 2 shows a plurality of electrochemical systems 10, which, as described above, can be, for example, similar systems comprising SOECs, SOFCs, PEM-ELYs, or PEMFCs. The methods according to the invention are also applicable to only a single electrochemical system 10, but preferably to several such systems 10. Fig. Figure 2 further shows a device 100 on which the methods according to the invention are implemented, for example a computer, part of a cloud computing architecture or another programmable device, for example as a virtual sensor or as part of a digital twin for one or more electrochemical systems 10.

[0026] The device 100 and the electrochemical systems 10 are configured to transmit operating data from the electrochemical systems 10 to the device 100, in particular via suitable wireless communication modules such as cellular or WLAN modules. The device 100 is configured to receive this operating data and preferably also to transmit data to the systems 10, for example, requests for the transmission of operating data or control commands for changing the operating states of one or more of the systems 10.

[0027] The following embodiments of the invention describe the methods according to the invention using the example of this one in Fig. The systems 10 and device 100 shown in Figure 2 are examples of systems comprising SOFCs. The methods according to the invention can be applied to the entire fleet or only to a part 11 of the fleet, i.e., only to selected systems of the fleet.

[0028] First, an embodiment of the method for training a correction model is described, wherein the correction model is used to determine a correction value for a value of a degradation parameter of an electrochemical system 13. This electrochemical system 13 can be one of the in Fig. 2 systems shown 10 or a further system (whose field data are then in particular not used for determining or training the correction value or the correction model), wherein in the latter case the further system is preferably similar, i.e. in particular of the same design as the systems shown in Fig. 10 is the number of systems shown in the 2. Fig. Figure 3 shows a flowchart with the associated process steps 500.

[0029] Thus, an example of procedure 500 is described, which determines an additive correction function as (part of) the correction model(s). Δydegradationcorrection=fcorrection(Xoperation,Xperformance) for a degradation quantity y degradation A comprehensive training process using field data from a fleet of systems α = 1, ..., N is permitted, such that the corrected degradation magnitude ydegradationcorrected out of ydegradationcorrected=ydegradation+Δydegradationcorrection a better approximation of the actual degradation magnitude ydegradationreal represents the mere value of a degradation quantity y determined via a model (hereinafter also referred to as the "uncorrected model") without including such field data. degradation· Method 500 uses two assumptions: 1. Considered separately, the correct degradation quantity ydegradationreal,α The function of any electrochemical system 10 α ∈ {1, ..., N} is a continuous function if a suitable continuous, age-relevant parameter ζ (one definition for all systems) is chosen as the argument, which increases monotonically with time. Examples of ζ are the accumulated operating time or the accumulated current density or hydrogen production density for fuel cells or electrolyzers. 2. There is at least one known reference operating state. Xoperationref for which the uncorrected degradation model provides a good prediction, so that ydegradation=f(Xoperationref,Xperformance)≈ydegradationreal can be considered sufficiently accurate and therefore does not need to be corrected.

[0030] For example, a degradation model, particularly for SOFCs, can be based on a numerical, especially data-driven, inversion of the approach by Zaccaria, V., Tucker, D., Traverso, A., 2016. A distributed real-time model of degradation in a solid oxide fuel cell, part I: Model characterization. Journal of Power Sources 311, 175-181. doi:10.1016 / j.jpowsour.2016.02.040., which can be parameterized for the specific application. This can be done, for example, as follows: • First, a model with suitable parameters is selected that determines the performance X performance of the system under consideration from the operating conditions X operation can predict, for example, the approach from the publication cited above, Zaccaria et al.: Xperformance=o(Xoperation) • In the next step, at least one parameter y will be used. degradationin the model selected that represents the significant effect of degradation on performance, for example, surface drag. Alternatively, y degradation It can also be incorporated into the model as a specific degradation parameter, for example as a dimensionless prefactor before the surface drag. The model thus allows the following representation: Xperformance=p(Xoperation,ydegradation) • Then a large number of simulations are run, in which both X operation as well as y degradation The value varies within the expected range of values ​​in the field. This allows the model to generate a data set. {Xoperation,ydegradation,Xperformance} • Finally, this dataset is used to train a regression model that has the following form: ydegradation=f(Xoperation,Xperformance)

[0031] This model can then be used as a degradation model according to the invention.

[0032] Method 500 preferably comprises the following six steps 501-506: 1. In a first process step 501, for each operating point (X) detected by the device 100 and measured in the field, operation , X performance ), where each operating point has values ​​X operation an operating state and a value X performance The performance of an electrochemical system in this operating state includes, via the degradation model, an associated value y. degradation determined for the degradation magnitude: ydegradation=f(Xoperation,Xperformance) As described above, field data, i.e., recorded operating points, can be used from all systems 10 or only from selected systems 10 of the fleet under consideration, i.e., a part 11 of the fleet. In particular, field data from a second part 12 of systems 10, which exhibit irregular behavior or can only provide limited field data close to the aforementioned reference operating state, cannot be considered for the procedure. 2. These values ​​of the degradation quantity are then plotted in a second step for each system 10 against the selected parameter ζ, resulting in N collections of points. (ξi,ydegradationi)α,α∈{1,…,N},i∈{1,…,Mα} result, where M α The number of operating points recorded for the respective system α from the field data, and thus the number of determinable values ​​of the degradation quantity, is represented. This is exemplified in Fig. Figure 5 is shown for a system 10. The value of the parameter ζ is transmitted, for example, by the systems 10 as part of the field data to the device 100, or calculated by the device 100 based on data transmitted by the systems 10, particularly by integration, for example in the case of accumulated operating time or accumulated current from recorded operating time or current profiles. For example, N=100 systems 10 are used, and M are available from each system 10. α =20 (for all α) operating points, so a total of 2000 operating points. In a real case, the number M α The usable operating points may differ for different systems. 3. In the following third step 503, a metric m is defined which calculates the distance between each operating point X measured in the field. operation and the aforementioned reference operating state Xoperationref defined: m(Xoperationref,Xoperation) This metric can take into account the expected varying influences of the individual operating parameters. Examples of the metric m include a simple Cartesian distance, a weighted and / or normalized Cartesian distance, or the maximum of the normalized distances. 4. Using this metric m, a function is defined in a fourth step (504) that describes how strongly an operating point should be considered in the fit performed in the subsequent fifth step (505). This function can either describe the weight g of an operating point as g(m) as a monotonically decreasing function in m, or specify the uncertainty u of an operating point as u(m) as a monotonically decreasing function in u. For example, a linear or quadratic function (for u) or an inverse quadratic function (for g) can be chosen for the function. The choice of metric and weight together determine the influence of individual operating points on the fit. 5. In the fifth step 505, the fit for determining the function is now performed. ydegradationfit,α=fα(ξ):=hα(ξ) for each system 10 α ∈ {1, ...,N}, as exemplified in Fig. Figure 5 shows a fitted function 330 for a system 10. For this purpose, the ζ-region to be fitted can preferably be restricted to regions where the density of operating points near the reference operating point is sufficiently high, whereby the metric m described above, or preferably the weighted metric g(m) or u(m), can be used as a measure for the distances to determine the density. These ζ-regions to be fitted should be restricted such that, firstly, the density of operating points near the reference operating point is not too low, and secondly, the set of more distant operating points remaining for the fit is not too small. The ideal choice therefore depends on the data under consideration. For these regions, a fit is then performed for each system 10 α ∈ {1, ..., N} using the weight and / or uncertainty functions: u(m) or g(m) with m(Xoperationref,Xoperation)→ydegradationfit,α=ha(ξ)

[0033] The fit function 330 can, for example, be its spline function using the weights g(m), or a heteroscedastic Gaussian process using the uncertainties u(m). Discrete individual correction values ​​then result for the fitted areas. (Δydegradationcorrection)i,α=hα(ζi,α)−ydegradationi,α as an example for a single correction value of 301 in Fig. 5 shown. These are referred to as individual correction values, since these correction values ​​were determined only by including field data from a single system 10.

[0034] Since for all ζ i,α also the operating conditions measured in the field Xoperationi,α and the performance Xperformancei,α The individual correction values ​​are known. (Δydegradation correction)i,α summarize all systems in a data tuple with the operating points {Xoperation,Xperformance,Δydegradationcorrection}j,with j∈{1,…,M′},M'≤∑α=1NMα.

[0035] Each data tuple thus comprises the values ​​of an operating point, i.e., the power output of a system 10 and the values ​​of the operating conditions present at that power output, as well as the associated individual correction value for the degradation parameter. The entirety of these data tuples then forms the training data for training the correction model. Dye degradation correction in the following sixth step 506.

[0036] 6. The training data thus obtained {Xoperation,Xperformance,Δydegradationcorrection}j In the sixth step, 506 is now used to create the correction model. Dye degradation correction to train via a regression algorithm r, such that the trained correction model as a function of an operating state X operation and a performance X operation the required correction Dye degradation correction predicts Δydegradationcorrection=r(Xoperation,Xperformance). In this case, r(X) operation , X performance ) basically any regression algorithm, for example a linear regression algorithm, a random forest algorithm or an explainable boosting machine.

[0037] With the correction model trained in this way, the degradation magnitude corrected using field data can be determined for each operating point. ydegradationcorrected using the inventive method 600 for determining a degradation quantity corrected with field data, the steps of which are described below by way of example and shown in the flowchart in Fig.4 are shown schematically.

[0038] In a first step, 601, a value y is assigned. degradation the degradation magnitude is determined using the (uncorrected) degradation model, in particular as a function of the relevant operating point (X) operation , X performance In a second step, 602, a correction value is applied. Dye degradation correction determined with the trained correction model, in particular as a function of the relevant operating point (X) operation, X performance ), where the second step 602 can occur before, after, or simultaneously with the first step 601. In a third step 603, the two values ​​are combined to obtain the corrected value. ydegradationcorrected added to the corrected degradation amount: ydegradationcorrected=ydegradation+Δydegradationcorrection In particular, when several systems 10 continuously generate data during field testing or series production, the described training procedure 500 can be applied at regular intervals. It is expected that the generated correction model will continuously improve and become more robust. When modifying the systems 10 during further development, it is preferable to determine separate correction models for groups of technically sufficiently similar systems 10. QUOTES CONTAINED IN THE DESCRIPTION

[0000] This list of documents submitted by the applicant was generated automatically and is included solely for the convenience of the reader. This list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions. Cited non-patent literature

[0000] Zaccaria, V., Tucker, D., Traverso, A., 2016. A distributed real-time model of degradation in a solid oxide fuel cell, part I: Model characterization. Journal of Power Sources 311, 175-181. doi:10.1016 / j.jpowsour.2016.02.040

[0030]

Claims

[1] Method (500) for training a correction model for determining a correction value for a value of a degradation variable of an electrochemical system (10), in particular a fuel cell system (10), wherein the correction model is trained with training data, wherein the training data contain acquired field data from at least one, preferably a plurality of electrochemical systems in data tuples, wherein each data tuple comprises a value of a measured power of one of the electrochemical systems (10) and values ​​of a acquired operating state of the system (10) in terms of power as well as an individual correction value for the degradation variable associated with the power and the operating state, wherein the individual correction value was determined taking into account at least some of the acquired field data and taking into account values ​​determined with a model for the degradation variable. [2] The method (500) of claim 1, wherein the correction model is trained with a regression algorithm using the training data. [3] Method (500) according to claim 1 or 2, wherein the associated individual correction values ​​are calculated as differences between a value determined with the model for the degradation variable and a function value of a fitted degradation function for the recorded values ​​of the operating states and the measured powers, wherein the model determines the value of the degradation variable as a function of a power and an operating state of the electrochemical system (10) present at the power, and wherein the degradation function is determined as a fit of a continuous function by values ​​of the degradation variable determined with the model for the recorded values ​​of the operating states and the measured powers. [4] Method (500) according to claim 3, wherein the degradation function indicates the degradation of the electrochemical system (10) as a function of a continuous ageing-relevant parameter and the fit of the degradation function is carried out as a fit of value pairs of the determined value of the degradation variable and the respectively associated value of the ageing-relevant weighted metrics, wherein the value pairs are preferably included in the fit with different weights, wherein the weights are in particular dependent on a distance between at least one reference operating state and the respective operating state belonging to the value pair. [5] Method (500) according to claim 4, wherein a metric for the distance is defined in order to determine the influence of the value pairs and in particular the influence of individual operating conditions of the operating state in the fit depending on the distance. [6] Method (600) for determining a degradation variable of an electrochemical system (10), in particular a fuel cell system (10), corrected with field data, wherein a model for the degradation variable is used to determine a value of the degradation variable, wherein the value is determined by adding a correction value determined with a correction model as a corrected value of the corrected degradation variable, wherein the correction model is trained with the field data of at least one electrochemical system (10) and values ​​determined as a function of the model for the degradation variable, in particular according to a method (500) of claims 1 to 5. [7] Method (500, 600) according to one of the preceding claims, wherein the trained correction model is further trained with further field data, wherein preferably only field data originating from a selected group of electrochemical systems (10) are used as further field data. [8] Method (500, 600) according to one of the preceding claims, wherein the model for the degradation variable determines the value of the degradation variable as a function of a power, in particular an electrical voltage, and an operating state of the electrochemical system (10), and wherein preferably the correction model determines the correction value as a function of the power, in particular the electrical voltage, and the operating state. [9] Method (500, 600) according to one of the preceding claims, wherein the value of the degradation quantity and the correction value are determined for a measured power and a detected operating state of the electrochemical system (10). [10] Method (500, 600) according to one of the preceding claims, wherein the model determines the value of the degradation quantity as a value independent of current operating conditions. [11] Device (100), in particular a virtual sensor, for determining a degradation variable of an electrochemical system (10), in particular a fuel cell system (10), corrected with field data, wherein the device (100) is configured to carry out a method (500, 600) according to one of the preceding claims. [12] Digital process twin, in particular for process and / or quality monitoring of one or more electrochemical systems (10), wherein the twin is configured to carry out a method (500, 600) according to one of claims 1 to 10. [13] A computer program comprising instructions which, when executed by a computer, cause the computer to carry out the method according to any one of claims 1 to 10. [14] A computer-readable data carrier on which the computer program according to claim 13 is stored.

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