Degradation trajectory equation solving method and device, storage medium and product

Abstract

The invention discloses a degradation trajectory equation solving method and device, a storage medium and a product. The method comprises the following steps: fitting a degradation trajectory equation according to accelerated degradation test data of different stress groups; solving a first pseudo life according to the degradation path equations of different stress groups and a first failure threshold; solving an undetermined coefficient of the acceleration model according to the first pseudo-life of the different stress groups so as to obtain an acceleration equation; solving a second pseudo life according to the degradation path equations of different stress groups and different second failure thresholds; resolving parameters irrelevant to stress according to the ith stress group and a second pseudo life different from a second failure threshold value; updating the acceleration equation according to parameters irrelevant to stress under different second failure thresholds; substituting the actual stress group into an acceleration equation under different second failure thresholds to obtain a third pseudo life; and solving a degradation trajectory equation of the normal stress group according to the third pseudo-life under different failure thresholds. According to the method, the solution of the multi-parameter degradation trajectory equation is realized.

Description

Technical Field

[0001] The present invention belongs to the field of energy storage power supply reliability research, and in particular relates to a method for solving a multi-parameter degradation trajectory equation under a normal stress group, a method for solving supercapacitor performance, a device, a storage medium and a product. Background Art

[0002] Supercapacitors are widely used in the field of rail transit energy storage power supply due to their high power density, short charge and discharge time, and long cycle life. However, supercapacitors have performance parameter degradation problems such as capacity attenuation and increased internal resistance during use. In order to better utilize supercapacitor energy storage technology, optimize the design, and perform subsequent maintenance and prediction, it is necessary to study and summarize the degradation law of supercapacitors, obtain the supercapacitor performance degradation trajectory curve through accelerated degradation tests, establish a degradation trajectory model, and predict the life of supercapacitors.

[0003] When processing accelerated degradation test data, after obtaining the degradation trajectory under each stress group, the parameters in the degradation trajectory model are generally used as acceleration parameters to construct the acceleration model, and the acceleration equations of each parameter in the degradation trajectory model are obtained. When the product degradation trajectory model contains more than 3 parameters, the normal acceleration model is used to solve the acceleration equations of each parameter, and then the degradation trajectory under the specified stress group is solved, the error will increase or the solution will be unable to proceed. This is because with the increase of parameters, the degradation trajectory model is more complex and has more degrees of freedom, which may cause the degradation trajectory model to overfit the random fluctuations in the data rather than the real degradation trend; there may be correlation or interaction between different parameters, which may lead to multicollinearity problems during parameter estimation, making the estimation of some parameters unstable or inaccurate; the acceleration model usually assumes that the degradation behavior follows a similar pattern at different stress levels. If there are too many parameters, it may be difficult to find a universal acceleration model to accurately describe the changes of all parameters at different stress levels; in the accelerated degradation test, it is usually extrapolated from high stress levels to normal use conditions. There are too many parameters. This extrapolation may be based on fewer data points and greater uncertainty, which increases the prediction error.

[0004] If the pseudo-life method is used, for the degradation trajectory model with more than 3 parameters, only the life under the normal use stress group can be obtained, and the degradation trajectory cannot be obtained.

[0005] Terminology explanation:

[0006] Degradation trajectory model: a mathematical model that describes the degradation of supercapacitor performance (e.g., capacitance) over time or usage cycle. The parameters in the mathematical model are to be determined.

[0007] Degradation trajectory equation: Degradation trajectory model with known parameters;

[0008] Acceleration model: used in accelerated degradation tests to describe the change in supercapacitor life (the number of charge and discharge cycles corresponding to the failure threshold of performance parameters) under different stress groups (such as temperature and voltage); the parameters in the acceleration model are to be determined;

[0009] Acceleration equation: An acceleration model with known parameters. Summary of the invention

[0010] The purpose of the present invention is to provide a method, device, storage medium and product for solving a degenerate trajectory equation, so as to solve the problem that when the degenerate trajectory model contains more than three parameters, the solution error increases or the solution cannot be solved.

[0011] The present invention solves the above technical problems through the following technical solutions: a method for solving a degenerate trajectory equation, comprising:

[0012] Obtain accelerated degradation test data of supercapacitors under different stress groups;

[0013] According to the accelerated degradation test data under different stress groups, the degradation trajectory equation under the corresponding stress group is fitted;

[0014] Obtaining a first failure threshold; solving a first pseudo life under the corresponding stress group according to the degradation trajectory equation under different stress groups and the first failure threshold;

[0015] Obtaining an acceleration model, solving undetermined coefficients of the acceleration model according to the first pseudo-life under different stress groups, and then obtaining an acceleration equation;

[0016] Obtain multiple second failure thresholds; solve the second pseudo life under the corresponding stress group and the corresponding second failure threshold according to the degradation trajectory equation under different stress groups and different second failure thresholds;

[0017] Resolve the stress-independent parameters in the acceleration equation according to the second pseudo-life of the i-th stress group and different second failure thresholds, and obtain the stress-independent parameters under different second failure thresholds;

[0018] The acceleration equation is updated according to the stress-independent parameters at different second failure thresholds to obtain the acceleration equations at different second failure thresholds;

[0019] Obtaining an actual stress group; substituting the actual stress group into the acceleration equation under different second failure thresholds to obtain a third pseudo life under different second failure thresholds;

[0020] The degradation trajectory equation of the normal stress group is solved according to the third pseudo-life under different failure thresholds.

[0021] Furthermore, the least square method is used to fit the accelerated degradation test data under different stress groups to obtain the degradation trajectory equation under the corresponding stress group.

[0022] Furthermore, the degradation trajectory equations under different stress groups are:

[0023] P i (N i )=a i exp(-N i / b i )+c i N i +d i ;

[0024] Among them, P i represents the performance parameters of the supercapacitor under the i-th stress group, N i represents the number of charge and discharge cycles or degradation tests under the i-th stress group, a i 、b i 、c i and d i They all represent the coefficients under the i-th stress group, i = 1, 2, …, M, and M represents the number of stress groups.

[0025] Furthermore, the acceleration model is:

[0026]

[0027] Where V represents the life of the supercapacitor, A represents the parameter related to the failure threshold L, B represents the parameter related to temperature, T represents the test temperature, and E represents the d Indicates the discharge termination voltage, E c Indicates the charging termination voltage, n d 、n c Indicates parameters related to voltage.

[0028] Further, a plurality of the second failure thresholds are obtained according to the first failure threshold.

[0029] Based on the same concept, the present invention provides a method for solving supercapacitor performance, comprising:

[0030] Get the number of charge and discharge cycles of the supercapacitor;

[0031] The degradation trajectory equation of the normal stress group solved by the degradation trajectory equation solving method as described above is called, and the supercapacitor performance parameters are solved according to the degradation trajectory equation of the normal stress group and the number of charge and discharge cycles.

[0032] Based on the same concept, the present invention provides an electronic device, including a memory, a processor, and a computer program / instructions stored in the memory, wherein the processor executes the computer program / instructions to implement the degradation trajectory equation solving method or supercapacitor performance solving method as described above.

[0033] Based on the same concept, the present invention provides a computer-readable storage medium having a computer program / instruction stored thereon, which, when executed by a processor, implements the above-mentioned method for solving the degradation trajectory equation or the method for solving the supercapacitor performance.

[0034] Based on the same concept, the present invention provides a computer program product, including a computer program / instruction, which, when executed by a processor, implements the above-mentioned method for solving the degradation trajectory equation or the method for solving the supercapacitor performance.

[0035] Beneficial Effects

[0036] Compared with the prior art, the advantages of the present invention are:

[0037] The present invention can solve the multi-parameter (including more than 3 parameters) degradation trajectory equation of the supercapacitor under the normal stress group, and utilizes the solved degradation trajectory equation to realize the solution of the performance parameters of the supercapacitor during normal use, thereby solving the problem that the degradation trajectory equation containing more than 3 parameters has large solution errors or cannot be solved, and provides guidance for the design optimization, use maintenance and life prediction of the supercapacitor energy storage system. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the technical solution of the present invention, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only one embodiment of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0039] Figure 1 is a flow chart of a method for solving a degenerate trajectory equation in an embodiment of the present invention;

[0040] Figure 2 It is a comparison diagram of the fitted degradation trajectory curve and the solved degradation trajectory curve in the embodiment of the present invention. DETAILED DESCRIPTION

[0041] The following is a clear and complete description of the technical solutions in the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0042] The technical solution of the present application is described in detail with specific embodiments below. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described in detail in some embodiments.

[0043] Example 1

[0044] like Figure 1 As shown, a method for solving a degenerate trajectory equation provided by an embodiment of the present invention includes the following steps:

[0045] Step 1: Obtain accelerated degradation test data of supercapacitors under different stress groups.

[0046] The accelerated degradation test is performed on the supercapacitor to obtain accelerated degradation test data. The accelerated degradation test data is the value of the supercapacitor performance parameters (such as capacitance, internal resistance) under specific test conditions (i.e., stress groups) and different charge and discharge cycle numbers (or test numbers). Each stress group includes at least one stress, such as temperature stress, electrical stress (such as charge and discharge voltage, charge and discharge current), etc.

[0047] Step 2: According to the accelerated degradation test data under different stress groups, the degradation trajectory equation under the corresponding stress group is fitted.

[0048] The degradation trajectory is the relationship curve between the performance parameters of the supercapacitor and the number of charge and discharge cycles. There are many forms of degradation trajectory models, such as second-order models, third-order models, exponential linear models, etc. The least squares method or other parameter fitting algorithms are used to fit the accelerated degradation test data under different stress groups, and the degradation trajectory equation under the corresponding stress group can be obtained. In this embodiment, the degradation trajectory model is an exponential linear model as an example, and the degradation trajectory model is set as:

[0049] P(N)=aexp(-N / b)+cN+d (1)

[0050] Where P represents the performance parameter of the supercapacitor, N represents the number of charge and discharge cycles or the number of degradation tests, and a, b, c and d all represent unknown coefficients. For the i-th stress group, the degradation trajectory equation under the i-th stress group can be expressed as:

[0051] P i (N i )=a i exp(-N i / b i )+c i N i +d i (2)

[0052] Among them, P irepresents the performance parameters of the supercapacitor under the i-th stress group, N i represents the number of charge and discharge cycles or degradation tests under the i-th stress group, a i 、b i 、c i and d i All represent the coefficients under the i-th stress group, i = 1, 2, ..., M, M represents the number of stress groups. Based on the accelerated degradation test data under the i-th stress group, a can be calculated i 、b i 、c i and d i , so a i 、b i 、c i and d i All are known parameters.

[0053] Step 3: Obtain the first failure threshold; solve the first pseudo life under the corresponding stress group according to the degradation trajectory equation and the first failure threshold under different stress groups.

[0054] Pseudo-lifetime refers to the number of accelerated degradation tests corresponding to when the supercapacitor performance parameters (such as capacitance value, internal resistance value) degrade to the failure threshold under specific test conditions (i.e. stress group). The first failure threshold can be determined according to the relevant standards or industry regulations of supercapacitors. For example, the first failure threshold corresponding to the capacitance of the supercapacitor is 80% of the initial value of the capacitance (i.e. rated capacitance), and the first failure threshold corresponding to the internal resistance of the supercapacitor is 200% of the initial value of the internal resistance.

[0055] Determining the first failure threshold is to determine the performance parameters of the supercapacitor. Substituting the first failure threshold into formula (2), the corresponding N can be obtained. i , thus we can get M groups of data: L f 、i、N if , where L f represents the first failure threshold (which is the same as P in formula (2) i Corresponding), N if It represents the number of charge and discharge cycles or degradation tests under the i-th stress group (i.e., the first pseudo life under the i-th stress group), i=1,2,…,M.

[0056] Step 4: Select the acceleration model, solve the unknown coefficients of the acceleration model according to the first pseudo-life under different stress groups, and then obtain the acceleration equation.

[0057] The acceleration model is used to represent the change of supercapacitor life under different stress groups; there are many acceleration models, and different acceleration models have different parameters to be determined. The acceleration model selected in this embodiment is:

[0058]

[0059] Where V represents the life of the supercapacitor, A represents the parameter related to the failure threshold L, B represents the parameter related to temperature, T represents the test temperature, and E represents the d Indicates the discharge termination voltage, E c Indicates the charging termination voltage, n d 、n c Indicates parameters related to voltage. A, B, n d and n c All are undetermined coefficients.

[0060] The first pseudo life N under the i-th stress group if Corresponding to V in the acceleration model, the i-th stress group corresponds to T and E in the acceleration model d 、E c , that is, the stress group of this embodiment includes temperature stress and electrical stress. The first pseudo life N under different stress groups obtained in step 3 is if Substituting into formula (3), we can solve the unknown coefficients A, B, and n d and n c , we get the acceleration equation. The acceleration equation can be expressed as:

[0061]

[0062] Among them, A f , B f 、n df and n cf All represent the first pseudo lifespan N if The parameter to be solved, A f , B f 、n df and n cf All parameters are known. When the two acceleration equations are divided, only parameter A f will be eliminated, so A f is a parameter that is independent of stress, B f 、n df and n cf These are parameters related to stress.

[0063] Step 5: Obtain multiple second failure thresholds; solve the second pseudo life under the corresponding stress group and the corresponding second failure threshold according to the degradation trajectory equation under different stress groups and different second failure thresholds.

[0064] The number of the second failure thresholds is not less than 5. The more the number of the second failure thresholds is, the more accurate the performance prediction is. In this embodiment, the number of the second failure thresholds is 5. In a specific embodiment of the present invention, 5 second failure thresholds are determined according to the first failure threshold. Taking the capacitance of a supercapacitor as an example, the 5 second failure thresholds Lsj The first failure threshold is 80%, the first failure threshold is 60%, the first failure threshold is 40%, the first failure threshold is 20%, and the first failure threshold is 10%. In another specific embodiment of the present invention, multiple second failure thresholds can be set, and the numerical intervals between the multiple second failure thresholds are the same, so as to better perform interpolation calculations.

[0065] Determining the second failure threshold is to determine the performance parameter of the supercapacitor. sj Substituting into formula (2), we can get the corresponding N i , thus we can get M×n groups of data, where n represents the number of second failure thresholds, n≥5. Table 1 shows the second pseudo lifespan under different corresponding groups and different second failure thresholds, where N ij represents the second pseudo life under the i-th stress group and the j-th second failure threshold, i = 1, 2, ..., M, j = 1, 2, ..., n. Each second pseudo life N ij Corresponding to V in formula (4).

[0066] Table 1 Second pseudo lifespan under different corresponding groups and different second failure thresholds

[0067]

[0068] Step 6: Resolve the stress-independent parameters in the acceleration equation according to the second pseudo-life of the i-th stress group and different second failure thresholds to obtain stress-independent parameters under different second failure thresholds.

[0069] For the i-th stress group, T,E in the acceleration equation d ,E c The value of remains unchanged, only the performance parameters and life of the supercapacitor are different, so the stress-related parameters in the fixed acceleration equation, that is, parameter B f 、n df and n cf The second failure threshold L sj Substituting into the degradation trajectory equation under the i-th stress group (i.e., formula (2)), we can obtain the i-th stress group and different second failure thresholds L sj The second pseudo life of the i-th stress group and different second failure thresholds L sj Substitute the second pseudo-lifetime of into the acceleration equation (parameter B f 、n df and n cf Corresponding to the i-th stress group), different second failure thresholds L sj stress-independent parameters, namely, different second failure thresholds L sj Parameter A jTable 2 shows different second failure thresholds L sj Parameter A j .

[0070] Table 2 Parameter A under different second failure thresholds

[0071]

[0072] Step 7: Update the acceleration equation according to the stress-independent parameters at different second failure thresholds to obtain the acceleration equations at different second failure thresholds.

[0073] The acceleration equation under different second failure thresholds can be expressed as:

[0074]

[0075] Among them, V j represents the life under the jth second failure threshold, A j Denotes the parameters A and B under the jth second failure threshold f 、n df and n cf All remain unchanged.

[0076] Step 8: Obtain an actual stress group; substitute the actual stress group into the acceleration equation under different second failure thresholds to obtain the third pseudo life under different second failure thresholds.

[0077] The third pseudo lifespan at different second failure thresholds is the value of the supercapacitor performance parameter at different charge and discharge cycle numbers.

[0078] Step 9: Solve the degradation trajectory equation of the normal stress group according to the third pseudo-life under different failure thresholds.

[0079] Substituting the third pseudo-life under different failure thresholds into the degradation trajectory model (i.e., formula (1)), the coefficients a, b, c, and d can be re-solved. Substituting the re-solved coefficients a, b, c, and d into formula (1), the degradation trajectory equation of the normal stress group can be obtained.

[0080] In order to verify the effectiveness of the method of the present invention, the degradation trajectory equation solved by the method of the present invention (i.e., the degradation trajectory equation of the normal stress group) is compared with the degradation trajectory equation obtained by fitting the test data. Specifically: the accelerated degradation test data under the first stress group is obtained, and the accelerated degradation test data under the first stress group is fitted to obtain the degradation trajectory equation under the first stress group (i.e., the fitted degradation trajectory curve); the accelerated degradation test data under other stress groups is obtained, and the accelerated degradation test data under other stress groups are processed by the method of the present invention to obtain the degradation trajectory equation solved by the method of the present invention (i.e., the solved degradation trajectory curve). Figure 2As shown, the fitted degradation trajectory curve and the solved degradation trajectory curve are almost coincident, which proves the effectiveness of the method of the present invention.

[0081] Example 2

[0082] The present invention provides a method for solving supercapacitor performance, comprising:

[0083] Step 1: Obtain the number of charge and discharge cycles of the supercapacitor;

[0084] Step 2: calling the degradation trajectory equation of the normal stress group solved by the degradation trajectory equation solving method as described in Example 1;

[0085] Step 3: Solve the supercapacitor performance parameters based on the degradation trajectory equation of the normal stress group and the number of charge and discharge cycles.

[0086] Substituting the number of charge and discharge cycles into the degradation trajectory equation of the normal stress group, the supercapacitor performance parameters are obtained.

[0087] Example 3

[0088] An embodiment of the present invention also provides an electronic device, which includes: a memory, a processor, and a computer program / instruction stored in the memory, and the processor executes the computer program / instruction to implement the degradation trajectory equation solving method or supercapacitor performance solving method in the embodiment of the present application.

[0089] Although not shown, the electronic device includes a processor, which can perform various appropriate operations and processes according to the program and / or data stored in the read-only memory (ROM) or the program and / or data loaded from the storage portion into the random access memory (RAM). The processor can be a multi-core processor, or it can include multiple processors. In some embodiments, the processor can include a general main processor and one or more special coprocessors, such as a central processing unit, a graphics processing unit (GPU), a neural network processor (NPU), a digital signal processor (DSP), etc. In RAM, various programs and data required for device operation are also stored. The processor, ROM and RAM are connected to each other via a bus. The input / output (I / O) interface is also connected to the bus.

[0090] The processor and memory are used together to execute the program / instructions stored in the memory. When the program / instructions are executed by the computer, the methods, steps or functions described in the above embodiments can be implemented.

[0091] Although not shown, an embodiment of the present invention further provides a computer-readable storage medium having a computer program / instruction stored thereon, which, when executed by a processor, implements the method for solving the degradation trajectory equation or the method for solving the supercapacitor performance in the embodiment of the present application.

[0092] Storage media in embodiments of the present invention include permanent and non-permanent, removable and non-removable items that can be implemented by any method or technology to store information. Examples of storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, magnetic disk storage or other magnetic storage devices or any other non-transmission medium that can be used to store information that can be accessed by a computing device.

[0093] Readable storage media include permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. Information can be computer-readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer-readable media does not include temporary computer-readable media (transitory media), such as modulated data signals and carrier waves.

[0094] Although not shown, an embodiment of the present invention further provides a computer program product, including: a computer program / instruction, which, when executed by a processor, implements the method for solving the degradation trajectory equation or the method for solving the supercapacitor performance in the embodiment of the present application.

[0095] What is disclosed above is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of changes or modifications within the technical scope disclosed in the present invention, which should be covered within the protection scope of the present invention.

Claims

1. A method for solving a degenerate trajectory equation, characterized in that: The solution method includes: Obtain accelerated degradation test data of supercapacitors under different stress groups; According to the accelerated degradation test data under different stress groups, the degradation trajectory equation under the corresponding stress group is fitted; Obtaining a first failure threshold; solving a first pseudo life under the corresponding stress group according to the degradation trajectory equation under different stress groups and the first failure threshold; Obtaining an acceleration model, solving undetermined coefficients of the acceleration model according to the first pseudo-life under different stress groups, and then obtaining an acceleration equation; Obtain multiple second failure thresholds; solve the second pseudo life under the corresponding stress group and the corresponding second failure threshold according to the degradation trajectory equation under different stress groups and different second failure thresholds; Resolve the stress-independent parameters in the acceleration equation according to the second pseudo-life of the i-th stress group and different second failure thresholds, and obtain the stress-independent parameters under different second failure thresholds; The acceleration equation is updated according to the stress-independent parameters at different second failure thresholds to obtain the acceleration equations at different second failure thresholds; Obtaining an actual stress group; substituting the actual stress group into the acceleration equation under different second failure thresholds to obtain a third pseudo life under different second failure thresholds; The degradation trajectory equation of the normal stress group is solved according to the third pseudo-life under different failure thresholds.

2. The method for solving the degenerate trajectory equation according to claim 1, characterized in that: The least square method was used to fit the accelerated degradation test data under different stress groups, and the degradation trajectory equations under the corresponding stress groups were obtained.

3. The method for solving the degenerate trajectory equation according to claim 1, characterized in that: The degradation trajectory equations under the different stress groups are: P i (N i )=a i exp(-N i / b i )+c i N i +d i ; Among them, P i represents the performance parameters of the supercapacitor under the i-th stress group, N i represents the number of charge and discharge cycles or degradation tests under the i-th stress group, a i 、b i 、c i and d i They all represent the coefficients under the i-th stress group, i = 1, 2, …, M, and M represents the number of stress groups.

4. The method for solving the degenerate trajectory equation according to claim 1, characterized in that: The acceleration model is: Where V represents the life of the supercapacitor, A represents the parameter related to the failure threshold L, B represents the parameter related to temperature, T represents the test temperature, and E represents the d Indicates the discharge termination voltage, E c Indicates the charging termination voltage, n d 、n c Indicates parameters related to voltage.

5. The method for solving the degenerate trajectory equation according to claim 1, characterized in that: The plurality of second failure thresholds are obtained according to the first failure threshold.

6. A method for solving supercapacitor performance, characterized in that: The solution method includes: Get the number of charge and discharge cycles of the supercapacitor; The degradation trajectory equation of the normal stress group solved by the degradation trajectory equation solving method according to any one of claims 1 to 5 is called, and the supercapacitor performance parameters are solved according to the degradation trajectory equation of the normal stress group and the number of charge and discharge cycles.

7. An electronic device comprising a memory, a processor, and a computer program / instruction stored in the memory, wherein the processor executes the computer program / instruction to implement the method for solving the degradation trajectory equation as described in any one of claims 1 to 5 or the method for solving the supercapacitor performance as described in claim 6.

8. A computer-readable storage medium having a computer program / instruction stored thereon, which, when executed by a processor, implements the method for solving the degenerate trajectory equation as described in any one of claims 1 to 5 or the method for solving the supercapacitor performance as described in claim 6.

9. A computer program product, comprising a computer program / instruction, which, when executed by a processor, implements the method for solving the degradation trajectory equation as described in any one of claims 1 to 5 or the method for solving the supercapacitor performance as described in claim 6.

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