System and method for estimating durability test results for fuel cell systems

Abstract

To provide a technology capable of estimating the durability of a fuel cell system regardless of using conditions that a fuel cell system experiences.SOLUTION: A system comprises: a first storage device that stores a durability test result actually conducted over a first period under a first using condition as learning data; and a first arithmetic device that has a machine learning model to perform machine learning using the learning data stored in the first storage device, the machine learning model estimating the result when the durability test is conducted under a second using condition. The first using condition is the one that prescribed operation parameters influencing on the deterioration of a fuel cell system appear with equal frequency over all domains of the operation parameter. The second using condition is the one that the operation parameter appears with unequal frequency at least in the partial domain.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The technology disclosed in this specification relates to a system and method for estimating the results of a durability test on a fuel cell system. [Background technology]

[0002] Patent Document 1 describes a technology for reusing batteries installed in vehicles in other products. In this technology, both operation data of the battery before reuse and operation data of the battery after reuse are collected, and a machine learning model that estimates the durability (lifespan) of the battery is created by machine learning using the collected operation data as learning data. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] JP 2020-162309 A Summary of the Invention [Problem to be solved by the invention]

[0004] In general, before offering a new product such as a vehicle to the public, it is necessary to carry out a durability test of the fuel cell system to be installed in the vehicle. However, if the durability test is carried out until the end of the life of the fuel cell system, it will take a huge amount of time. As one means for solving this problem, it is considered to estimate the durability of the fuel cell system by using an estimation model that has been subjected to machine learning, as in Patent Document 1 mentioned above.

[0005] However, even for the same fuel cell system, the usage conditions experienced by the fuel cell system vary widely depending on the type and use of the vehicle in which it is installed. That is, a fuel cell system has various operating parameters (e.g., current, rate of change of voltage, outside air temperature, etc.), but the range of values ​​that each operating parameter can take and the frequency of occurrence vary depending on the type and use of the vehicle in which it is installed. These operating parameters affect the deterioration of the fuel cell system. Therefore, according to the conventional idea, it is necessary to individually prepare an estimation model that has been subjected to machine learning depending on the usage conditions experienced by the fuel cell (e.g., the type and use of the vehicle in which it is installed).

[0006] The present specification provides a technique that allows for the durability of a fuel cell system to be estimated regardless of the usage conditions experienced by the fuel cell system. [Means for solving the problem]

[0007] The technology disclosed in this specification is embodied in a system for estimating the results of a durability test on a fuel cell system. In a first aspect, the system may include a first storage device that stores the results of a durability test actually performed over a first period under a first use condition as learning data, and a first computing device having a machine learning model that performs machine learning using the learning data stored in the first storage device and estimates the results when the durability test is performed under a second use condition. In this case, the first use condition may be a use condition in which a predetermined operating parameter that affects the deterioration of the fuel cell system appears with equal frequency over the entire range of the operating parameter, and the second use condition may be a use condition in which the operating parameter appears with unequal frequency in at least a part of the range.

[0008] In the above-mentioned system, the results of a durability test actually performed under the first use condition are stored as learning data. Then, machine learning is performed using the learning data to create a machine learning model that estimates the durability of the fuel cell system under the second use condition (more specifically, the results of the durability test). Under the first use condition, a predetermined operating parameter that affects the deterioration of the fuel cell system appears with equal frequency over the entire range of the operating parameter. By using such unbiased durability test results, a highly versatile machine learning model that can be widely adapted to various use conditions can be prepared. This makes it possible to estimate the durability of the fuel cell system regardless of the content of the second use condition, i.e., regardless of the use conditions experienced by the fuel cell system.

[0009] In a second aspect, in the first aspect described above, the system may further include a second storage device that stores the results of a durability test actually performed under a second use condition for a second period shorter than the first period as first evaluation data, and a second arithmetic device that compares and evaluates the results within the second period estimated by the first arithmetic device with the first evaluation data stored in the second storage device. By performing such a comparison evaluation, for example, a user can objectively confirm the validity of the estimation by the system. If the reliability is lower than the reference value, the results of an actual durability test under the second use condition may be learned, and the first arithmetic device may be caused to correct the machine learning model.

[0010] In a third aspect, in the second aspect described above, the second storage device may further store the results of a durability test actually performed under the third use condition for the first period as second evaluation data, and the first arithmetic device may further estimate the results of a durability test performed under the third use condition until the second period or later using the second evaluation data stored in the second storage device, and the second arithmetic device may further compare and evaluate the results under the third use condition estimated by the first arithmetic device with the second evaluation data stored in the second storage device. By performing such a comparison and evaluation, for example, a user can objectively confirm the validity of the estimation by this system. If the estimation accuracy is lower than the reference value, the results of an actual durability test under the third use condition may be learned and the first arithmetic device may be caused to correct the machine learning model.

[0011] In a fourth aspect, in the third aspect described above, the second storage device may further store the results of a durability test actually performed over a second period under a fourth use condition as third evaluation data, the first arithmetic device may further estimate the results of a durability test performed under the fourth use condition up to the second period using the third evaluation data stored in the second storage device, and the second arithmetic device may further compare and evaluate the results under the fourth use condition estimated by the first arithmetic device with the third evaluation data stored in the second storage device. By performing such a comparison and evaluation, for example, a user can objectively confirm the validity of the estimation by this system for a plurality of use conditions.

[0012] The technology disclosed in this specification is embodied in a method for estimating the results of a durability test on a fuel cell system. The method may include a step of storing the results of a durability test actually performed under a first use condition for a first period in a first storage device as learning data, and a step of causing a machine learning model, which is a machine learning model that uses the learning data stored in the first storage device to perform machine learning and is possessed by a first computing device, to estimate the results when the durability test is performed under a second use condition. In this case, the first use condition may be a use condition in which a predetermined operating parameter that affects the deterioration of the fuel cell system appears with equal frequency over the entire range of the operating parameter, and the second use condition may be a use condition in which the operating parameter appears with unequal frequency in at least a part of the range. With this configuration, the durability of the fuel cell system can be estimated regardless of the content of the second use condition, i.e., regardless of the use condition experienced by the fuel cell system. [Brief description of the drawings]

[0013] [Figure 1] FIG. 1 is a block diagram showing a configuration of an estimation system according to a first embodiment. [Diagram 2] A diagram showing the durability test time carried out under each operating condition [Diagram 3] Graph showing cumulative time (t) versus current (I) under equal frequency of use. [Figure 4] 1 is a graph showing cumulative time (t) versus current (I) under first product usage conditions. [Diagram 5] Graph showing cumulative time (t) versus current (I) under second product usage conditions. [Figure 6] 3 is a graph showing cumulative time (t) versus current (I) under the third product usage condition. [Figure 7] 4 is a graph showing cumulative time (t) versus current (I) under the fourth product usage condition. [Figure 8] FIG. 4 is a diagram for explaining a learning model of the first arithmetic device. [Figure 9] FIG. [Figure 10] A diagram explaining equal frequency (especially the Gini coefficient). [Figure 11] 1 is a flowchart showing the steps of an estimation method. [Figure 12] FIG. 11 is a block diagram showing a configuration of an estimation system according to a second embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0014] (Example 1) The configuration of an estimation system 10 of this example will be described with reference to Fig. 1. This estimation system 10 estimates the results of a durability test on a fuel cell system. As an example, the fuel cell system estimated by the estimation system 10 is mounted on a vehicle.

[0015] As shown in FIG. 1, the estimation system 10 is communicatively connected to a measuring device 12. The measuring device 12 is a device that performs a durability test of the fuel cell system. The measuring device 12 acquires values ​​of various parameters measured by sensors at predetermined time intervals, and stores the values ​​as time-series data in association with time information together with control signals for controlling the fuel cell system (e.g., target current, etc.). The various parameters here refer to the voltage, current, voltage speed, temperature, gas flow rate, gas pressure, etc. of the fuel cell system. The measuring device 12 transmits the results of the durability test of the fuel cell system to the estimation system 10 as learning data D1 and evaluation data D2.

[0016] The estimation system 10 includes a first storage device 14, a second storage device 16, a first arithmetic device 18, and a second arithmetic device 20. The first storage device 14 is communicatively connected to the measurement device 12 and the first arithmetic device 18. The first storage device 14 has a memory. The first storage device 14 stores learning data D1 provided from the measurement device 12. The first storage device 14 transmits the stored learning data D1 to the first arithmetic device 18. The second storage device 16 is communicatively connected to the measurement device 12 and the second arithmetic device 20. The second storage device 16 has a memory. The second storage device 16 stores evaluation data D2 provided from the measurement device 12. The first storage device 14 transmits the stored learning data D1 to the first arithmetic device 18.

[0017] The first arithmetic device 18 has a memory and a CPU. The first arithmetic device 18 causes the CPU to execute various processes based on programs previously stored in the memory. The first arithmetic device 18 has a learning model 19 stored in the memory. The first arithmetic device 18 causes the learning model 19 to perform machine learning on the learning data D1 received from the first storage device 14. The first storage device 14 uses the learning model 19 to estimate the results of a durability test of the fuel cell system. The first arithmetic device 18 is connected to the second arithmetic device 20 so as to be able to communicate with each other. The first arithmetic device 18 transmits the results of the durability test estimated by the learning model 19 to the second arithmetic device 20.

[0018] The second arithmetic device 20 has a memory and a CPU. The second arithmetic device 20 causes the CPU to execute various processes based on programs previously stored in the memory. The second arithmetic device 20 evaluates the estimated result of the durability test received from the first arithmetic device 18 by comparing it with the evaluation data D2 received from the second storage device 16. Specifically, the second arithmetic device 20 outputs the error between the estimated result of the durability test by the first arithmetic device 18 and the evaluation data D2.

[0019] The learning data D1 and the evaluation data D2 will be described with reference to Fig. 2 to Fig. 7. The results of a durability test of a fuel cell system are affected by the usage conditions (type of vehicle, application, usage environment, etc.) experienced by the fuel cell system. That is, depending on these usage conditions, the range of values ​​that various operating parameters (hereinafter referred to as deterioration parameters) that affect the deterioration of the fuel cell system can take and the frequency of occurrence (i.e., accumulated time) differ. The deterioration parameters are, for example, the current, the rate of change of voltage, and the outside air temperature.

[0020] As shown in FIG. 2, the learning data D1 includes durability test data (hereinafter simply referred to as data) under equal-frequency use conditions. The data under equal-frequency use conditions is the result of a durability test carried out over a first period (T1) under equal-frequency use conditions. The first period (T1) is a period required as a test period for a durability test in a fuel cell system. The equal-frequency use conditions are use conditions that appear with equal frequency in all ranges of the deterioration parameters in the fuel cell system. Under equal-frequency use conditions, for example, the current (I), which is one of the deterioration parameters, has the same cumulative time (t) over all ranges of possible values, as shown in FIG. 3.

[0021] The evaluation data D2 includes data on the first product use condition, the second product use condition, the third product use condition, and the fourth product use condition. The data on the first product use condition is the result of a durability test carried out over a first period (T1) under the first product use condition. In the first product use condition, as shown in FIG. 4, for example, the current (I) has a long cumulative time (t) in a relatively low current range and a short cumulative time (t) in a relatively high current range. The relatively low current range here means a current range lower than half the maximum current value among all ranges of the range of values ​​that the current (I) can take, and the relatively high current range means a current range higher than half the maximum current value among all ranges of the range of values ​​that the current (I) can take.

[0022] The data for the second to fourth product use conditions are the results of durability tests carried out over a second period (T2) under the second to fourth product use conditions. The second period (T2) is shorter than the first period. The second period (T2) is, for example, one-tenth of the first period. Under the second product use condition, the current (I) has a short cumulative time in a relatively low current range and a long cumulative time (t) in a relatively high current range, as shown in FIG. 5, for example. Under the third product use condition, the current (I) has the longest cumulative frequency (t) at half the maximum current value, as shown in FIG. 6, for example. Under the fourth product use condition, the current (I) has a relatively long cumulative time (t) near half the maximum current value, as shown in FIG. 7, for example. The distribution under the fourth product use condition is broader than that under the first to third use conditions.

[0023] As described above, the first to fourth product use conditions are use conditions under which a deterioration parameter (e.g., current) appears with unequal frequency in at least a part of its range. The first, second, third and fourth product use conditions are use conditions with different frequencies of appearance. Here, the "equal frequency use condition", "first product use condition", "second product use condition" and "third product use condition" are examples of the "first use condition", "third use condition", "second use condition" and "fourth use condition" in the technology disclosed in this specification.

[0024] The learning model 19 will be described with reference to FIG. 8. When the product use condition to be estimated, for example, the second product use condition, is input, the learning model 19 of the first arithmetic device 18 outputs an estimate of the result of the durability test under the second product use condition. The input parameters (use conditions) include a current value, a temperature, a voltage change rate, and an operating time. Here, the output parameter (result of the durability test) is, for example, a voltage value of the fuel cell system when the current of the fuel cell system is a predetermined value. The higher the voltage value, the higher the durability of the fuel cell system is determined to be, and the lower the voltage value, the lower the durability of the fuel cell system is determined to be. The learning model 19 may be optimized using a part of the learning data D1 read from the first storage device 14 so that when the input of the use condition is given, the error between the estimated value of the output and the result of the durability test actually performed is minimized. In addition, in order to ensure the generalization performance of the learning model 19, a part of the learning data D1 may be secured in the first arithmetic device 18 for verification. In this case, the secured data may be used to avoid overlearning.

[0025] The output parameter of the learning model 19 is not limited to a voltage value at a specific current value, but may be a voltage value under a specific condition, such as a voltage value at a specific temperature / gas supply amount. The output parameter may be an index value that represents the degree of deterioration of the fuel cell system. In a modified example, the output parameter may be, for example, the amount of gas leaking from a gas tank when hydrogen is pressurized under specific conditions.

[0026] In this embodiment, ElasticNet is used as the learning model 19. However, the learning model 19 is not particularly limited, and other machine learning models such as regression other than ElasticNet (e.g., Ridge regression, Lasso regression, etc.) and neural networks may be used.

[0027] The second arithmetic device 20 can compare and evaluate the results of the durability test under the second product use condition estimated by the learning model 19 of the first arithmetic device 18 with the data of the second product use condition in the evaluation data D2 stored in the second storage device 16. In this case, the results of the durability test under the second product use condition estimated up to the second period (T2) are compared with the data of the second product use condition actually performed up to the second period (T2), and the second arithmetic device 20 outputs the error between these two values. This allows the user to objectively confirm the validity (reliability) of the estimation of the results of the durability test by the estimation system 10, even though it is short-term data. If the validity of the estimation is lower than the reference value, that is, if the output error is larger than the reference value, the results of the actual durability test under the second product use condition may be machine-learned, and the first arithmetic device 18 may be caused to correct the machine learning model. The error here may be a mean squared error or a root mean squared error (RMSE). Furthermore, the estimation system 10 estimates the durability results not only for the second product use condition, but also for the first product use condition, the third product use condition, or the fourth product use condition. In this case, the estimated durability test results up to the second period (T2) under the same use condition are compared with the data of the durability test actually performed up to the second period (T2) for a comparative evaluation. By performing such a comparative evaluation, for example, the user can objectively confirm the validity of the estimation by this system for a plurality of use conditions.

[0028] Further, the second arithmetic device 20 estimates the result of the durability test under the first product use condition by the learning model 19 of the first arithmetic device 18. Therefore, the second arithmetic device 20 can compare and evaluate the result of the durability test under the first product use condition estimated by the learning model 19 of the first arithmetic device 18 with the data of the first product use condition in the evaluation data D2 stored in the second storage device 16. In this case, the result of the durability test under the first product use condition estimated up to the first period (T1) is compared with the data of the first product use condition actually performed up to the first period (T1), and the second arithmetic device 20 outputs the error between these two values. This allows the user to objectively confirm the validity (reliability) of the estimation of the durability test result by the estimation system 10, even for the period required for the durability test.

[0029] Although the period of the results is short, the estimation system 10 makes it possible to confirm the validity (reliability) of the estimation of the results of the durability test under the four use conditions. Therefore, the user can also confirm the validity of the estimation based on the data for the first period (T1) of the first product use condition described above, i.e., the entire period of the durability test, from the error trends under these four use conditions.

[0030] Here, the equal frequency will be described with reference to FIG. 11 and FIG. 12. In this specification, the equal frequency is defined as "the variance of the parameter is A / 2 or more and 2A or less. Here, A is the variance (upper limit-lower limit)^2 / 12 when the parameter is uniformly distributed in the range (operation guarantee range) that the parameter can take." and "the Gini coefficient of the frequency of a set in which one or more data exist in the data of the parameter value is 0.5 or less." The former indicates that the range of data change is on the same order as the uniform distribution. The latter indicates that the Gini coefficient can take values ​​from 0 to 1, and a Gini coefficient of 0.5 or less indicates that the data is not unevenly distributed at a specific value. Preferably, from the viewpoint of the reliability of the machine learning results, the degradation parameter should be uniformly distributed over the range of values ​​that the degradation parameter can take, since the usage conditions when the product is specified are not known in advance. In this case, the variance of the parameter is A, and the Gini coefficient is 0. As for the variance, since it can be any value depending on the data, the range should not be determined by absolute values, but by orders of magnitude (digits) so as to be close to a uniform distribution. In other words, it is better to determine the range by ratio (equally spaced in logarithms). There are cases where the degradation parameters cannot be specified independently of each other. For example, when the current and voltage are determined while other conditions are fixed, once one is determined, the other is determined by the IV characteristics, and it is not possible to simultaneously specify each at an arbitrary value depending on the test conditions. In particular, when the IV characteristics are nonlinear, it is impossible to simultaneously achieve a uniform distribution. In such cases, data can be obtained under conditions that make the frequency distribution of each parameter in the divided time periods approximately the same, and the continuum / collection of these can be used as the learning data D1.

[0031] In general, before a new vehicle is released to the market, it is necessary to conduct durability tests on the fuel cell system installed in the vehicle. However, if durability tests are conducted until the end of the life of the fuel cell system, it will take a huge amount of time. One of the means to solve this problem is to estimate the durability of the fuel cell system by using an estimation model that uses machine learning.

[0032] However, even for the same fuel cell system, the usage conditions experienced by the fuel cell system vary widely depending on the type and use of the vehicle in which it is installed. That is, a fuel cell system has various operating parameters (e.g., current, voltage fluctuation rate, outside air temperature, etc.), but the range of values ​​that each operating parameter can take and the frequency of occurrence vary depending on the type and use of the vehicle in which it is installed. These operating parameters affect the deterioration of the fuel cell system. Therefore, according to the conventional idea, it is necessary to individually prepare an estimation model that has been subjected to machine learning depending on the usage conditions experienced by the fuel cell (e.g., the type and use of the vehicle in which it is installed).

[0033] In view of the above-mentioned problems, in the estimation system 10 of this embodiment, the results of a durability test actually performed under equal-frequency use conditions are stored as learning data D1. Then, by performing machine learning using the learning data D1, a learning model 19 is created that estimates the durability (more specifically, the results of the durability test) of the fuel cell system under, for example, the second product use conditions. Under equal-frequency use conditions, a predetermined deterioration parameter that affects the deterioration of the fuel cell system appears with equal frequency over the entire range of the deterioration parameter. By using such unbiased durability test results, a highly versatile learning model 19 that can be widely adapted to various use conditions can be prepared. This makes it possible to estimate the durability of the fuel cell system regardless of the contents of the second product use conditions, i.e., regardless of the use conditions experienced by the fuel cell system.

[0034] Therefore, even if the usage conditions for which it is desired to estimate the results of the durability test are other usage conditions such as the first product use conditions, the third product use conditions, the fourth product use conditions, etc. instead of the second product use conditions, it is possible to estimate the durability of the fuel cell system under the desired usage conditions.

[0035] Next, referring to FIG. 11, the procedure of the durability estimation process (estimation method) executed by the estimation system 10 will be described. Here, it is assumed that the usage condition under which the durability of the fuel cell system is to be estimated is the second product usage condition. First, in step S12, the estimation system 10 executes a storage process. In the storage process, the estimation system 10 stores learning data D1 under the equal frequency usage condition in the first storage device 14. Next, in step S14, the estimation system 10 executes a machine learning process. In the machine learning process, the estimation system 10 causes the first arithmetic device 18 to machine-train the learning data D1 stored in the first storage device 14 in S12 into the learning model 19. Next, in step S16, the estimation system 10 executes an estimation process. In the estimation process, the estimation system 10 causes the first arithmetic device 18 to estimate the result of the durability test under the second product usage condition. Specifically, by inputting the second product use condition to the learning model 19, the learning model 19 is caused to output an estimated value of the result of the durability test under the second product use condition. From the above steps S12 to S16, the durability under the second product use condition is estimated.

[0036] In the estimation system 10 of this embodiment, the second storage device 16 stores the results of durability tests under four use conditions, namely, the first to fourth product use conditions. The results of the durability tests stored in the second storage device 16 are not limited to the four specification conditions, and the results of durability tests under two, three, or five or more use conditions may be stored. Preferably, the more durability test results there are, the more accurately the validity of the estimation can be verified. Also, the closer the durability test period of the results of the actually performed durability test is to the first period (T1), the more accurately the validity of the estimation can be verified. However, the present technology is effective even when the durability test period is short.

[0037] (Example 2) The configuration of the estimation system 100 of this example will be described with reference to FIG. 12. As shown in FIG. 12, the estimation system 100 includes a storage device 114 and a calculation device 118. The storage device 114 of Example 2 is a device in which the first storage device 14 and the second storage device 16 of Example 1 are integrated. The calculation device 118 of Example 2 is a device in which the first calculation device 18 and the second calculation device 20 of Example 1 are integrated. That is, the storage device 114 has the same functions as the first storage device 14 and the second storage device 16 of Example 1, and the calculation device 118 has the same functions as the first calculation device 18 and the second calculation device 20 of Example 1. Therefore, the estimation system 100 of Example 2 is configured similarly to the estimation system 10 of Example 1, except that the two storage devices 14, 16 and the two calculation devices 18, 20 of Example 1 are each configured as an integrated device. As a result, even with the configuration of the estimation system 100 of this example, the durability of the fuel cell system can be estimated regardless of the usage conditions experienced by the fuel cell system.

[0038] Specific examples of the technology disclosed in this specification have been described in detail above, but these are merely examples and do not limit the scope of the claims. The technology described in the claims includes various modifications and changes to the specific examples exemplified above. The technical elements described in this specification or the drawings exhibit technical utility alone or in various combinations, and are not limited to the combinations described in the claims at the time of filing. The technology exemplified in this specification or the drawings can achieve multiple objectives simultaneously, and achieving one of the objectives itself has technical utility. [Explanation of symbols]

[0039] 10, 100: Estimation system 12: Measurement equipment 14, 16, 114: Storage device 18, 20, 118: Arithmetic device 19: Learning model D1: Training data D2: Evaluation data

Claims

1. A system for estimating a result of a durability test on a fuel cell system, comprising: a first storage device that stores, as learning data, results of the durability test that is actually performed under first usage conditions for a first period of time; a first arithmetic unit having a machine learning model that performs machine learning using the learning data stored in the first storage device, the machine learning model estimating a result when the durability test is performed under second usage conditions; and Equipped with the first use condition is a use condition in which a predetermined operating parameter that affects deterioration of the fuel cell system appears with equal frequency over an entire range of the operating parameter, the second use condition is a use condition in which the operating parameter appears with unequal frequency in at least a portion of the domain; system.

2. a second storage device that stores, as first evaluation data, a result of the durability test that is actually performed under the second usage conditions for a second period that is shorter than the first period; The system according to claim 1 , further comprising a second calculation device that evaluates the results within the second period estimated by the first calculation device against the first evaluation data stored in the second storage device.

3. the second storage device further stores, as second evaluation data, a result of the durability test that is actually performed under third usage conditions for the first period; the first computing device further estimates a result in the case where the durability test is conducted under the third usage condition until the second period or later, using the second evaluation data stored in the second storage device; and 3. The system according to claim 2, wherein the second computing device further evaluates the result under the third usage condition estimated by the first computing device against the second evaluation data stored in the second storage device.

4. the second storage device further stores, as third evaluation data, a result of the durability test that is actually performed under fourth usage conditions for the second period; the first computing device further estimates a result in the case where the durability test is performed under the fourth usage condition up to the second period using the third evaluation data stored in the second storage device; and The system according to claim 3 , wherein the second computing device further evaluates the result under the fourth usage condition estimated by the first computing device against the third evaluation data stored in the second storage device.

5. 1. A method for estimating a result of a durability test on a fuel cell system, comprising: a step of storing, in a first storage device, a result of the durability test that has actually been performed under first usage conditions for a first period of time as learning data; a step of estimating a result of the durability test being performed under second usage conditions by a first arithmetic device having a machine learning model that performs machine learning using the learning data stored in the first storage device; Equipped with the first use condition is a use condition in which a predetermined operating parameter that affects deterioration of the fuel cell system appears with equal frequency over an entire range of the operating parameter, the second use condition is a use condition in which the operating parameter appears with unequal frequency in at least a portion of the domain; method.

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