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

Abstract

The invention relates to a method (600) for determining a field-data-corrected degradation value of an electrochemical system (13), in particular a fuel cell system or an electrolysis system (13) with a database correction model, and 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 monitoring the quality of one or more electrochemical systems (13).

Description

[0001] R. 407673 - 1 - Description Title Method and virtual sensor for determining a field data electrochemical in particular one State of the art: During the operation of electrochemical cells (both in high-temperature systems such as SOFCs and SOECs and in low-temperature systems such as PEMFCs or PEM-ELYs) or cell stacks comprising such cells – so-called stacks – a continuous degradation occurs, which can manifest itself, for example, in an increase in the effective surface resistance of the active surfaces or a reduction in the active surface area, thereby continuously reducing the performance and efficiency of the systems over time. Under constant operating conditions, this continuous degradation can be seen in the performance of the systems, i.e., the voltage for fuel cells (PEMFCs and SOFCs) and the H2 volume flow during electrolysis (PEM-ELYs, alkaline electrolysis, AEM-ELYs, and SOECs).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. This means that degradation can no longer be directly determined from power. In order 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 that describes the progression of continuous degradation independently of the changing operating conditions.The evolution of the reference variable (i.e., the degradation rate) can certainly depend on the operating conditions; only the current value should be independent of the current operating state to enable comparison of states between different points in time and between different units. This reference variable can be a physically motivated, operating-condition-independent degradation parameter, such as the percentage increase in sheet resistance, but it can also be a conversion of the power measured under potentially varying operating conditions in the field into a power under specified reference operating conditions. The reference variable thus obtained allows comparison of the progress of degradation between different points in time and different systems.Methodologically, there are basically two approaches, both of which allow the calculation of the reference value, i.e., the degradation value, as a function of power and the prevailing operating condition. One approach is to use a data-based model to calculate the degradation value, for example, as a reference voltage of the systems that is independent of operating conditions. The other approach is to use physical models that allow a link between power and the prevailing operating condition using an internal, operating-condition-independent degradation parameter as a reference value. These models must be inverted (possibly with the help of machine learning for real-time capability) to determine the reference value for a given combination of power and operating conditions, thus enabling monitoring of the progress of degradation.Using the model, the determined reference value can then be converted back into a performance under given reference operating conditions. The quality of the information provided by both approaches depends primarily on the fact that the combined effect of degradation and operating conditions on the R. 407673 - 3 - performance is correctly represented by physically based or data-based 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 or insufficiently represented in the training data of the data-based model, an incorrect prediction can be expected. This may manifest itself in jumps in the calculated degradation value that result not from the degradation but from changed operating conditions.Such jumps occur because, due to practical limitations, the models typically only use individual (depending on the method, stationary) operating points from the field or limited intervals. Figure 1 shows examples of values ​​50 of the degradation quantity (^^^^^^^^^^^^) calculated using an inverted physical model for various operating states 70 (^). ^^^^^^^^^ ) and depending on an age-relevant parameter ^ 70, for example the cumulative operating time of the system in question, as well as the jumps occurring in this case, as just described 55.

[0002] R. 407673 - 4 - Disclosure of the Invention Advantages of the Invention Against this background, the invention relates to a method for determining a correction value for a degradation variable of an electrochemical system. The value of the corrected degradation variable, also referred to below as the corrected value, is determined as the sum of a value determined using a model for the degradation variable, which can be referred to as the uncorrected value, and a correction value determined using a correction model. The model for the degradation variable is also referred to below as the degradation model. The electrochemical system can in particular be a fuel cell system or an electrolyzer cell system comprising one or more fuel cells orElectrolyzer cells, in particular 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.The correction model is a data-based model, preferably a regression model, which was trained with field data and as a function of values ​​determined with the degradation model (in particular for this field data). Field data refers to recorded data from R. 407673 - 5 - operating parameters of at least one, preferably several (hereinafter also referred to as the fleet) used electrochemical systems, in particular measured values ​​for the performance of the system(s) as well as recorded, in particular measured values ​​for operating conditions, in particular for these measured performances, i.e., the operating state of the system(s) or the operating states of the systems.In the context of the invention, system performance 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 in the case of electrolysis. The method according to the invention advantageously makes it possible to measure a state of degradation of the electrochemical system based on the determination of the corrected degradation variable, wherein the determination or the indirect measurement has a particularly high level of 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 field data from multiple electrochemical systems is used, a particularly reliable correction is achieved, as this covers a wider range of operating conditions and the distribution of differences, particularly during manufacturing, is better captured. The invention particularly solves the problem that such degradation variables cannot usually be measured directly due to the overlap of the influences of operating conditions and degradation on performance. Therefore, errors cannot be directly quantified and no trivial correction approaches for the degradation models used can be derived. In other words, with this problem, there is no "ground truth" for the degradation variable, which would allow a directly determinable correction of the degradation model.The invention advantageously effectively circumvents this problem, which, due to the resulting knowledge of the degradation state being as precise as possible, brings with it further useful advantages for the operation of electrochemical systems, in particular the following advantages: R. 407673 - 6 - • The most precise knowledge possible of the degradation variable allows the detection of unusual or critical states, e.g. when the rate of change of the degradation variable changes suddenly, in particular increases. • The most precise knowledge possible of the degradation variable allows a more accurate prediction of the behavior of the systems in the near future, e.g. for quickly regulating the operating conditions to a desired performance. • The most precise knowledge possible of the degradation variable allows optimal distribution of the load in a network of cells or stacks or systems each with several stacks.• The most precise knowledge possible of the degradation magnitude allows the derivation of limit values ​​or models with additional parameters for targeted and degradation-dependent planning of maintenance interventions ("smart / predictive maintenance"). • The most precise knowledge possible of the degradation magnitude is the necessary basis for the development of algorithms that predict the evolution of degradation in the future. • The most precise knowledge possible of the degradation magnitude allows 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 the basis for optimizing production and operating conditions.Preferably, the trained correction model is further trained, in particular retrained, with additional field data not yet used for training the correction model, which 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 field series operation of the systems. Alternatively or additionally, the fleet can also be expanded to include further, in particular similar, systems which provide additional field data. For example, further training with additional field data can be carried out at regular intervals or when a minimum amount of additional data not previously used for training is available.407673 - 7 - field data. Alternatively, the correction model can be retrained with the field data, in particular all of the recorded field data. This means that all trainable parameters are reset to initial values ​​and then the correction model is trained with a training data set that includes both training data already used for training and data not yet used for training, in particular all usable training data. This has the advantage that all training data used is used equally for training and, in particular, that the training is not subsequently influenced by the additional training data used later. According to a special embodiment, only field data originating from a selected group of electrochemical systems is used as additional field data.This is particularly advantageous if 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 technically sufficiently similar to the other systems. In such a case, two different instances of the correction model and / or the degradation model are preferably used separately for further training and the further determination of the correction values ​​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 further field data from a first group of electrochemical systems and the second instance being further trained with further field data from a second group of electrochemical systems.The two groups of systems preferably each comprise only systems that are sufficiently similar in technical terms. 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 a power output, in particular an electrical voltage in the case of fuel cells or an H2 volume flow rate in the case of electrolysis, and an operating state of the electrochemical system at this power output. The correction model is thus preferably designed as an additive correction function R. 407673 - 8 - for the degradation variable determined via the degradation model or preferably comprises 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, without the need for complex calculations, the determination and thus indirect measurement of the corrected degradation variable can take place directly in real time. This advantageously exploits the fact that aging and thus degradation typically have a negative impact on performance. In other words, the potential performance for a specific operating state typically decreases with progressive aging / degradation due to wear of the components of the electrochemical system. The operating values, in particular the performance and the operating state, can, as mentioned above, be included as measured values ​​in the degradation model and / or the correction model, which is particularly advantageous when using the method as a virtual sensor as mentioned above.The degradation model can, in particular, be a model based on the two approaches described above, i.e., in particular, a data-based and / or physically based model for determining the degradation variable as a function of the power and the operating state prevailing at this power. Preferably, a model is selected 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 variable determined with the model can be considered sufficiently accurate, so that no correction is necessary using a correction value of the correction model. Preferably, the model is a degradation model for steady-state operating states of the system.The degradation rate of a respective electrochemical system is preferably a continuous function of an aging-relevant parameter, where an aging-relevant parameter is understood to be a parameter of the electrochemical system that increases monotonically over 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 selected for all electrochemical systems, in particular for all systems used in a considered fleet.The invention also relates to a method for training such a correction model, i.e., a method for training a correction model for determining a correction value for a value of a degradation variable 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 using a regression algorithm. Training data containing data tuples with measured field data from at least one, preferably several, electrochemical systems are used for the training method. Each data tuple comprises a measured value of a 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, wherein 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 comprises operating points of different electrochemical systems, wherein each operating point can be assigned to exactly one electrochemical system. Furthermore, each data tuple comprises an individual correction value for the degradation variable associated with the power and the operating state. The individual correction value was determined by taking into account at least some of the recorded field data and values ​​determined for the degradation variable using a model, wherein the determined values ​​for the degradation variable were determined using the model as a function of, in particular, the at least some recorded field data.Preferably, field data from exactly one electrochemical system is 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. The method according to the invention for training the correction model thus advantageously comprises two-step training. In a first step R. 407673 - 10 -, individual correction values ​​for individual electrochemical systems are determined as a function of recorded field data of the respective system and are combined with the values ​​of the associated operating points to form a data tuple for training data of the correction model. In a second step, the correction model is trained with this training data, wherein the training data now comprises field data from several, in particular all, electrochemical systems used as well as the individual correction values ​​determined in the first step.According to a preferred embodiment, the individual correction values ​​are calculated as differences between a value for the degradation variable determined with 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 variable 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 variable determined with 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 selected 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 degradation value determined using the model is plotted against the corresponding value of the aging-relevant parameter, and the fit is then performed for the pairs of values ​​(determined value of the system's degradation variable 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, in particular as part of the recorded operating states, or determined from a recorded history of use of the system in question.Preferably, the value pairs used for fitting the degradation function are taken into account to varying degrees in the fit. This advantageously makes it possible to take the value pairs, and thus different operating states, into account to varying degrees for the fit, in particular depending on a distance between the operating state of the respective value pair and one or more reference operating states (explained above). For this purpose, a function of the distance can preferably be defined which determines how strongly a value pair is to be taken into account in the fit. In particular, the function which is used in particular 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 in order to determine the influence of the value pairs 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 selected, 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 varying degrees of consideration 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.As described above, the method for training the correction model for the already trained correction model can be applied again, preferably as often as desired, in particular if further field data not yet used for training the correction model is available, in particular, as described above, further training with further field data from only certain electrochemical systems. The methods according to the invention, i.e. the method for determining a degradation variable 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 comprises a computer program comprising instructions that can be used with R.407673 - 12 - its execution by a computer, causing the computer to carry out the respective method according to the invention, and a computer-readable data carrier on which this computer program is stored. Finally, the invention also encompasses 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, in this case, implemented as part, in particular as a virtual sensor, of such a process twin, in particular for process and / or quality monitoring of one or more electrochemical systems.

[0003] R. 407673 - 13 - Brief description of the drawings Embodiments of the invention are shown schematically in the drawings and explained in more detail in the following description. They show: Figure 1 the problem of unphysical jumps in models for determining the degradation value described at the outset, Figure 2 a fleet of electrochemical systems with an embodiment of the device according to the invention and Figures 3 & 4 flow diagrams for embodiments of the method according to the invention and Figure 5 a fit for determining a degradation function for an individual electrochemical system for determining an individual correction value for the degradation value for this system. Embodiments of the invention Figure 2 shows a plurality of electrochemical systems 10, which, as described at the outset, can be, for example, similar systems comprising SOECs, SOFCs, PEM-ELYs or PEMFCs.The methods according to the invention can also be applied to only a single electrochemical system 10, but preferably to a plurality of such systems 10. Figure 2 further shows a device 100 on which the methods according to the invention are implemented, for example a computer, a 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. R. 407673 - 14 - The device 100 and the electrochemical systems 10 are designed to transmit operating data from the electrochemical systems 10 to the device 100, in particular via suitable wireless communication modules such as mobile radio or WLAN modules.The device 100 is designed to receive this operating data and preferably also to transmit data to the systems 10, for example requests for transmitting the operating data or control commands for changing the operating states of one or more of the systems 10. The following exemplary embodiments of the invention describe the methods according to the invention using the example of the systems 10 or device 100 shown in Figure 2, for example for systems comprising SOFCs or PEM-ELYs. The methods according to the invention can be applied to the entire fleet or just to a part 11 of the fleet, i.e. only to selected systems of the fleet. First, an exemplary 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 variable of an electrochemical system 13.This electrochemical system 13 can be one of the systems 10 shown in Figure 2 or a further system (whose field data are then in particular not used to determine or train the correction value or the correction model), wherein in the latter case the further system is preferably of the same type, i.e. in particular of the same design, to the systems 10 shown in Figure 2. Figure 3 shows a flowchart with the associated method steps 500. Thus, by way of example, a method 500 is described which determines an additive correction function as (part of) the correction model(s). for a degradation quantity ^^^^^^^^^^^^ via a training comprising field data of a fleet of systems ^ = allowed, so that the corrected R. 407673 - 15 - degradation quantity ^ ^^^^^^^^^ ^^^^^^^^^^^from ^ ^^^^^^^^^ ^^^^^^^ ^^^^^^^^^^^= ^ ^^^ ^^^^^^^^^^^+ ∆^^^^^^^^^^^^ represents a better approximation of the actual degradation quantity ^ ^^^^ ^^^^^^^^^^^ than the mere value of a degradation quantity determined via a model (hereinafter also referred to as "uncorrected model") without incorporating such field data ^^^^^^^^^^^^. The method 500 uses two assumptions: 1. Considered separately, the correct degradation quantity ^ ^^^^,^ ^^^^^^^^^^^ of each electrochemical system 10 ^ ∈ {1, ... , represents a continuous function if one chooses as argument a suitable continuous aging-relevant parameter ^ (a definition for all systems) that increases monotonically with time. Examples of ^ 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 ^ ^^^ ^^^^^^^^^ , for which the uncorrected degradation model provides a good prediction, so that can be considered sufficiently accurate and therefore does not need to be corrected. For example, as a degradation model, particularly for SOFCs, a model based on a numerical, particularly data-based 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. can be used, which can be parameterized for the application. For example, R. 407673 - 16 - can be proceeded as follows: ^ First, a model with suitable parameters is selected that determines the performance ^^^^^^^^^^^^ of the system under consideration from the operating conditions ^ ^^^^^^^^^ can predict, for example the approach from the above-cited publication Zaccaria et al.: ^^^^^^^^^^^^= ^^^ ^^^^^^^^^^ ^ In the next step, at least one parameter ^^^^^^^^^^^^ is selected in the model that represents the significant effect of degradation on performance, for example, sheet resistance. Alternatively, ^^^^^^^^^^^^ can also be incorporated into the model as a specific degradation variable, for example, as a dimensionless prefactor before sheet resistance. The model thus allows the following representation: ^ Afterwards, a large number of simulations are carried out in which both ^ ^^^^^^^^^ and ^^^^^^^^^^^^varying within the range of values ​​expected in the field. This creates a data set using the model ^^ ^^^^^^^^^ , ^^^^^^^^^^^, ^^^^^^^^^^^^^ ^ Finally, this dataset is used to train a regression model that has the following form: ^^^^^^^^^^^^= ^^^ ^^^^^^^^^, ^^^^^^^^^^^^^ This model can then be used as a degradation model according to the invention. The method 500 preferably comprises the following six steps 501-506: R. 407673 - 17 - 1. First, in a first method step 501, for each operating point detected by the device 100 and measured in the field where each operating point has values ​​^ ^^^^^^^^^ an operating state and a value ^^^^^^^^^^^^a power of an electrochemical system at this operating state, using the degradation model an associated value ^^^^^^^^^^^^for the degradation quantity is determined: ^^^^^^^^^^^^= ^^^ ^^^^^^^^^, ^^^^^^^^^^^^^ As described above, field data, i.e. recorded operating points, from all systems 10 or only from selected systems 10 of the fleet under consideration, i.e. a part 11 of the fleet, can be used for this purpose. In particular, field data from a second part 12 of systems 10, which show irregular behavior or can only provide a few field data close to the above-mentioned reference operating state, can be disregarded for the method. 2. These values ​​of the degradation quantity are then plotted in a second step for each system 10 over the selected parameter ^, so that ^ collections of points where ^ ^represents the number of operating points recorded for the respective system ^ from the field data and thus the number of determinable values ​​of the degradation variable. This is shown as an example in Figure 5 for a system 10. The value of the parameter ^ is transmitted, for example, from the systems 10 as part of the field data to the device 100 or is calculated by the device 100 on the basis of data transmitted by the systems 10, in particular by integration, for example in the case of the accumulated operating time or the accumulated current from recorded courses of the operating time or current. For example, ^=100 systems 10 are used and from each system 10 ^ ^ =20 (for all ^) R. 407673 - 18 - operating points, i.e. a total of 2000 operating points. In a real case, the number ^ ^of the usable operating points may vary for different systems. 3. In the subsequent third step 503, a metric ^ is defined which allows the calculation of a distance between an operating point measured in the field ^ ^^^^^^^^^ and the above-mentioned reference operating state ^ ^^^ ^^^^^^^^^ defined: This metric can take into account the expected different influences of the individual operating parameters. Examples of the metric ^ are a simple Cartesian distance, a weighted and / or normalized Cartesian distance, or the maximum of the normalized distances. 4. Using this metric ^, a function is defined in a fourth step 504 that describes how strongly an operating point should be taken into account in the fit provided in the subsequent fifth step 505. This function can either describe the weight ^ of an operating point as ^(^) as a monotonically decreasing function in ^ or specify the uncertainty ^ of an operating point as ^(^) as a monotonically increasing function in ^. For example, a linear or a quadratic function (for ^) or an inversely quadratic function (for ^) can be selected 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 ^ ^^^,^ ^^^^^^^^^^^ = ^. ^( ^ ) ∶= for every system 10 ^ ∈ { 1, … , ^ }carried out, as shown by way of example in Figure 5 as a fitted function 330 for a system 10. For this purpose, the ^-range of the systems to be fitted can preferably be restricted to ranges in which the density of operating points close to the reference operating point is sufficiently high, whereby the above-described metric ^ or R. 407673 - 19 - preferably the weighted metric ^(^) or ^(^) can be used as a measure of the distances for determining the density. These ^-ranges to be fitted should be restricted in such a way that, on the one hand, the density of operating points close to the reference operating point is not too small and, at the same time, the number of operating points further away remaining for the fit is not too small either. The ideal choice therefore depends on the data under consideration. For these ranges, a fit is then carried out for each system 10 ^ ∈ {1, … , ^} using the weighting or uncertainty functions: The fit function 330 can, for example, calculate its spline function using the weights ^ ( ^ ) or a heteroscedastic Gaussian process using the uncertainties ^ ( ^ ) . For the fitted areas, discrete individual correction values ​​are then obtained from as shown for an individual correction value 301 in Figure 5. These are referred to as individual correction values ​​because these correction values ​​were determined using only field data from a single system 10. Since for all ^ ^,^ also the operating conditions measured in the field ^ ^,^ ^^^^^^^^^ and the power ^ ^,^ ^^^^^^^^^^^ are known, the individual correction values Summarize systems in a data tuple with operating points Each data tuple thus comprises the values ​​of an operating point, i.e., the value of a system's 10 power output and the values ​​of the operating conditions prevailing at this power output, as well as the associated individual correction value for the degradation variable. The totality of these data tuples then forms the R. 407673 - 20 - training data for training the correction model ∆^ ^^^^^^^^^^ ^^^^^^^^^^^ subsequent sixth step 506. 6. The training data thus obtained are used in the sixth step 506 to train the correction model ∆^ ^^^^^^^^^^ ^^^^^^^^^^^ via a regression algorithm ^, so that the trained correction model as a function of an operating state ^ ^^^^^^^^^ and a performance ^ ^^^^^^^^^ predicts the required correction ∆^ ^^^^^^^^^^ ^^^^^^^^^^^predicts, This can ^^^ ^^^^^^^^^, ^^^^^^^^^^^^^ can basically be any regression algorithm, for example a linear regression algorithm, a Random Forest algorithm, or an Explainable Boosting Machine. With the correction model trained in this way, the degradation variable corrected with the aid of field data ^ ^^^^^^^^^ ^^^^^^^^^^^ can be determined for respective operating points using the inventive method 600 for determining a degradation variable corrected with field data, the steps of which are described below by way of example and schematically illustrated in the flow chart in Figure 4. In a first step 601, a value ^^^^^^^^^^^^ of the degradation variable is determined using the (uncorrected) degradation model, in particular as a function of the relevant operating point ^^ ^^^^^^^^^, ^^^^^^^^^^^^^. In a second step 602, a correction value ∆^ ^^^^^^^^^^ ^^^^^^^^^^^ is determined using the trained correction model, in particular as a function of the relevant operating point ^^ ^^^^^^^^^ , ^^^^^^^^^^^^^, where the second step 602 can take place before, after, or simultaneously with the first step 601. In a third step 603, the two values ​​are added together to form the corrected value ^ ^^^^^^^^^ ^^^^^^^^^^^ of the corrected degradation quantity: R. 407673 - 21 - In particular, when multiple systems 10 continuously generate data during field testing or series operation, the described training method 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, separate correction models should preferably be determined for groups of technically sufficiently similar systems 10.

Claims

R. 407673 - 22 - Claims 1. A method (500) for training a correction model for determining a correction value for a value of a degradation variable of an electrochemical system (13), in particular a fuel cell or electrolysis system (13), 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 (10, 11, 13) in data tuples, wherein each data tuple comprises a value of a measured power of one of the electrochemical systems (10, 11, 13) and values ​​of a acquired operating state of the system (10, 11, 13) with respect to the 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 using a model for the degradation variable. 2.The method (500) according to claim 1, wherein the correction model is trained with a regression algorithm using the training data.

3. The 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.The method (500) of claim 3, wherein the degradation function determines the degradation of the electrochemical system (10) as a function of a continuous. R. 407673 - 23 - aging-relevant parameter, and the fit of the degradation function is performed as a fit of value pairs of the determined value of the degradation variable and the respectively associated value of the aging-relevant parameter, 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. The method (500) according to claim 4, wherein a metric is defined for the distance 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 correction value for a degradation variable of an electrochemical target system (13), in particular a fuel cell or electrolysis system (13), wherein an uncorrected value of the degradation variable of the system (13) can be determined using a model for the degradation variable, in particular for stationary operating states of the system (13), wherein the correction value is determined by a correction model, wherein the correction model is trained with field data from at least one electrochemical system (10, 11, 13) 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 (600) according to claim 6, wherein the correction model is designed to output the correction value upon input of operating values ​​of the target system (13), in particular a value of a power and a value of an operating state of the target system (13) present at this power.

8. The method (600) according to claim 6 or 7, wherein a corrected degradation variable of an electrochemical system (13), in particular a fuel cell or electrolysis system (13), is determined, wherein the model for the degradation variable is used to determine the uncorrected value of the degradation variable, wherein the uncorrected value is determined by adding a correction value determined with a correction model according to claim 6 or 7 as a corrected value of the corrected degradation variable. R. 407673 - 24 - 9. The method (500, 600) according to one of the preceding claims, wherein the trained correction model is further trained with additional field data, wherein preferably only field data originating from a selected group of electrochemical systems (10) is used as additional field data.

10. The 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.

11. The method (500, 600) according to one of the preceding claims, wherein the model determines the value of the degradation variable as a value independent of current operating conditions.Device (100), in particular a virtual sensor, for determining a degradation variable of an electrochemical system (10), in particular a fuel cell system or an electrolysis 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.

13. 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.

14. Computer program comprising instructions which, when executed by a computer, cause the computer to carry out the method according to one of claims 1 to 11.

15. Computer-readable data carrier on which the computer program according to claim 15 is stored.

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