Method and virtual sensor for determining a field-data-corrected degradation value of an electrochemical system, in particular a fuel cell system or electrolysis system, to take into account transient behaviour

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 electrolysis system (13), having a database correction model for taking into account transient behaviour of the system (13). The invention also relates 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 monitoring the quality of one or more electrochemical systems (13).

Description

[0001] R. 412767 - 1 -Description Title Method and virtual sensor for determining a field-corrected degradation parameter of an electrochemical system to take into account transient behavior, in particular a fuel cell or electrolysis system State of the art During the operation of electrochemical cells (both in high-temperature systems such as SOFC and SOEC or in 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.Under constant operating conditions, this continuous degradation can be observed in the system's power output, specifically the voltage in fuel cells (PEMFC and SOFC) and the H2 volume flow rate in 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, degradation can no longer be directly determined from the power output. To be able to draw conclusions about the progression of continuous degradation even under varying operating conditions, methods are needed to derive degradation from the combination of power output and R. 412767. 2 -Under operating conditions, a reference value is calculated that describes the progression of continuous degradation independently of 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 comparison of states 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 the power measured under potentially varying operating conditions in the field into a power value under defined reference operating conditions. The reference value obtained in this way allows for the comparison of the progress of degradation between different points in time and different systems.Methodologically, there are two fundamental approaches, both of which allow the calculation of the reference value, i.e., the degradation value, as a function of the power and the prevailing operating state. Firstly, a data-based model can be used to calculate the degradation value, for example, as an operating-condition-independent reference voltage of the systems. Secondly, one can utilize physical models that allow a link between power and the prevailing 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 and operating conditions, thus enabling monitoring of the degradation progress.Using the model, the determined reference value can then be converted back into a power output under given reference operating conditions. R. 412767 -. 3 -The validity of these approaches is limited to the range of validity of the physical models used, which are typically near-stationary points. Stationary points are defined here as states at which the system has reached a sufficiently stable equilibrium. Often, the time it takes for the system to reach a stationary state, for example after a load change, is defined by its thermal mass and the magnitude of the change. This time can range from seconds to several hours. If the data-based models described above are applied to non-stationary states, significant and inaccurate deviations of the degradation value determined by the model from an expected continuous behavior can occur.Figure 1 shows, by way of example and illustration, values ​​of the degradation quantity calculated from field data using a model for the degradation quantity (^^^^^^^^^^^^) for various operating states measured in the field 70 (^. ^^^^^^^^^), where the line thickness of the drawn crosses illustrates the transience of the respective operating states, and depending on an aging-relevant parameter ^ 70, for example, the cumulative operating time of the system in question. Since at least some of the field data used were acquired from systems that were in a non-steady, i.e., transient, state at the time of acquisition, the deviations described above can occur as examples. As can be seen, the model is not readily applicable here due to the steady-state base model used and leads to incorrect predictions of the degradation magnitude (^^^^^^^^^^^^). Especially in dynamic operation (e.g., power control), it is a significant limitation to have to filter out these transient states before applying the model; an expansion of its applicability is desirable.However, extending the model to include such transient states presents a significant challenge, as the complete description of transient states as input for the aforementioned data-based or physical models requires considerably more dimensions than for stationary states. In particular, in addition to the values ​​of the operating conditions, their evolution, especially their rates and / or histories within a specific time window prior to the given point in time, must also be considered. This increases the number of dimensions required for R. 412767. 4 - The data required for training data-driven models increases significantly, and the complexity and parameterization effort of the necessary physical models rise considerably. As a result, degradation states can often only be evaluated for times with sufficiently steady-state operation and are not available for transient states, making continuous monitoring of the degradation state impossible.

[0002] R. 412767 - 5 -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 parameter of an electrochemical system in order to take into account a transient behavior of the system. This electrochemical system is hereinafter also referred to as the target system. The value of the corrected degradation parameter, hereinafter also referred to as the corrected value, can then be determined as the sum of a value determined with a model for the degradation parameter for steady-state operating conditions of the target system, which can be referred to as the uncorrected value, and the correction value determined with a correction model.The model for the degradation quantity is hereinafter also referred to as the degradation model and is suitable for determining the degradation quantity under steady-state operating conditions of the target system, while the correction model takes into account deviations from steady-state behavior under transient operating conditions. The degradation model can also be a model for the degradation quantity that can already at least estimate or approximately represent transient behavior of the electrochemical target system. When such a model is used, the correction model advantageously improves the consideration of transient behavior. The electrochemical target system can, in particular, be a fuel cell system or an electrolyzer cell system comprising one or more fuel cells or...Electrolyzer 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), R. 412767 -. 6 -Anion exchange membrane electrolyzer cells (AEM-ELY) or anion exchange membrane fuel cells (AEMFC) are examples of suitable electrochemical target systems. The electrochemical target system can also 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-driven model, preferably a regression model, which was trained using field data and values ​​determined with the degradation model (especially for these field data), as well as a measure of the transience of the systems belonging to the included field data.Field data refers to recorded operating values, i.e., 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 power of the system(s) and recorded, in particular measured, values ​​relating to operating conditions, especially at these measured power levels, i.e., the operating state of the system(s). The field data preferably also includes recorded trends of the operating values, in particular power and operating state, i.e., in particular changes, preferably rates, of the operating states, preferably within a time window between a query time of the systems and a prior time, wherein the time window can be several seconds, several minutes, or several hours long, depending on the embodiment of the invention.In the context of the invention, the term "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 rate in the case of electrolysis. The method according to the invention advantageously enables the detection of a state of degradation of the electrochemical system based on R. 412767-. 7 -The method according to the invention allows for the determination of the corrected degradation quantity, whereby the determination or indirect measurement, due to the correction by the field data, exhibits particularly high accuracy and reliability even for unsteady, i.e., transient, operating states of the electrochemical system. The method according to the invention can thus advantageously be used as a virtual sensor for degradation. The invention advantageously enables the extension of the applicability of steady-state approaches for determining the degradation quantity to transient states, which brings with it the following further advantages in particular: • The most continuous possible knowledge of the degradation quantity allows the detection of unusual or critical states, e.g., when the rate of change of the degradation quantity changes abruptly, especially when it increases.Especially in critical states, behavior can become particularly non-stationary, making continuous determination of degradation especially important. • Comprehensive knowledge of the degradation level allows for more accurate prediction of system behavior in the near future, e.g., for rapid control of operating conditions to achieve a desired performance. Non-stationary states are to be expected, particularly during system control. • Comprehensive knowledge of the degradation level allows for optimal load distribution in a network of cells or stacks, or systems with multiple stacks, even during control phases. • Comprehensive knowledge of the degradation level allows for the derivation of limit values ​​or models with additional parameters for targeted and degradation-dependent planning of maintenance interventions ("Smart / Predictive Maintenance").• Comprehensive knowledge of the degradation rate is the necessary basis for developing algorithms that predict the evolution of degradation in the future. • Comprehensive knowledge of the degradation rate allows for the calculation of degradation rates and the correlation of these rates with operating conditions and production data to identify essential R. 412767 -. 8 -Degradation drivers. This can serve as a basis for optimizing manufacturing 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. This advantageously leads to a continuously improving 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 extended to include further, in particular similar, systems that provide further 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 are treated equally for training purposes, and, in particular, the training is not subsequently influenced by later-used training data.According to a specific embodiment, only field data originating 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 from a technical standpoint. Preferably, in such a case, two different instances of the correction model and / or R. 412767 are used. 9 -The degradation model is used separately for further training and for determining the correction and degradation values. In particular, the previously 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.The degradation model is designed to determine the degradation value of the target system 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 as a function of an operating state of the electrochemical system at that power. The correction model is preferably designed to output the correction value when values ​​of one or more functionals related to the operating values ​​are input, in particular when a value of a power functional and a value of a functional representing an operating state of the electrochemical system at that power are input.The functionals can, in particular, take into account a change, especially a rate, and / or history, i.e., a specific progression, of performance and / or operating states, especially a progression between a first point in time and a subsequent second point in time, where the second point in time can be, in particular, the time of querying this data. 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, which serve as the basis for the input values ​​for the degradation model and the correction model, can be easily queried from the system in question without complex calculations, i.e., measured, the determination and thus indirect measurement of the corrected degradation quantity can be carried out directly in real time.This advantageously exploits the fact that aging and thus degradation usually have a negative impact on R. 412767 -. 10 -Performance is affected. In other words, the potential power output at a given operating state typically 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. The degradation model can be, in particular, a model for steady-state operating conditions based on the two approaches described earlier; that is, a data-driven and / or physically based model for determining the degradation magnitude as a function of the power output and the operating state present at that power output.Preferably, a model is selected that has at least one steady-state reference operating condition or that can be parameterized for at least one such reference operating condition, 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. The degradation quantity of a respective electrochemical system is preferably a continuous function of an aging-relevant parameter, wherein 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 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 to determine a correction value for a value of a degradation quantity R. 412767 -. 11 -of an electrochemical system, in particular a fuel cell system or an electrolysis system. The correction model is preferably a regression model, i.e., a model with parameters determined by a regression algorithm. For the training procedure, training data is used which includes data tuples with measured field data from at least one, preferably several, electrochemical systems. Each data tuple comprises values ​​of at least one functional of operating values, in particular a value of a functional of a measured power of an electrochemical system, and a value of a functional of a recorded operating state at this power.In other words, each data tuple comprises functionals for an operating point of an electrochemical system, wherein the operating point is characterized by the operating values, in particular the measured power at the recorded operating state, and wherein the functional may also include measured changes and / or profiles of the power and the associated operating state. When using field data from multiple electrochemical systems, the training data thus considers operating points of different electrochemical systems, with each operating point being assignable to exactly one electrochemical system. Furthermore, each data tuple includes an individual correction value for the degradation parameter associated with the operating values, in particular the power and the operating state.The individual correction value was determined by including at least some of the acquired field data as well as values ​​determined with a model for the degradation quantity for steady-state operating conditions of the system, i.e., in particular with the degradation model described above, wherein the determined values ​​for the degradation quantity were determined with the model as a function of, in particular as a function of, the at least some acquired field data. Preferably, field data from exactly one electrochemical system were used for determining 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 inventive method for training the correction model thus advantageously comprises a two-step training process. In a first step, R. 412767 -. 12 -Individual correction values ​​for each electrochemical system are determined based on acquired field data of the respective system and combined with the values ​​of the corresponding 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, which now includes 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 training can be performed under the condition that for steady-state operating conditions, in particular for operating points where the degree of transience is zero, the correction value output by the correction model is zero. This condition can be taken into account during training, in particular in the form of a cost function.Alternatively, the correction model can be configured to take the transience measure as an input value. According to a preferred embodiment, the individual correction values ​​are calculated as the differences between a value for the degradation quantity determined by the model and a function value of a degradation function fitted using at least some of the acquired field data. The model determines, in particular calculates, the value of the degradation quantity as a function of power and the operating state of the electrochemical system at that power level. In other words, the model is configured to output the value of the degradation quantity when given a power level and an operating state of the electrochemical system at that power level as inputs.The degradation function is determined as a fit of a continuous function using values ​​of the degradation quantity determined with the model for the recorded values ​​of the operating states and the measured power, 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, 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 with the model is thus compared to R. 412767. 13 -The respective value of the aging-relevant parameter is plotted, and the fit is then performed for the value pairs (determined value of the system's degradation magnitude 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. Preferably, the value pairs used for fitting the degradation function are weighted differently in the fit.This advantageously allows the value pairs and thus different operating states to be considered to varying degrees for the fit, in particular depending on the degree of transience of the respective operating state of the respective value pair, wherein the value of the degree of transience depends on the operating state belonging to the value pair and preferably its rate and / or history, and depends on the power belonging to the value pair and preferably its rate and / or history.In particular, the value of the transience measure can be designed as a function of the operating state associated with the value pair and as a function of the power associated with the value pair. The power function is determined from recorded, especially measured, values ​​of a power, a change in power, and / or a power profile of the target system. The operating state function can also be determined from recorded, especially measured, values ​​of an operating state, a change in power, and / or a profile of the operating state of the target system. Preferably, a function of the transience measure can be defined to determine the degree to which a value pair should be considered in the fit.In particular, the function used especially as a weighting function can be a function negatively correlated with the measure of transience, especially a monotonically decreasing function, for example, a linearly, polynomially, or exponentially increasing function. Furthermore, a metric for the measure of transience is preferably used or defined to determine the influence of the pairs of values ​​depending on the measure, and the function is designed as a function of this metric. In particular, R. 412767 -. 14 -A metric, a variance, in particular a standard deviation, can encompass one or more measurable quantities of an associated electrochemical system, which are then part of the acquired field data. For example, a standard deviation of temperature or pressure at a given point in the electrochemical system can be used as a metric and thus as a measure of the transience of this electrochemical system. If, for example, the temperature or pressure does not change or changes only slightly over several time points of a measurement series, for example mainly due to typical sensor noise, then the variance, in particular the standard deviation, of this quantity is zero or very small. Therefore, a low transience or near-stationary state of the system's operation during the measurement series can be assumed, and the corresponding pair of values ​​can be given significant weight 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. The invention thus particularly encompasses the approach of applying degradation models developed for steady-state operating conditions also to transient operating conditions, thereby fitting continuous functions through the operating points for all systems considered for training, with the operating points being weighted differently depending on the degree of transience. In simplified terms, the distances between the operating points and the calculated fit then represent the training data for the correction model.As described above, the method for training the correction model can be applied again, preferably as often as desired, to the already trained correction model, particularly if further field data not yet used for training the correction model are available, especially, as described above, further training with additional field data from only certain electrochemical systems. The methods according to the invention, i.e., the method for determining a degradation quantity of an electrochemical system corrected with field data and the method for training a correction model, can be found in R. 412767. 15 -The invention may be designed, in particular, as computer-implemented methods. Accordingly, the invention also comprises a computer program containing instructions that, when executed by a computer, cause the computer to execute the respective method according to the invention, and a computer-readable data carrier on which this computer program is stored. Finally, the invention also comprises a computer that includes such a computer-readable data carrier, as well as an evaluation and control unit that includes such a computer-readable data carrier and further comprises 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.

[0003] R. 412767 - 16 -Brief description of the drawings: Exemplary embodiments of the invention are schematically depicted in the drawings and explained in more detail in the following description. Figure 1 shows the problem of unphysical jumps in models for determining the degradation quantity, as described above. Figure 2 shows a fleet of electrochemical systems with an exemplary embodiment of the device according to the invention, and Figures 3 and 4 show flowcharts for exemplary embodiments of the methods according to the invention. Figure 5 shows a fit for determining a degradation function for a single electrochemical system for determining the 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 above, can be, for example, similar systems comprising SOECs, SOFCs, PEM-ELYs, or PEMFCs.The methods according to the invention are also applicable to a single electrochemical system 10, but preferably to several such systems 10. 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. R. 412767 -. 17 -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. The following exemplary embodiments of the invention describe the methods according to the invention using the example of these systems 10 and the 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 only to a part 11 of the fleet, i.e., only to selected systems of the fleet.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, which can also be referred to as the target system 13, can be one of the systems 10 shown in Figure 2 or another system (whose field data are then specifically not used for determining or training the correction value or the correction model), wherein in the latter case the other system is preferably similar, i.e., in particular of the same design, to the systems 10 shown in Figure 2. Figure 3 shows a flowchart with the associated process steps 500. Thus, an exemplary method 500 is described which determines an additive correction function for correcting steady-state to transient behavior as (part of) the correction model(s). R. 412767 - 18 - for a degradation size ^ ^^^^^^^^^^^^^^^ over a training comprehensive field data of a fleet of systems ^ = 1, … , allowed, so that the corrected degradation size ^^ ^^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^^ out of an approximation of the actual degradation magnitude ^ ^ ^^ ^ ^ ^ ^ ^ ^^^^^^^also represents transient system states. Here, ℱ is a functional and can, in particular, include the value itself, the rate, and / or the history of ^^^^^^^^^^ or ^^^^^^^^^^^^. Such a functional is generally required because the transient behavior of a system, and consequently any associated correction, cannot generally be described based on the operating state at a single point in time. Thus, Method 500 enables an approximation of the actual degradation reference value ^. ^ ^^ ^ ^ ^ ^ ^ ^^^^^^^ also for transient states. Method 500 uses two assumptions: 1. Considered separately, the degradation quantity ^^ ^^ ^ ^ ^ ^ ^ ,^ ^ ^^^^^^ of any electrochemical system 10 ^ ∈ {1, … , A continuous function is represented if a suitable continuous aging-relevant parameter ^ is chosen as the argument (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 a measure ^^^^^^^^^^ that quantifies the degree of transient behavior of the system, and a model ^(^^^^^^^^^^, ^^^^^^^^^^^^) that is suitable for approximately steady-state conditions with ^ ^^^^^^^^^ =0 provides a good approximation of the real degradation, so that R. 412767 - 19 - for stationary states, it can be considered sufficiently accurate. The larger the value of the measure ^ ^^^^^^^^^The more complex the approach, the less accurate it becomes. For example, a degradation model, especially for SOFCs, can be based on a numerical, particularly 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. This model can be parameterized for the specific application. For example, the following procedure can be used: ^First, a model with suitable parameters is selected that represents the performance of the system under consideration for steady-state operating conditions. ^^^^^^^^^ can predict, for example, the approach from the publication cited above by Zaccaria et al.:^^^^^^^^^^^^ = ^^^^^^^^^^^^ ^^ In the next step, at least one parameter ^^^^^^^^^^^^ ModellThe variable selected represents the significant effect of degradation on performance, for example, the surface drag. Alternatively, 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 mapping: = . Subsequently, a large number of simulations (typically hundreds to thousands – depending on the number of operating conditions and the nonlinearity of the behavior) are performed, in which both are varied within the expected range of values ​​in the field. This generates a dataset R using the model. 412767 - 20 - ^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 for steady-state conditions according to the invention. The method 500 preferably comprises the following six steps 501-506: 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 comprises values ​​^^^^^^^^^^ of an operating state and a value ^^^^^^^^^^^^ of the power of an electrochemical system present in that operating state, and where the recorded operating points include both operating points with transient and steady-state operating conditions, via the degradation model an associated value ^ ^ ^^ ^ ^ ^ ^ ^ ^^^^^^^ for the degradation quantity, which is generally not correct for transient operating conditions: 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, for example, can only provide a small amount of field data close to the reference operating state mentioned above, cannot be considered for the procedure. R. 412767 - 21 - 2. These values ​​of the degradation magnitude are then, in a second step, plotted for each system 10 against the selected parameter ^, so that ^ collections of points are obtained. This results in , 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 parameter. This is illustrated by way of example in Figure 5 for a system 10. The value of the parameter ^ 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, in particular by integration, for example in the case of accumulated operating time or accumulated current from recorded operating time or current profiles. For example, ^=100 systems 10 are used and ^ are available for each system 10. ^ =20 (for all ^) operating points, so a total of 2000 operating points. In a real case, the number ^ ^The usable operating points may differ for different systems. 3. In the following third step 503, the measure of transience already mentioned above is defined, which quantifies the degree of transient behavior at a considered operating point: Here, ℱ, as already explained above, is a functional and can in particular represent the value itself, the rate and / or the history of ^. ^^^^^^^^^ or include over a defined time window. Exemplary forms of such a functional are given below: ^ℱ^^^(^)^ = ^(^ − ^) ^(^) d^ , where ^(^′) represents a kind of weighting function of past time points and, for example, an exponential function ^(^′) = ^ ⋅ exp(−^^ / ^) with a possible normalization factor ^ and decay length ^ or a Heaviside ^(^′) = R. 412767 - 22 - {0: ^^ < ^^ , 1: ^^ ≥ ^^} with a past time window to be considered ^ ^ may be. ^ d^, where ^(^′) represents a kind of weighting function of past points in time, as in the previous example, except that in this functional past time derivatives, i.e. rates, are integrated. , i.e., the rate of a quantity at the considered time.^ ℱ^^^(^)^ = std(^(^)) ^ ^^^^ , i.e., the standard deviation of a quantity over a period of time using t ^ defined, past time window ^ i.e., the maximum of a quantity over a period of time using t ^ defined, past time window ^ℱ^^^(^)^ = min(^(^)) ^ ^^^^ , i.e., the minimum of a quantity over a range using t ^ defined, past time window ^ = x(t − t^), i.e., the value of a quantity at a time ^deferred. In particular, the combination of several such support points can again represent a suitable functional. Here, ^(^) is either an operational or power quantity, i.e., from ^^^^^^^^^^ or ^^^^^^^^^^^^ . Functionals of different forms and including different quantities can then be assembled into a complete functional via addition, multiplication, etc. For example, the maximum difference of an operational quantity in a time interval is... Differenz One possible approach to calculating ^ ^^^^^^^^^A standard deviation is a metric, for example the standard deviation or the maximum difference of a relevant measured quantity (for example, one or more operating variables such as temperature or pressure at a point in the system 10), calculated over a defined time window. In the form of the functionals defined above, and for example when choosing temperature as a significant operating condition, this can be expressed as ^^^^^^^^^^ = ℱ^ ^^^^^^(^)^ (standard deviation) oder ^ = Write ^^^^^^(^)^ (maximum difference). If the calculated transient is to be measured against both the standard deviation of a temperature and differences in the achieved voltage as a measure of performance, this could be done, for example, via an R. 412767 - 23 - Linear combination ^^^^^^^^^^ = ^ (^)^ mitWeighting coefficients ^ and ^ are possible. Such a metric becomes small when the chosen measured quantity, for example, the measured temperature, changes little, but typically not exactly 0, since a certain amount of noise is always to be expected from any sensor. To achieve exact values ​​of 0, the determined value can be scaled and another function, for example, a "Rectified Linear Unit (ReLU)", applied (symbolically: ^). ^^^^^^^^^ =^^^^(^^^({^}^,…,^−Δ^)-Gw) so that ^ ^^^^^^^^^ The value becomes exactly 0 above a selected limit value (Gw). Such or similar calculations can also be extended to several relevant measured quantities, so that, for example, a value ζ^ ^ can be calculated for each relevant measured quantity. ^^^^^^^^ is calculated and ^ ^^^^^^^^^then formed from their maximum, geometric sum, or similar. 4. Using this measure, a function is defined in a fourth step (504) that describes how strongly an operating point should be considered in the subsequent fifth step (505). This function can either be a monotonically decreasing function in ^ ^^^^^^^^^ The weight ^ of an operating point can be described as ^( ^^^^^^^^^^ ) or the uncertainty ^ of an operating point can be expressed as a monotonically increasing function in ^. For example, a linear or quadratic function (for ^) or an inverse quadratic function (for ^) can be chosen for the function. For example, other exponents can also be used, e.g. Beispiel or an exponential approach with ^( ^^^^^^^^^^) = exp(−^^^^^^^^^^ / ^), or ^( ^^^^^^^^^^ ) = exp(^^^^^^^^^^ / ^), with ^ > 0, can be chosen. 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 each system 10 ^ ∈ {1, … , ^}, as exemplified in Figure 5 as a fitted function 330 for a system 10. For this purpose, the ^-range to be fitted of the systems can preferably be restricted to regions in which the density of operating points with approximately steady-state (and thus assumed steady-state) operation R. 412767 - 24 - is sufficiently high, with the measure ^ serving as a measure for the distances to determine the density. ^^^^^^^^^ or preferably the weighted metric ^(^ ^^^^^^^^^) or ^(^^^^^^^^^^) can be used. The ^-ranges to be fitted should be restricted such that, firstly, the density of operating points with near-steady-state operation is not too low, and secondly, the number 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 ranges, a fit is then performed for each system 10 ^ ∈ {1, … , ^} using the weight and uncertainty functions: ^(^^^^^^^^^^) or ^(^^^^^^^^^^) with → ^ ^^^,^ ^^^^^^^^^^^^ = ℎ The fit function 330 can, for example, be its spline function using the weights ^(^^^^^^^^^^ ), or a heteroscedastic Gaussian process using the uncertainties ^ ( ^ ^^^^^^^^^ ) For the fitted areas, discrete individual correction values ​​then result from as shown by way of example for a single correction value 301 in Figure 5. These are referred to as single correction values ​​because these correction values ​​were determined only by including field data from a single system 10. Since for all ^ ^,^ also the operating conditions measured in the field ^ ^,^ ^ ^^^^^^^^ and the performance ^ ^ ^, ^ ^ ^ ^^^^^^^^ as well as their rates and histories, especially over a period of time chosen depending on the case, ranging from several minutes to several hours, the individual correction values ​​can be determined. Group systems into a data tuple with the operating points R. 412767 - 25 - 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 this power output, as well as the associated individual correction value for the degradation quantity. The entirety of these data tuples then forms the training data for training the correction model ∆^ ^ ^^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^^ in the following sixth step 506.6. The training data thus obtained In the sixth step, 506 is now used to create the correction model ∆^^ ^^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^^ to train a regression algorithm ^ so that the trained correction model functions as a function of an operating state ^^^^^^^^^^ and a power^ ^^^^^^^^^and preferably their rates and stories provide the necessary correction predicts In this context, ^^^^^^^^^^ ^ℱ(^^^^^^^^^^), ℱ^^^^^^^^^^^^^^^^ ^ can be any regression algorithm, in particular, depending on the design of the functional ℱ(^^^^^^^^^^) or ℱ^^^^^^^^^^^^^^, for example, a linear regression algorithm, a random forest algorithm, an explainable boosting machine, or even a recurrent algorithm. For example, deviations of physical systems from a steady state are sometimes characterized by the fact that they converge exponentially towards a potentially new equilibrium state. A functional that exponentially weights operating conditions and performance values ​​so that distant fluctuations have a small effect could be applied in this case.Since the different operating states ^^^^^^^^^^ have different effects on performance, the values ​​calculated using the functional should be entered differently into the regression algorithm r, for example in R. 412767 -. 26 -A polynomial approach using different exponents and coefficients. So-called recurrent approaches such as RNNs (specifically GRUs or LSTMs) or NARX (GP-NARX or NN-NARX) approaches, which take history into account, are also suitable. In one variant, the training of ^^^^^^^^^^ can be performed under the boundary condition ^^^^^^^^^^ (. , . , ^^^^^^^^^^(^) = 0) = 0, with ^^^^^^^^^^(^) as a measure of the degree of transient behavior of the system at time ^, whereby this condition can be incorporated into the training, particularly in the form of a cost function. This additional condition ^^^^^^^^^^ (. , . , ^^^^^^^^^^ (^) = 0) = 0 then allows us to stipulate that the function only corrects non-stationary time points and ignores stationary time points.Thus, it can also be designed as a function of (^). With the correction model trained in this way, the degradation quantity, extended from merely stationary to transient operating states using field data, can be determined for each operating point. ^^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^^ The inventive method 600 determines a degradation quantity corrected with field data, the steps of which are described below by way of example and schematically illustrated in the flowchart in Figure 4. In a first step 601, a value ^^^^^^^^^^^^ of the degradation quantity is determined with the (uncorrected and thus stationary) degradation model, in particular as a function of the relevant operating point and its rates and histories as well as the degree of transience. In a second step, 602, a correction value ∆^ is applied. ^^^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^^ determined with the trained correction model, in particular as a function of the relevant operating point ^, 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 form the corrected value ^ ^ ^^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^^ Added to the corrected degradation value: R. 412767 - 27 - In particular, when several systems 10 continuously generate data in 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, separate correction models should preferably be determined for groups of technically sufficiently similar systems 10.

Claims

R. 412767 - 28 -Claims 1. Method (500) for training a correction model to determine a correction value for an uncorrected value of a degradation parameter of an electrochemical target system (13), in particular a fuel cell or electrolysis system (13), to take into account transient behavior of the target system (10) via the correction value, wherein the correction model is trained with training data including acquired field data from at least one, preferably several, electrochemical systems (10, 11, 13), wherein the training data comprise data tuples, each data tuple containing values ​​of at least one functional of operating values, in particular a value of a functional determined from field data of a measured power of one of the electrochemical systems (10, 11, 13) and a value of a functional determined from field data of an acquired operating state of the system (10, 11, 13) at the power, as well as a value corresponding to the operating values,1. Method (500) according to claim 1, wherein the correction model is trained using a regression algorithm using the training data.

2. Method (500) according to claim 1, wherein the individual correction value for the degradation magnitude is determined by including at least some of the acquired field data, values ​​determined with a model suitable for steady-state operating conditions of the system (10, 11, 13), and a measure of the transience of the systems (10, 11, 13) when acquiring the at least some of the acquired field 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 magnitude and a function value of a degradation function fitted using at least some of the acquired field data.where the model determines the value of the, R. 412767 - 29 -The degradation quantity is determined as a function of power and an operating state of the electrochemical system (10) present at that power level, and the degradation function is determined as a fit of a continuous function by values ​​of the degradation quantity determined with the model for the recorded values ​​of the operating states and the measured power levels.4.Method (500) according to claim 3, wherein the degradation function specifies the degradation of the electrochemical system (10) as a function of a continuous aging-relevant parameter, and the fitting of the degradation function is performed as a fitting of pairs of values ​​of the value of the degradation quantity determined with the model and the respective associated value of the aging-relevant parameter, wherein the pairs of values ​​preferably enter into the fit with different weights, wherein the weights are in particular dependent on the degree of transience of the respective value pair of the system (10, 11, 13) when acquiring the value of the aging-relevant parameter, wherein the value of the degree of transience depends on the operating state belonging to the value pair and preferably its rate and / or history, and depends on the power belonging to the value pair and preferably its rate and / or history.Method (500) according to claim 4, wherein a metric for the measure of transience is used or defined to determine the influence of the value pairs in the fit depending on the measure of transience.

6. Method (500, 600) according to any one of the preceding claims, wherein the correction model is trained under the condition that for steady-state operating conditions, in particular for operating conditions where the measure of transience is zero, the correction value output by the correction model is zero.

7. Method (600) for determining a correction value for a degradation parameter of an electrochemical target system (13), in particular a fuel cell or electrolysis system (13), in order to account for transient behavior of the target system (13), wherein an uncorrected value of the degradation parameter of the target system (13) is compared with a model for steady-state operating conditions. R. 412767 - 30 -Operating states of the target system (13) can be determined, and wherein the correction value is determined by a correction model, wherein the correction model is trained by including acquired field data of at least one electrochemical system (10, 11, 13) and values ​​determined with the model for the degradation quantity, wherein the correction model is trained by including a measure of the transience of the systems (10, 11, 13) belonging to the included field data, in particular according to a method (500) of claims 1 to 5.8.Method (600) according to claim 7, wherein the correction model is configured to output the correction value upon input of values ​​of at least one functional of operating values ​​of the target system (13), in particular a value of a functional of the power and a value of a functional of the operating state of the target system (13), wherein the functional of the power is determined from recorded values ​​of a power, a change in power and / or a course of the power of the target system (13) and wherein the functional of the operating state is determined from recorded / measured values ​​of an operating state, a change in power and / or a course of the operating state of the target system (13).Method (600) according to claim 7 or 8, wherein a corrected degradation value of an electrochemical system (13), in particular a fuel cell or electrolysis system (13), is determined, wherein a model for steady-state operating conditions of the system (13) is used to determine an uncorrected value of the degradation value, wherein the uncorrected value is determined as the corrected value of the corrected degradation value by adding a correction value determined with a correction model according to claim 6 or 7.

10. Method (500, 600) according to any one of the preceding claims, wherein the trained correction model is further trained with additional field data, wherein preferably only field data from a selected group of electrochemical systems (10) are used as additional field data.

11. Method (500, 600) according to any one of the preceding claims, wherein the model for the degradation value determines the value of the degradation value as a function of a. R. 412767 - 31 -Power, in particular an electrical voltage, and an operating state of the electrochemical system (10) are determined, and the correction model determines the correction value depending on a functional of the power, in particular the electrical voltage, and a functional of the operating state, and preferably depending on a measure of the transience of the operating state.

12. Device (100), in particular a virtual sensor, for determining a degradation quantity 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 execute 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 execute a method (500, 600) according to one of claims 1 to 11. 14.Computer program comprising instructions which, when executed by a computer, cause the computer to execute the method according to any one of claims 1 to 11.

15. Computer-readable data carrier on which the computer program according to claim 14 is stored.

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