Method and device for determining degradation variables of an electrochemical device, in particular a fuel cell or electrolysis cell

Abstract

The invention relates to a method (500) and a device (100) for determining degradation variables of an electrochemical device (10, 20, 30), in particular of an electrochemical system, in particular a fuel cell or a fuel cell system, wherein a degradation of the device (10, 20, 30) can be characterized via multiple degradation variables. The invention additionally relates to a method (600) for monitoring the aging state of one or more electrochemical devices and to a method (700) for controlling multiple electrochemical devices (10, 20, 30).

Description

[0001] R. 410619 - Description TitleMethod and device for determining degradation parameters of an electrochemical device, in particular a fuel cell or The present invention particularly relates to a method and a device for determining the aging state, also called degradation state, and preferably the determination of local internal state variables of electrochemical devices using a hybrid approach that combines a physical model with advanced data methods, including measurement data. The disclosed approach is particularly directed toward determining degradation states defined by more than one degradation variable. State of the Art: Electrochemical systems, such as polymer electrolyte membrane or solid oxide fuel cells or electrolyzers, or lithium or sodium-ion batteries, must meet demanding requirements throughout their entire service life, which sometimes range from several thousand to several tens of thousands of operating hours.Due to today's rapid development cycles, advance testing up to the end of the service life is practically impossible. Therefore, even with short operating hours, it is necessary to make the most accurate statements possible about the current aging state and aging rate in order to estimate whether degradation is developing at an acceptable rate. Furthermore, a reliable determination of the degradation state of electrochemical systems is also essential for more advanced applications and business models, such as demand-driven maintenance ('predictive R. 410619 - maintenance') or aging-optimized operating modes of individual or multiple systems in a network. However, the degradation state of typical electrochemical systems is usually not determined without further processing of the measured data. This is because a direct comparison of performance-relevant variables, such as the operating temperature, is not possible.the voltage, between different points in time is usually not sufficiently meaningful because the associated operating conditions are not identical. This is partly because different loads can be applied to an electrochemical system at different points in time, for example in the form of electrical currents of different levels. On the other hand, there are also boundary conditions that cannot be controlled by the system operator, or can only be controlled incompletely. Examples of this are completely freely fluctuating variables, such as the exact natural gas composition in fuel cells running on natural gas, or variables that change even due to the degradation of the system, such as certain temperatures or volume flows. The operation of an electrochemical system, particularly in a steady state, can be described using physical models. Such models are available as simulation models in commercial programs (e.g.The model is available in COMSOL Multiphysics® 1 or AVL Fire™ 2) or in open source projects (e.g., OpenFCST 3 or OpenFuelCell 4). An example of a physical model describing the effect of degradation on a solid oxide fuel cell system is the work of Zaccaria et al., 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 describes the effect of aging by applying an aging-dependent prefactor to the ohmic component of the internal voltage losses. As a consequence, the internal resistance of the fuel cell increases over the operating time, and the available power decreases.410619 - Disclosure of the Invention Advantages of the Invention Against this background, the invention relates to a method for determining degradation variables of an electrochemical device, wherein a degradation of the device can be characterized using multiple degradation variables. In a measurement step, values ​​for the operating conditions of the device and performance values ​​of the device are provided for multiple points in time. In particular, these values ​​are recorded and / or at least partially measured, for example, retrieved from a control system for the device and / or, in particular the performance values, measured via sensors.In a selection step, a time window is selected in which several of these points in time lie, and during the time window, a predetermined value curve, for example a linear curve, a constant value, or another parameterizable curve, is assumed for all degradation variables except for a selected degradation variable. Taking into account the measured values ​​of the operating conditions and the measured power values, the time window is selected such that at least one of the operating conditions changes its value during the time window. This at least one operating condition, for example a current density or current intensity requested by the device, is an operating condition that has a varying effect on at least one of the power values, in particular on the voltage drawn at the device output, depending on the value of the selected degradation variable.In a determination step, a value of the selected degradation variable is then determined, taking into account a physical model that can determine the performance values ​​of the device for specified operating conditions and specified values ​​of the degradation variables, and using the provided, in particular measured, values ​​of the operating conditions and the provided, in particular measured, performance values ​​at the times within the time window. As explained above, the values ​​of the other degradation variables, i.e., the degradation variables with the exception of the selected degradation variable, are specified, for example in the form of constant values ​​and / or a specified parameterizable curve, for example, linear or exponential changes, during the time window. The electrochemical device can, in particular, be a fuel cell, an electrolyzer cell, or a fuel cell system.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), anion exchange membrane electrolyzer cells (AEM-ELY) or anion exchange membrane fuel cells (AEMFC).The electrochemical device can also comprise a plurality of spatially separated parts, for example, each comprising one or more cells, wherein the parts can preferably exchange data via a wired or wireless communication connection. Furthermore, the electrochemical device 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 degradation variables characterize, in particular, the effects of the physical aging of the device, which manifests itself in a change in internal system variables, for example, an increase in internal resistances in the system, particularly in cells of the system, or a decrease in the electrochemically active surface area (ECSA), particularly of a catalyst-coated membrane (CCM).The changing degradation of the system can thus be characterized by changing values ​​of the degradation variables in the form of preferably location-dependent prefactors (aging prefactors) of the internal variables in the physical model of the device. The above-mentioned selected degradation variable is preferably a prefactor of the electrochemically active surface (in particular, an ECSA prefactor). In the context of the invention, system performance can generally be understood as a measure of the system's performance during its operation, for example, an electrical voltage or electrical power provided by the system, particularly in the case of a fuel cell, or a hydrogen volume flow in the case of electrolysis. The selected time window can in particular be a period of preferably one or more minutes or even several hours.In addition to considering a change in at least one operating condition that has a varying impact on performance depending on the degradation state, as described above, the time window is selected such that the lead of the values ​​of the other degradation variables is well-defined during the time window, i.e., as described above, it can be specified as constant during the time window or following a predetermined curve. The method according to the invention is thus advantageously suitable for electrochemical devices whose aging state can be defined by more than one degradation variable. For this purpose, the method uses an advantageous hybrid approach that combines a physical model with measured data.The method according to the invention can thus advantageously be used as a virtual sensor for degradation, for example, for a real-time application, for example, as part of a digital process twin for such an electrochemical device. The method according to the invention is advantageously independent of the specific physical model used, provided that the model provides an input of the operating conditions as boundary conditions and an output of the power occurring in the R. 410619 electrochemical device (in particular, the voltage in fuel cells, and the hydrogen volume flow in electrolyzers), as well as several degradation variables to describe the age-related power loss of the device. According to a particularly advantageous development, the determination step is carried out iteratively several times in an optimization step, whereby the values ​​of the other degradation variables are optimized with respect to a target variable.The target variable can comprise a fluctuation, in particular a variance, of the value of the selected degradation variable during the optimization step. Preferably, the values ​​of the other degradation variables are optimized for an extreme value, in particular a minimum, of the target variable. In particular, the values ​​of the other degradation variables during the respective inversion step follow the respective predefined value or predefined course during the time window, whereby the respective predefined value or the respective predefined course can change due to the optimization over the inversion steps until the desired optimization with respect to the target variable is achieved. The optimization with respect to the target variable can be defined as achieved, in particular, when a predefined termination criterion is met, whereby the termination criterion can be selected as is customary in optimization methods.Consideration of the physical model in the determination step can include use of the physical model or a surrogate model. Preferably, the surrogate model outputs values, in particular for at least part of the space of possible parameter values ​​and / or at least part of the space of possible input values ​​of the physical model, at least for one output variable of the physical model that lie within a tolerance range to the output values ​​of this variable of the physical model. The surrogate model can preferably be a data-based surrogate model, i.e., a model in which one or more parameter values ​​are determined based on data outside the model. These parameter values ​​are preferably determined via machine learning of the surrogate model, i.e., via training of the surrogate model.410619 - According to a preferred embodiment, the physical model is taken into account in the determination step by inverting the physical model or a surrogate model to the physical model, so that the inverted model determines the value of the selected degradation variable as a function of the measured values ​​of the operating conditions, the measured performance values, and the specified values ​​of the other degradation variables. The inversion, in particular of the physical model, can generally be carried out analytically or numerically, if mathematically possible. According to an advantageous embodiment, the physical model or the surrogate model is taken into account in an optimization method for an optimized determination of the value of the selected degradation variable. The optimization method can, for example, comprise Bayesian optimization, simulated annealing, or gradient descent approaches.In particular, taking the physical model into account in the determination step can comprise using a data-based surrogate model, in particular a regression model, wherein the surrogate model is pre-trained using data generated with the physical model. As in the case of inverting the model described above, the trained surrogate model directly outputs a value of the selected degradation variable upon input of respective values ​​of the operating constraints and respective performance value, and preferably also upon input of values ​​of the other degradation variables. Such a surrogate model for the inverted physical model can also be referred to as an inverted surrogate model, in particular as an inverted data-based model.If necessary, the method can comprise a processing step between the selection step and the determination step, in which the measured values ​​of the operating conditions and the measured power values ​​at the times within the time window are processed for input into the physical model. In particular, these values ​​can be summarized and / or converted in the form and units of the R. 410619 physical model or the surrogate model. According to a preferred embodiment, the method is repeated for different time windows, preferably in each case, in the selection step in order to determine the value of the selected degradation variable and preferably the values ​​of the other degradation variables for these different time windows. This advantageously allows an evolution of the degradation variable or variables to be determined for all selected time windows.The different time windows can directly adjoin one another, at least for some time windows, or even partially overlap. Alternatively, the time windows can also be partially spaced apart from one another in time, in particular in order to disregard irrelevant time periods. According to a particularly advantageous development of the method, the physical model contains at least one internal physical variable of the electrochemical device, wherein at least one value of one of these internal physical variables is determined after the determination step has been completed and preferably after the optimization step has been completed, preferably using the physical model or the trained surrogate model.The internal physical quantities can, in particular, be internal local or averaged quantities, for example (local) temperatures or (local) current densities in the cell or stack, local hydrogen or oxygen concentrations and gradients, local relative humidity, local partial pressures, local mechanical stress values, or a distribution of overpotentials. Typically, no direct sensor data is available for these internal quantities. However, using the method according to the invention, such quantities can advantageously be estimated and made available for further data analysis. The invention also relates to a method for monitoring an aging state of one or more electrochemical devices, wherein the method described above is carried out to determine degradation quantities of the one or more electrochemical devices, preferably for a plurality of R, each different in the selection step.410619 - Time window, wherein a notification is issued if the determined values ​​of the degradation variables deviate from predetermined values ​​by more than a respective predetermined tolerance. The invention further relates to a method for controlling a plurality of electrochemical devices, wherein for each device, values ​​of at least one, preferably several, degradation variables are determined using a method for determining the degradation variables described above. Depending on the determined values, a total load requested of the devices is distributed among the devices, preferably depending on a prioritization of the devices depending on the degradation of the devices derived from the determined values. This has the advantage that more severely degraded devices have to provide a smaller proportion of the total requested load, thus slowing down their further degradation.The methods according to the invention can in particular be designed as computer-implemented methods. Accordingly, the invention also encompasses a computer program for each of the methods, which includes 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 encompasses a computer, a part of a cloud computing architecture, or another programmable device with a processor 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 respective 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, in particular for process and / or quality monitoring of one or more electrochemical devices. Brief Description of the Drawings R. 410619 - Embodiments of the invention are schematically illustrated in the drawings and explained in more detail in the following description. The same reference numerals are used for the elements shown in the various figures and having a similar effect; a repeated description of the elements is omitted.Figure 1 shows a flowchart of an exemplary embodiment of the method according to the invention for determining degradation variables of an electrochemical device. Figure 2 shows an exemplary embodiment of a device according to the invention. Figure 3 shows a flowchart of an exemplary embodiment of the method according to the invention for monitoring an aging state of one or more electrochemical devices. Figure 4 shows a flowchart of an exemplary embodiment of the method according to the invention for controlling a plurality of electrochemical devices. Embodiments of the Invention. Figure 1 shows a flowchart of an exemplary embodiment of the method 500 according to the invention, described below.Figure 2 schematically shows an embodiment of a device 100 according to the invention on which the method according to the invention is implemented, for example a computer, part of a cloud computing architecture or another programmable device with a processor, for example for use as a virtual sensor or as part of a digital twin for an electrochemical device 10. The determination device 100 and the electrochemical device 10 are designed to transmit data, in particular R. 410619 measurement data and operating data, of the electrochemical device 10 to the determination device 100, in particular via suitable wireless communication modules such as mobile radio or WLAN modules.The determination device 100 is configured to receive this data and preferably also to transmit data to the electrochemical device 10, for example, requests for transmitting the data or control commands for changing the operating conditions of the electrochemical device 10. The determination device 100 can accordingly also be connected to further electrochemical devices 20, 30. The electrochemical devices 10, 20, 30 can in particular be, as described above, similar SOECs, SOFCs, PEM-ELYs, or PEMFCs, or systems comprising several such cells. Without limiting the generality, the following exemplary embodiment is explained using a PEMFC as the electrochemical device 10, in which the reduction of the electrochemically active area and the increase in electrical (contact) resistance can be considered as degradation mechanisms.For this purpose, the expression of the electrochemically active surface, where the relevant reactions take place, can be multiplied by a prefactor that decreases with increasing aging. Second, one or more electrical resistances that affect charge transport in the electrochemical system can be multiplied by separate prefactors that increase with increasing aging. The choice and number of aging factors selected in the form of these prefactors, which are referred to as degradation variables, is preferably limited in the approach described here only by the fact that their effects on the electrochemical system should, in principle, be distinguishable through measurements.To represent inhomogeneous degradation of the electrochemical system, the initially simplified, purely scalar degradation variables, which affect all relevant components of the electrochemical system regardless of location, can be multiplied by location-dependent R. 410619 function sets or, alternatively, can represent location-dependent functions themselves. For example, a function set that has a value of 1 near the fuel gas inlet of a PEMFC fuel cell and decreases to 0 toward the fuel gas outlet can describe degradation that has a stronger effect at the fuel gas inlet and a weaker effect at the fuel gas outlet. The location dependence of the function sets can be motivated physically or derived from further experiments and investigations.Alternatively or additionally, a single aging effect and thus the degradation variable can be decomposed into several prefactors and associated location-dependent degradation functions (analogous to the basic idea of ​​degradation functions in the finite element method). This allows even inhomogeneous degradation distributions to be represented and measured indirectly. The various components should also have sufficiently different effects on performance under given operating conditions. This then results in a larger number of aging factors that at least partially describe the same physical effect, but with different local weightings. The progressive aging state, also called degradation state, can thus be characterized using values ​​of several fundamentally time-dependent degradation variables.For this purpose, a physical model ^^^^^^ is used, which determines the available power, i.e., the power values, as a function of the operating conditions and the degradation, i.e., the values ​​of the degradation variables. The physical model ^. ^^^^^is implemented, for example, as a simulation model in commercial programs (e.g., in COMSOL Multiphysics® www.comsol.de / model / download / 813751 / models.fce.sofc_unit_cell.pdf for a SOFC or AVL Fire™ https: / / www.avl.com / documents / 10138 / 3372595 / Solution+Sheet+for+PEMFC for a PEMFC), open source projects (e.g., OpenFCST3 or OpenFuelCell4) or in self-written code, particularly in the form of a finite element method. For example, in the case of a PEMFC, the physical model^^^^^^ in the case of a PEMFC is based on a model implemented in COMSOL® with the "Application ID: 103241" https: / / www.comsol.com / model / pem-fuel-cell-stack- 103241. R. 410619 - In a first step 501 of the method (measurement step 501), values ​​of the operating conditions ^^^^^^^^^^(^) and power values^^^^^^^^^^^^(^) of the electrochemical device 10 are recorded for several points in time.A point in time with the data measured or recorded at that time, in particular the values ​​of the operating conditions and / or the power values ​​at that time, is also referred to below as a data point. Depending on the model and device used, values ​​of set operating conditions can be retrieved from a processor for controlling the electrochemical device 10 or from a memory of the device 10, while values ​​of emerging operating conditions and / or values ​​of power provided by the device 10 can be measured, in particular, by sensors on the electrochemical device 10 or on devices connected to the device, in particular electrically.For example, the operating conditions include a requested load current, temperatures, volume flows, pressures, and gas compositions, the presence of which can be adjusted, for example, at the inlet of the fuel gas and air sides of the device and / or measured at the outlet of the device, depending on the control strategy. The recorded power value can, for example, be the output voltage currently provided by the device, also referred to as the stack voltage in a stack of several cells. For each time ^, a state vector ^ ^ can thus be determined for the electrochemical cell under consideration. Device) comprising the recorded values ​​of the operating conditions at this time and the recorded power values ​​at this time are provided for the method 500. The set of these vectors thus forms a time series at the selected times. In a second step 502 (selection step 502), a degradation variable ^^^^[^] with ^ ≤ ^ is selected from the ^degradation variables. Furthermore, a time window [^^ , ^^^^] comprising at least some of the above-mentioned times and thus the above-mentioned state vectors, for example comprising several minutes. The time window and thus the times contained therein are preferably selected such that the states of the R. 410619 - electrochemical device at these times can be described by the physical model^^^^^^, thus preferably that the respective values ​​of the operating conditions each lie within a permissible parameter and functional range of the model ^ ^^^^^If the model ^ ^^^^^For example, if the algorithm is only applicable to steady-state operating conditions, only field data for which at least a quasi-steady state can be assumed should be used. A variety of approaches exist for detecting such steady-state conditions, ranging from evaluating the gradient of characteristic quantities to statistical methods, as described, for example, in Jeffrey D. Kelly, John D. Hedengren, 2013. "A steady-state detection (SSD) algorithm to detect non-stationary drifts in processes", Journal of Process Control 23 (3) 326-331. doi:10.1016 / j.jprocont.2012.12.001, S. Narasimhan, Chen Shan Kao, and R.S. H. Mah. “Detecting changes of steady states using the mathematical theory of evidence”, AIChE journal 33.11 (1987), pp. 1930-1932, Minsung Kim et al"Statistics manual: with examples taken from ordnance development," Vol. 3369. Courier Corporation, 1960. The selection of the degradation variable and the choice of the time window are also carried out in such a way that a curve can be specified for each of the other degradation variables, i.e., preferably for all degradation variables with the exception of the selected degradation variable (hereinafter referred to as the "other" or "^ − 1" degradation variables). The specification of a curve is to be understood in particular as meaning that a value for each of these other degradation variables can be specified for the points in time within the selected time window, in particular from an assumed, preferably continuous or even steady, value curve of the respective degradation variable during the time window.In the simplest case, a constant value or at least a linear progression can be assumed for one or more degradation variables during the time window, especially as an estimated approximation of an actual progression. It is recommended to use the aging factor with the shortest time scale, R. 410619—that is, the aging factor whose value changes most rapidly compared to the other aging factors. Third, the values ​​of at least one of the operating conditions at the points in time encompassed by the time window should exhibit such a large variation that different effects of the degradation variables on the electrochemical system can be separated from one another. For example, in electrochemical systems, there are aging effects whose impact on the system's performance depends strongly on the required current density, and others whose impact is independent of this.To determine the associated degradation variables as clearly as possible in this example, data with at least two sufficiently different current densities is required within the selected time window. Suitable time windows can be selected or the available time windows classified for sufficient variation in operating conditions using appropriate pre-filtering. Possible approaches include, for example, checking the range of values ​​covered by specific operating conditions or so-called clustering with regard to the operating conditions, which involves counting how many data points in the selected time window fall into which class of values.Taking the points explained into account, the degradation quantity can generally be selected first, and then, depending on this, a time window can be selected in which at least some of the above-mentioned times occur and in which the above-mentioned conditions are met or approximately met. Alternatively, the time window with at least some of the times can be selected first according to the conditions, and a degradation quantity can be selected depending on this. A desired time window can also be divided into two or more sub-time windows, whereby when changing from one of the sub-time windows to the subsequent sub-time window, a different one of the degradation quantities is specified as the selected degradation quantity. Furthermore, the subsequent sub-time window can be selected such that it differs from the last sub-time window by only one data point.The calculated degradation variables can then be assigned, for example, to the first, last or R. 410619 - middle data point, so that a separately calculated set of degradation variables is available for each data point. In an optional third step 503 (processing step 503), which depends in particular on the physical model used, the input and output variables of the physical model, i.e. the operating conditions and the power provided, are processed. that they have a required form and units for the implementation of the physical model as a simulation model. For example, in a fuel cell system with multiple stacks, an average can first be calculated across the individual stacks, or the total current measured in the field can be converted into a current density that may be required by the simulation model. An exemplary list of the form d ann look like this: {[[Current i , …, Electricity i+k ], [Fuel gas utilization i , …, fuel gas utilization i+k ], [Temperatur i ,…,Temperature i+k ], …], [[Stack voltage i , …, stack voltage i+k ], …]}. In a fourth step 504 (determination step) and a preferably fifth step 505 (optimization step), the values ​​of the selected degradation variable and preferably of the other degradation variables are determined. In the fourth step 504, the physical model ^^^^^^: ^^^^ , ^^^^^^^^^^ →^^^^^^^^^^^^ , (^^^^^^^^^) is used (where ^^^^^^^^^ can be further internal parameters of the model and in particular of the electrochemical device) to determine the value of the selected degradation variable {^^^^[^](^ ∗ )} ^ for ^ ∗ ∈{^^ , … , ^^^^} for which the model ^^^^^^ together with the^ operating conditions ^^ ^^^^^^ (^ measured ^ ^ for the others Degradation quantities, ie ^ ∗ ^^^ [^](^) m ^ ∈ {1, … , ^ {^}, as described above, values ​​or value curves are specified and preferably initialized with a physically consistent value. For the determination of the values ​​R. 410619 - {^ ^^^ [^](^∗)}^ at the respective time points, depending on the structure of the model, various optimization methods can be used, in particular Bayesian optimization, simulated annealing, or gradient descent approaches. If the physical model ^ ^^^^^ is analytically invertible, the values ​​{^ ∗ ^^^[^](^)}^ can alternatively also be calculated directly, i.e., without optimization or other numerical approximation methods. Alternatively, instead of the physical model ^^^^^^, a surrogate model can be used, in particular a data-based model based on machine learning, which has preferably been trained with the aid of the physical model to directly determine the value of the selected degradation variable as a function of the operating conditions and performance. In the fifth step 505, the values ​​of the other degradation variables, aging factors ^ ∗ ^^^ [^](^) for ^ ∈ {1, … , {^} is determined. For this purpose, the fourth step 504 is repeated several times with differently selected value curves, each predetermined over the selected time window, in the simplest case constant values ​​^^^^[^] for ^ ∈ {1, … , {^} is repeated. Possible optimization methods can be, in particular, Bayesian optimization, simulated annealing, or gradient descent approaches. The choice of ^^^^[^] is optimized with respect to a defined target variable, whereby the target variable is chosen according to the expected course of the selected degradation variable ^ ∗^^^[^](^ ) in the time window. For example, if one expects an approximately constant value for ^^^^[^](^ ∗ ), the choice of ^ ∗ ^^^ [^](^) for ^ ∈ {1, … , {^} is particularly good if the scatter of ^ ∗ ^^^ [^](^) is small in the time window. The target value can then be the smallest possible standard deviation ^ of ^ ∗^^^[^](^ ) for^∗ ∈ {^^ , … , ^^^^}. The optimization then corresponds to a minimization of ^ Target variables can, for example, have a small L1 norm of ^ ^^^[^], the smallest possible difference between the minimum and maximum value of ^^^^[^], or the smallest possible standard deviation of the logarithm of ^^^^[^]. For the convergence of the iterative optimization in the fourth step 504 and the fifth step 505, the exact form in which the ^ ∗^^^(^ ) enter the model should be designed so that the mapping is, in a practical sense, unique and invertible. In a practical sense, this also includes the R. 410619 - possibility that, if the mapping is not unique, physically meaningless outputs are filtered out, so that the filtering makes the mapping unique again. For example, in a quadratic relationship, where both negative and positive degradation factors are possible, the negative values ​​can be neglected. The values ​​of the degradation variables {^^^^(^)} determined in this way ∗ )} ^or quantities derived therefrom can then be used as a measure of the degradation, i.e. the state of health of the electrochemical device10. Optionally, depending on the nature of the model ^ ^^^^^ in a sixth step 506 also internal physical quantities {^^^^^^^^^^ (^ ∗ )} ^ such as local temperatures, current densities or similar can be read out after performing the fifth step 505. For this purpose, the determined degradation quantities {^ ^^^ (^ ∗ )} ^together with the operating state considered for the selection of the internal variables, i.e. the values ​​of the operating conditions ^^^^^^^^^^([^^ , … , ^^^^]) present in this operating state, are used in the optimized simulation model or a corresponding surrogate model. Further exemplary embodiments of developments and variants of the method according to the invention, for example of the described exemplary embodiment 500, are presented below. The surrogate model that can be used as an alternative to the physical model ^^^^^^ in the fourth step 504 can be generated in particular on the basis of results previously simulated with the physical model. In particular, "Design of Experiment" methods (DoE) can be used for this purpose. For this purpose, a DoE is generated from parameter combinations using a suitable approach, for example via Latin Hypercube Sampling or adaptively via Active Learning, on which the physical model ^^^^^^ is then evaluated.The DoE can also be designed to contain only data points that are as close as possible to the actual operating conditions in the field. This can be achieved by defining an appropriate distance norm and filtering the original DoE according to R. 410619. Possible advantages include shorter training times and improved accuracy of the regression model in the relevant parameter range. The results are then used to train a regression model, particularly one based on linear regression, random forest, Gaussian processes, or neural networks. This is a particularly advantageous approach when calculating a single simulation of the physical model requires a comparatively large amount of time or computational resources, or when similar or identical operating points are repeatedly calculated when using the approach.The actual simulation step is then preceded, and the evaluation of the surrogate model derived from it requires only a comparatively short amount of time to determine the degradation variable. In addition, as already described above, the surrogate model can also be trained directly so that the regression model predicts the selected degradation variable from operating conditions and performance for given other degradation variables, thus completely eliminating the need for model inversion. The method 500 according to the invention can advantageously take place at the system level; with multiple stacks per system, also at the stack level and also at the repeat unit level (if the required measured variables are available), provided that the required data can be acquired in measurement step 501 and prepared for the physical model ^^^^^^ or surrogate model used. The physical model ^^^^^^ can be part of a system model into which further aging effects (e.g.Power losses at the air blower, changes to heat exchangers, etc.) are taken into account. When applying the method 500 to several electrochemical devices 10, 20, 30, the physical model ^. ^^^^^ in the same way, in particular generically or with the same initial parameterization, for all devices 10, 20, 30 or systems ^ = 1, ^. Alternatively, the model ^^^^^^ can also be individually adapted to the respective device or system by adapting it to production parameters, for example layer thicknesses or density differences, or so-called R. 410619 pass-off tests to ensure performance criteria after production, for example in the form of slightly different open-circuit voltages, for which the degradation and optionally values ​​of internal variables are to be determined. The determined degradation variables and in particular their temporal progression{^ ^ ^^^(^)}can then be used in various applications. In a first application, one or more of the determined degradation variables can be used as key figures for age- or condition-based maintenance ('predictive maintenance') of the electrochemical devices, for example, to postpone or advance scheduled maintenance appointments if the ageing state is better or worse than expected. In a second application, one or more of the determined degradation variables can be used to control electrochemical devices or systems operating in a microgrid so that their ageing state remains within a similar range. For example, during low load requests, those devices 20 that currently have a higher ageing state than other devices 10, 30 could be paused.This could compensate for fluctuations in production that affect the aging rate of the systems, so that all devices 10, 20, 30 have a similar service life and similar maintenance intervals. Further possible applications arise from the use of the internal variables {^. ^ ^^^^^^^^(^)}. Here, the invention can be used to avoid unsafe system states by adapting the load profile, i.e., changing the distribution of a total load across multiple electrochemical devices 10, 20, 30, depending on the determined values ​​of the internal variables. For example, a respective, optionally location-dependent, internal temperature of the electrochemical devices can be determined using the physical model optimized according to method 500. For this purpose, the physical model used for the method can be based on spatially resolved models implemented in COMSOL®, for example, which co-describe such internal variables. If predetermined, optionally step-shaped R.410619 - Limits by this internal temperature, the load applied to the respective device can be reduced by adjusting the operating conditions, in particular by shifting part of the load to another electrochemical device that has a comparatively lower internal temperature. A load distribution across several electrochemical devices can thus preferably be correlated or anti-correlated with the values ​​of one or more internal variables. Furthermore, an analysis of the correlation between the internal variables {^. ^^^^^^^^ (^)} ^and the development of the degradation variables ^^^^(^) provide further indications as to which operating states and strategies are particularly harmful with regard to aging. These can then in turn be avoided in an optimized operating mode. Particularly in an interconnected network of several electrochemical systems, this results in great optimization potential for avoiding such unsafe or particularly aging-relevant states. Figure 3 shows a flow diagram of an embodiment of the method 600 for monitoring an aging state of one or more electrochemical devices, for example the devices 10, 20, 30 described above in Figure 2. In a first step 601 of the method 600, the method 500 according to the invention for determining the degradation variables is carried out for at least one of the devices 10, 20, 30, preferably for a plurality of different time windows in the selection step 502.In a second step 602 of the method, an indication is issued if the determined values ​​of the degradation variables deviate from predetermined values ​​by more than a predetermined tolerance. For example, the indication can be issued as an acoustic, optical, or digital alarm signal. Figure 4 shows a flowchart of an embodiment of the method 700 for controlling a plurality of electrochemical devices, for example the devices 10, 20, 30 described above in Figure 2, for example in an interconnected network as described above. In a first step 701 of the method, values ​​of at least one, preferably several, degradation variables are determined for each device 10, 20, 30 using the method 500 according to the invention for determining the degradation variables. In a second step 702 R.410619 - Depending on the determined values, a total load requested from the devices 10, 20, 30 is distributed among the individual devices 10, 20, 30, preferably depending on a prioritization of the devices 10, 20, 30 depending on the degradation of the devices derived from the determined values. For example, the load distribution can be inversely proportional to the determined degradation values ​​or otherwise anticorrelated with the determined degradation values.

Claims

R. 410619 - Claims 1. Verfahren (500) zur Bestimmung von Degradationsgrößen einer elektrochemischen Vorrichtung (10, 20, 30), insbesondere eines elektrochemischen System, in particular a fuel cell or a fuel cell system, wobei eine Degradation der Vorrichtung (10, 20, 30) über mehrere Degradation variables can be characterized, ^ wobei in einem Messschritt (501) für mehrere Zeitpunkte jeweils Werte zu Betriebsbedingungen der Vorrichtung und Leistungswerte der Vorrichtung bereitgestellt, insbesondere gemessen werden, ^ wobei in einem Auswahlschritt (502) ein Zeitfenster umfassend mehrere der Time points are selected, whereby during the time window a value or a predetermined value progression is assumed for all degradation variables except for a selected degradation variable, and whereby during the time window at least one of the operating conditions, which has a different impact on at least one of the performance values ​​depending on the value of the selected degradation variable, changes in value, ^ wobei in einem Bestimmungsschritt (504) unter Berücksichtigung eines physical model, which for given operating conditions and given values ​​of the degradation variables, determines the performance values ​​of the V orrichtung bestimmen kann, oder eines insbesondere datenbasierten Surrogatmodells und unter Benutzung der bereitgestellten Werte der Betriebsbedingungen und der bereitgestellten Leistungswerte zu den im Time window at the assumed values ​​or W erteverläufen der anderen Degradationsgrößen ein Wert der ausgewählten Degradationsgröße bestimmt wird. R. 410619 - 2. Verfahren (500) nach Anspruch 1, wobei in einem Optimierungsschritt (505)the determination step (504) is carried out iteratively several times, whereby the values ​​of the other degradation variables are optimized with respect to a target variable.

3. Verfahren (500) nach Anspruch 2, wobei die Zielgröße eine Schwankung, in particular a variance of the value of the selected degradation quantity during the optimization step (505) and wherein the values ​​of the other Degradationsgrößen für ein Minimum der Zielgröße optimiert werden.

4. Verfahren (500) nach einem der vorhergehenden Ansprüche, wobei die Taking into account the physical model in the determination step (504), an inversion of the physical model or the surrogate model for a Bestimmung des Werts der ausgewählten Degradationsgröße als Funktion der gemessenen Werte der Betriebsbedingungen, der gemessenen Leistungswerte und the specified values ​​of the other degradation variables.

5. Verfahren (500) nach einem der vorhergehenden Ansprüche, wobei die Taking into account the physical model in the determination step (504), a use of the physical model or a surrogate model in an optimization method for an optimized determination (504) of the value of the ausgewählten Degradationsgröße erfolgt.

6. Verfahren (500) nach einem der vorhergehenden Ansprüche, wobei die Consideration of the physical model in the determination step (504) a use of a data-based surrogate model, in particular a Regressionsmodells, umfasst, wobei das Surrogatmodell unter Verwendung von mittrained on data generated by the physical model.

7. Verfahren (500) nach einem der vorhergehenden Ansprüche, wobei in einem zwischen dem Auswahlschritt (502) und dem Bestimmungsschritt (504) liegenden Processing step (503) the values ​​of the operating conditions and the performance values zu den im Zeitfenster liegenden Zeitpunkten für eine Eingabe in das physikalische model can be prepared. R. 410619 - 8. Verfahren (500) nach einem der vorhergehenden Ansprüche, wobei das Verfahren für im Auswahlschritt (502) vorzugsweise jeweils unterschiedliche Zeitfenster is repeated to determine the value of the selected degradation quantity and preferably the values ​​of the other degradation quantities for these different time windows.

9. Verfahren (500) nach einem der vorhergehenden Ansprüche, wobei das physical model at least one internal physical quantity of the elektrochemischen Vorrichtung beinhaltet und wobei zumindest ein Wert einer dieser internal physical quantities after the determination step and preferably after the optimization step, preferably using des physikalischen Modells oder des trainierten Surrogatmodells.

10. Verfahren (600) zur Überwachung eines Alterungszustands einer oder mehrerer elektrochemischer Vorrichtungen (10, 20, 30), wobei eine Vorrichtung in particular an electrochemical system, in particular a fuel cell or a fuel cell system, wherein for the determination of Degradationsgrößen der ein oder mehreren Vorrichtungen ein Verfahren (500) nach einem der vorhergehenden Ansprüche ausgeführt wird, vorzugsweise für imSelection step (502) each have different multiple time windows, wherein an indication is issued if the determined values ​​of the degradation variables deviate from predetermined values ​​by more than a predetermined tolerance.

11. Verfahren (700) zur Steuerung mehrerer elektrochemischer Vorrichtungen (10, 20, 30), wherein the devices can be in particular electrochemical systems, in particular fuel cells or fuel cell systems, wherein jede Vorrichtung Werte zumindest einer, vorzugsweise mehrerer Degradationsgröße mit einem Verfahren (500) nach einem der Ansprüche 1 bis 9 bestimmt werden, wobei depending on the determined values, a total load requested from the devices is distributed among the devices, preferably depending on a prioritization of the devices depending on the degradation of the devices derived from the determined values. R. 410619 - 12. Vorrichtung (100), insbesondere virtueller Sensor, zur Bestimmung von Degradationsgrößen einer elektrochemischen Vorrichtung (10, 20, 30), insbesondere an electrochemical system, in particular a fuel cell or a fuel cell system, wherein the device (100) is configured to carry out a method (500, 600, 700) according to one of the preceding claims.

13. Digitaler Prozesszwilling, insbesondere für eine Prozess- und / oderQuality monitoring of one or more electrochemical systems (10), wherein the twin is configured to carry out a method (500, 600, 700) according to one of claims 1 bis 11 auszuführen.

14. Computerprogramm, das Befehle umfasst, die bei seiner Ausführung by a computer causing it to carry out a process (500, 600, 700) according to einem Ansprüche 1 bis 11 auszuführen.

15. Computerlesbarer Datenträger, auf dem das Computerprogramm nach Anspruch 14 gespeichert ist.

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