Method for determining parameters during the modelling of a technical system, simulation computer

Abstract

The invention relates to a method for determining parameters during the modelling of a technical system, preferably a fuel cell stack or an electrolysis stack, wherein parameters of the technical system to be determined are subdivided into system-variable and system-invariable parameters. According to the invention, the following steps are carried out: a. creating a model of the technical system as a main model and a model of a reference system as a reference model, b. selecting at least one evaluation variable, on the basis of which a quality of the main model and / or of the reference model is measured, the at least one evaluation variable being influenced by all parameters to be determined and / or a portion of the parameters to be determined, c. calculating the at least one evaluation variable by analysing the main model and the reference model, d. calculating a particular model-specific quality error from a deviation of the at least one calculated evaluation variable from existing measured values, e. calculating a cross-model overall error from the quality errors, and f. adapting the parameters to be determined in the main model and in the reference model. The invention further relates to a use of a method according to the invention and to a simulation computer.

Description

[0001] R.416002

[0002] - 1 -

[0003] Description

[0004] Title:

[0005] Methods for parameter determination in the modeling of a technical system, simulation computer

[0006] The present invention relates to a method for determining parameters in the modeling of a technical system, preferably a fuel cell stack or an electrolysis stack. The invention further relates to the use of such a method and a simulation computer.

[0007] State of the art

[0008] In the development, design, and manufacturing of complex systems, a thorough understanding of the system is crucial. System models are simulated to predict system behavior and long-term changes, such as aging effects. However, models are always imperfect system replicas and can therefore only approximate reality. Consequently, resulting simulation results often deviate from reality. This is because physical relationships and certain parameters are frequently unknown or only very imprecisely integrated into the models. A good example of this is the modeling of a fuel cell stack. Knowledge of specific production tolerances, contact resistances, contact pressures, membrane aging, etc., is often lacking. Therefore, model predictions frequently do not exactly match a concrete, manufactured fuel cell stack.

[0009] Model parameters can generally be divided into three categories. The first is the category of fixed parameters, also called basic parameters. These are usually known or directly measurable. Furthermore, they are transferable between two systems, for example, between two manufactured fuel cell stacks, without modification. Fixed parameters include, for example, geometry, the number of installed cells, and nominal sizes. The second category is that of system-invariant parameters.

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[0011] These parameters are typically unknown and not directly measurable. Rather, they are often only observable indirectly through their effect on certain system behaviors. System-invariant parameters are generally transferable between systems without any change occurring. In the aforementioned case of the fuel cell stack, an example of a system-invariant parameter would be electrochemical activity. The third category is that of system-variable parameters. These are similar in nature to system-invariant parameters, with the difference that they are generally not transferable between systems without change. Continuing with the fuel cell stack example, examples include the thickness of individual membranes, contact pressures, production tolerances, and membrane aging.

[0012] The distinction between system-variable and system-invariable parameters depends on the systems under consideration and is often fluid. Furthermore, system-invariable and system-variable parameters cannot generally be observed in isolation, but only in their combined effect. This can complicate their determination or, in extreme cases, even make it impossible. However, determining or estimating system-variable and system-invariant parameters is of great value for model accuracy. Moreover, they can serve as reliable indicators of a system's state.

[0013] The invention therefore addresses the problem of enabling the determination of such system-invariant and system-variable parameters. To solve this problem, a method with the features of claim 1 is proposed. Preferred embodiments are described in the dependent claims. Furthermore, the use of a method according to the invention and a simulation computer are proposed.

[0014] Disclosure of the invention

[0015] A method for determining parameters in the modeling of a technical system, preferably a fuel cell stack or an electrolysis stack, is proposed, wherein the parameters of the technical system to be determined are system variables and system invariables. R.416002

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[0017] Parameters are subdivided. According to the invention, the following steps are carried out:

[0018] a. Creating one model of the technical system as the main model and one model of a reference system as the reference model,

[0019] b. Selecting at least one rating parameter by which the quality of the main model and / or the reference model is measured, wherein the at least one rating parameter is influenced by all parameters to be determined and / or a part of the parameters to be determined,

[0020] c. Calculate at least one rating parameter by evaluating the main model and the reference model,

[0021] d. Calculating a respective model-specific error in performance from a deviation of the calculated at least one evaluation parameter from existing measured values,

[0022] e. Calculating a model-wide overall error from the fit errors and

[0023] f. Adjusting the parameters to be determined in the main model and in the reference model.

[0024] Using the proposed method, parameters can be determined that may not be measurable, or not easily measurable, on the technical system. This applies particularly to parameters whose influence, in conjunction with other parameters and quantities, cannot be readily isolated.

[0025] The parameters to be determined are common to both the technical system and the reference system, or the main model and the reference model. System-invariant parameters are those that must be determined in each individual case but can be transferred unchanged from the technical system to the reference system and vice versa. R.416002

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[0027] System-variable parameters are those that must be determined on a case-by-case basis but cannot be transferred unchanged between the technical system and the reference system. The system-invariant and system-variable parameters together form part or all of the input variables to the main model and the reference model. The output variable of the models is the evaluation variable selected in section b. This variable depends on the system and the parameters to be determined. In the case of a fuel cell stack, these could include, for example, a current density distribution, a total voltage drop, a temperature distribution, a coolant temperature, a pressure drop in the anode and / or cathode path, a global or local impedance, a tempering humidity, or other parameters. The main model and the reference model do not necessarily have to use the same evaluation variables.The evaluation criteria need only depend on all or some of the parameters to be determined.

[0028] The previously available measured values ​​for at least one evaluation parameter used to determine the quality error are derived from previously conducted experiments and / or test bench measurements. The quality error corresponds, for example, to the difference between the measured values ​​and the respective calculated evaluation parameter.

[0029] The total error results from combining the various quality errors. This combination can be achieved, for example, by adding the quality errors, by scaling and subsequent addition, or by applying any other error measure. Minimizing the total error is the objective criterion for adjusting the parameters to be determined.

[0030] In a further development of the invention, it is proposed that steps c to f be repeated to minimize the overall error. With this preferred embodiment, a method according to the invention becomes accessible to mathematical optimization algorithms and the accuracy of parameter determination is increased. R.416002

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[0032] It is further proposed that a subsystem of the technical system be chosen as the reference system. Models of subsystems often provide more precise data and predictions. In the preferred embodiment, insights from such subsystems are incorporated into the main model. The subsystem is preferably a subscale system, for example, a single fuel cell. In this case, the technical system would be, for example, a fuel cell stack, and the reference system a single cell; system-invariant parameters could therefore be, for example, the electrochemical activity or membrane resistances. System-variable parameters would be, for example, contact resistances or pressure losses.

[0033] In a further embodiment of the invention, it is proposed that a system identical in construction to the technical system be selected as the reference system. Identical systems are fundamentally manufactured identically, but differ discretely in manufacturing-related degrees of freedom that are uncontrollable, for example, production tolerances. This preferred embodiment improves the modeling of a product series, enhances the understanding of the influence of tolerances on an overall system, and enables the use of a method according to the invention for qualifying a fuel cell stack. Extending the fuel cell stack example, in this case the technical system would be a fuel cell stack, the reference system an identical fuel cell stack; system-invariant parameters would be, for example, electrochemical activity, and system-variable parameters would consequently be production tolerances, contact pressures, membrane thicknesses, contact resistances, and the like.

[0034] In a further embodiment of the invention, it is proposed that the technical system in a more recent state of aging be selected as the reference system. This preferred embodiment enables the use of a method according to the invention for detecting aging phenomena. Extending the example of the fuel cell system, in the present case the reference system would be a fuel cell stack in its new condition, and the technical system would be a fuel cell stack in an aged state, for example, after 10,000 operating hours. System-invariant parameters would then be, for example, production tolerances and membrane thicknesses, while system-variable parameters would be...

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[0036] Parameters in this case would include, among other things, electrochemical activity or membrane aging.

[0037] It is further proposed that at least one parameter to be determined be initialized with a starting value before evaluating the main model and the reference model. This preferred embodiment generates a boundary condition for the simulation. The more accurately the starting value is estimated, the lower the computational and iteration effort.

[0038] Furthermore, it is proposed that the performance of the technical system and / or the reference system be chosen as the variable of motion. Performance is a strong comparison criterion because it is dependent on a multitude of influences. This makes it a meaningful evaluation parameter for most applications when determining parameters.

[0039] It is further proposed that the total error in step e be calculated by adding, weighted addition, averaging, and / or averaging a squared error of the quality errors. With this preferred embodiment, the quality errors are normalized for aggregation into a total error, thereby making them compatible. Furthermore, the measured values ​​determining the quality errors typically originate from experiments and test bench measurements of varying quality, and therefore have different levels of reliability. The preferred embodiment allows for greater consideration of more reliable results and quality errors in parameter determination than those with lower reliability.

[0040] Furthermore, it is proposed that an optimization algorithm, preferably a simplex algorithm, Gaussian optimization, or a gradient-based algorithm, be used to adjust the parameters in step f. Using an optimization algorithm quickly and efficiently leads to a set of parameters that ensures a high degree of agreement between model predictions and system behavior on the test bench. R.416002

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[0042] This preferred embodiment thus increases the quality and precision of the parameter determination.

[0043] Furthermore, it is proposed that in step f, the system-invariant parameters are adjusted in both models, while the system-variable parameters are adjusted only in the main model. The preferred embodiment allows for the system-variable parameters of the reference model, which, unlike the system-invariant parameters, can have a different value than in the main model, to be determined by other means, for example, through experiments and / or test bench measurements. This increases the precision of the parameter determination.

[0044] Furthermore, it is proposed that the system-variable parameters of the reference model be measured in whole or in part and / or determined experimentally. This preferred embodiment increases the additional information content contributed by the reference system to the parameter determination and improves the precision of the parameter determination.

[0045] Furthermore, it is proposed that at least one system-variable parameter of the main model be formulated as a scaling factor of a system-variable and / or system-invariant parameter of the reference model. With this preferred embodiment, parameters for which no measured values ​​can be generated can also be taken into account during parameter determination. In this case, the parameter determination does not provide a direct value for the individual parameter, but rather knowledge of the relative relationship between the parameter in the technical system and in the reference system.

[0046] Furthermore, the use of a method according to the invention for estimating an aging state, determining production tolerances, and / or improving an operating strategy of a fuel cell stack is proposed. A method according to the invention is particularly suitable for the aforementioned uses. Such a use has the aforementioned properties and advantages. R.416002

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[0048] A simulation computer is also proposed, which is configured to carry out steps of a method according to the invention. Such a simulation computer has the aforementioned properties and advantages.

[0049] The invention is described in more detail below with reference to figures. They show

[0050] Fig. 1: a schematic sequence of a method according to the invention in a preferred embodiment,

[0051] Fig. 2: a schematic sequence of the use of a method according to the invention for evaluating an aging state and improving an operating strategy.

[0052] Character description

[0053] Fig. 1 shows an exemplary schematic sequence of a method according to the invention. The physical relationships of the technical system are represented in a main model, and the physical relationships of a reference system are represented in a reference model. In a first process step S1.1, the parameters of the main model, in particular the parameters to be determined, are initialized, and a plurality of evaluation variables for the main model are calculated by evaluating the main model. In a further process step S1.2, the parameters, in particular the parameters to be determined, of the reference model are initialized, and a plurality of evaluation variables for the reference model are calculated. In a further multi-part process step, S2.1 and S2.2. A comparison of the respective evaluation parameters with previously obtained measurements M from experiments and / or test benches is performed, and the respective fit errors are calculated for both the main model and the reference model. In a subsequent process step S3, a total error is generated from these fit errors. This total error is used in a subsequent process step S4 as the target criterion of an optimization algorithm to calculate new parameters. In a subsequent process step S5.1, the newly calculated system invariants R.416002.

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[0055] Parameters are passed to the main model and the reference model. In a further process step S5.2, the newly calculated system variables are passed to the main model. Process steps S1.1 to S5.2 are iterated until altering the parameters to be determined no longer results in a significant reduction of the overall error.

[0056] Fig. 2 shows a schematic sequence of a preferred use of a method according to the invention for evaluating the aging state and adapting an operating strategy of a fuel cell stack. In a first process step V1, a reference system is modeled. In a concurrent process step V2, the technical system to be evaluated, for example, a fuel cell stack, is modeled. In a subsequent process step V3, a joint parameter determination is carried out according to a method according to the invention. In a subsequent process step V4, system-invariant parameters of the reference model and the main model are determined. Likewise, in a process step V5, the system-variable parameters for the main model are determined. In a subsequent process step V6, a characteristic value for the aging state is derived from the system-variable parameters, and this aging state is then evaluated.Subsequently, depending on requirements, an operating strategy for this fuel cell stack and / or for identical fuel cell stacks is adapted in a process step V7.

Claims

R.416002 - 10 - Claims 1. Method for determining parameters in the modeling of a technical system, preferably a fuel cell stack or an electrolysis stack, wherein the parameters of the technical system to be determined are subdivided into system-variable and system-invariable parameters, characterized by the following steps: a. Creating one model of the technical system as the main model and one model of a reference system as the reference model, b. Selecting at least one rating parameter by which the quality of the main model and / or the reference model is measured, wherein the at least one rating parameter is influenced by all parameters to be determined and / or a part of the parameters to be determined, c. Calculating at least one evaluation parameter by evaluating the main model and the reference model, d. Calculation of a respective model-specific error in performance from a deviation of at least one calculated evaluation parameter from existing measured values, e. Calculating a model-wide overall error from the fit errors and f. Adjusting the parameters to be determined in the main model and in the reference model.

2. The method of claim 1, characterized in that steps c. up to f. to minimize the overall error.

3. Method according to claim 1 or 2, characterized in that a subsystem of the technical system is selected as the reference system.

4. Method according to claim 1 or 2, characterized in that a system identical in construction to the technical system is selected as the reference system. R.416002 - 11 - 5. Method according to claim 1 or 2, characterized in that the technical system in a younger state of aging is selected as the reference system.

6. Method according to one of the preceding claims, characterized in that at least one parameter to be determined is initialized with a starting value before evaluating the main model and the reference model.

7. Method according to one of the preceding claims, characterized in that a performance of the technical system and / or the reference system is selected as the evaluation parameter.

8. Method according to one of the preceding claims, characterized in that the total error in step e. is calculated by adding, weighted adding, averaging and / or averaging a squared error of the quality errors.

9. Method according to one of the preceding claims, characterized in that an optimization algorithm, preferably a simplex algorithm, a Gaussian optimization or a gradient-based algorithm, is used to adjust the parameters in step f.

10. Method according to one of the preceding claims, characterized in that in step f. the system-invariant parameters are adjusted in both models, but the system-variable parameters are adjusted only in the main model.

11. Method according to one of the preceding claims, characterized in that the system variable parameters of the reference model are wholly or partially measured and / or experimentally determined.

12. A method according to any of the preceding claims, characterized in that at least one system-variable parameter of the main model is formulated as a scaling factor of a system-variable and / or system-invariant parameter of the reference model. R.416002 - 12 - 13. Use of a method according to claims 1 to 12 for estimating an aging state, determining production tolerances and / or improving an operating strategy of a fuel cell stack.

14. Simulation computer configured to perform steps of a method according to claims 1 to 12.

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