Support Methods

Abstract

To propose an optimal value of an explanatory variable.SOLUTION: A support method includes acquiring a distribution parameter A indicating a first distribution with which a determination probability of an explanatory variable is specified (Step S1C). The support method includes determining, based on the determination probability, a plurality of candidate values, which are candidates of explanatory variable (Step S4C). The support method includes determining a proposal value from among the candidate values and notifying a user of the proposal value (Step S30C).SELECTED DRAWING: Figure 20

Description

[Technical Field]

[0001] The present disclosure relates to an assistance method. [Background technology]

[0002] In recent years, various experiments have been conducted for the manufacture of objects, etc. In such experiments, observed values ​​are obtained through experiments using parameter values ​​determined by a user as conditions. Then, the object is manufactured, etc., using these parameter values ​​and observed values ​​as design values. Japanese Patent No. 6919770 (Patent Document 1) discloses a technology for searching for optimal parameter values ​​based on Bayesian optimization and notifying the user of the parameters. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Patent No. 6919770 Summary of the Invention [Problem to be solved by the invention]

[0004] Hereinafter, the parameter values ​​are also referred to as "explanatory variables," and the observed values ​​are also referred to as "target variables." Generally, there is a realistic appropriate range for the explanatory variables. However, in the invention described in Patent Document 1, there are cases where an explanatory variable outside the appropriate range is proposed. Therefore, even if a user conducts an experiment using an explanatory variable outside this appropriate range, the optimal target variable cannot be obtained.

[0005] The present disclosure has been made to solve the above-mentioned problems, and its purpose is to propose optimal values ​​of explanatory variables. [Means for solving the problem]

[0006] (1) A support method disclosed herein is a method for supporting a search for explanatory variables. The support method includes acquiring a distribution parameter A indicating a first distribution that defines a determination probability of the explanatory variables. The support method includes determining a plurality of candidate values ​​that are candidates for the explanatory variables based on the determination probability. The support method includes determining a proposed value from the plurality of candidate values ​​and notifying a user of the proposed value.

[0007] (2) The assistance method according to (1), further comprising: acquiring a plurality of values ​​used as explanatory variables; acquiring a range of a response variable corresponding to the explanatory variables; and calculating a variance and a mean of a second distribution of each of the plurality of candidate values ​​based on the plurality of values ​​and the range of the response variable. Notifying the user of the proposed value includes determining a proposed value from the plurality of candidate values ​​based on the variance and the mean of each of the plurality of candidate values ​​and notifying the user of the proposed value.

[0008] (3) In the support method according to (1) or (2), there are a plurality of types of explanatory variables, and the first distribution is a multivariate normal distribution of the plurality of types of explanatory variables.

[0009] (4) The support method according to any one of (1) to (3), wherein the explanatory variables are variables used in battery experiments. The support method further includes updating a prediction model that receives the explanatory variables and outputs a value as a dependent variable, based on the explanatory variables indicated by the proposed values ​​and dependent variables corresponding to the explanatory variables. The explanatory variables are variables related to battery materials. The dependent variables are variables related to battery characteristics. [Effects of the Invention]

[0010] According to the present disclosure, it is possible to propose optimal explanatory variable values. [Brief explanation of the drawings]

[0011] [Figure 1] 1 is a diagram illustrating a support device, a display device, a prediction device, and the like according to an embodiment of the present invention. [Figure 2]FIG. 10 is a diagram illustrating an example of distribution parameters. [Figure 3] FIG. 10 is a diagram illustrating an example of initial data. [Figure 4] FIG. 2 is a functional block diagram of the support device. [Figure 5] FIG. 10 is a diagram illustrating a candidate value combination. [Figure 6] FIG. 10 is a diagram illustrating correlation coefficients of a correlation matrix. [Figure 7] 4 is a flowchart showing a flow of processing by the support device of the first embodiment. [Figure 8] 10 is a flowchart illustrating a process of updating a prediction model. [Figure 9] FIG. 3 is a diagram for explaining the effect of the support device of the first embodiment. [Figure 10] FIG. 1 shows the positive and negative electrodes of a test battery. [Figure 11] FIG. 4 is a diagram illustrating a simulation result of the first embodiment. [Figure 12] FIG. 4 is a diagram illustrating a simulation result of the first embodiment. [Figure 13] 10 is a flowchart showing a processing flow of the support device of the second embodiment. [Figure 14] 10A and 10B are diagrams for explaining advantageous effects obtained by changing the threshold value Eth. [Figure 15] FIG. 10 is a diagram illustrating a simulation result of the second embodiment. [Figure 16] FIG. 10 is a diagram illustrating a simulation result of the second embodiment. [Figure 17] FIG. 10 is a functional block diagram of a support device according to a third embodiment. [Figure 18] FIG. 10 is a diagram showing an example of a multivariate normal distribution when there are two explanatory variables. [Figure 19] FIG. 2 is a diagram illustrating a first objective variable and a second objective variable. [Figure 20] 10 is a flowchart showing the processing of the support device of the third embodiment. [Figure 21] FIG. 10 is a diagram illustrating a simulation result of the third embodiment. [Figure 22]FIG. 10 is a diagram showing an example of a predetermined distribution when there is one type of explanatory variable. [Figure 23] FIG. 10 is a diagram for explaining conversion from a log-normal distribution to a normal distribution. [Figure 24] FIG. 1 is a diagram illustrating an example of a discrete probability distribution. DETAILED DESCRIPTION OF THE INVENTION

[0012] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the drawings. In the drawings, the same or corresponding parts are designated by the same reference numerals, and description thereof will not be repeated.

[0013] [First embodiment] 1 is a diagram showing an assistance device 100, a display device 200, and a prediction device 300 according to the present embodiment. The assistance device 100 is a device for assisting in the search for explanatory variables used in various experiments. The experiment in the present disclosure is an experiment for manufacturing a battery.

[0014] In this disclosure, the explanatory variables are variables related to the battery materials. In this disclosure, the variables related to the battery materials are the concentrations of battery additives C1 and C2. In this disclosure, the response variables are variables related to the battery characteristics. In this disclosure, the battery characteristics are the battery resistance value (IV resistance value).

[0015] The assistance device 100 and the prediction device 300 are, for example, computers such as a PC (personal computer), a tablet, or a smartphone. The display device 200 is connected to the assistance device 100. The display device 200 is an example of a notification device that notifies (displays) a proposed value output from the assistance device 100. The "proposed value" is a value of an explanatory variable proposed to the user.

[0016] The user inputs initial data (see FIG. 3) and distribution parameters (see FIG. 2) to the assistance device 100. The assistance device 100 determines a proposed value by performing a calculation (see FIG. 2) to be described later. The assistance device 100 then outputs the proposed value to the display device 200. The display device 200 displays the proposed value from the assistance device 100.

[0017] In the example of FIG. 1, the support device 100 calculates a % as the concentration of additive C1 and b % as the concentration of additive C2. The a % and b % correspond to "suggested values." The display device 200 displays information based on the suggested values ​​calculated by the support device 100. In the example of FIG. 1, the information is "Please conduct an experiment to measure the resistance value of a battery using additive C1...a % and additive C2...b %."

[0018] The user visually recognizes the information displayed on the display device 200 to understand the proposed additive concentration values. The user then conducts an experiment to measure the resistance value of a battery using the proposed concentration values. In this embodiment, the experiment is a DCIR (Direct Current Internal Resistance) measurement. The user then inputs a combination of the concentration values ​​proposed by the support device 100 and the resistance values ​​obtained by the experiment using those concentration values ​​into the prediction device 300 as training data.

[0019] The prediction device 300 holds a prediction model 350. The prediction device 300 is a device that predicts a target value based on the prediction model 350 and values ​​input by a user. For example, the prediction device 300 predicts a target variable (the IV resistance value of a battery) from an explanatory variable (the concentrations of additives C1 and C2 in a battery) input by a user based on the prediction model 350. This prediction allows the user to obtain the IV resistance value of a battery without conducting an experiment.

[0020] Furthermore, the prediction device 300 may predict explanatory variables (concentrations of additives C1 and C2 in a battery) from a response variable (IV resistance value of a battery) input by a user based on the prediction model 350. This prediction allows the user to obtain the concentrations of additives C1 and C2 in a battery that result in a desired IV resistance value.

[0021] The prediction device 300 can learn (update) the prediction model 350 based on the input training data. This update improves the prediction accuracy of the prediction device 300. Note that, although the support device 100 and the prediction device 300 are shown as separate configurations in FIG. 1, the support device 100 and the prediction device 300 may be integrated.

[0022] The objectives of the assistance device 100 of the present disclosure include the following first and second objectives. First, the first objective will be described. As described in FIG. 1, the prediction device 300 can perform the above predictions. The first objective of this embodiment is to "improve the prediction accuracy of the prediction device 300."

[0023] Next, the second objective will be described. For example, a user may search for explanatory variables to obtain a desired range of a response variable through an experiment. More specifically, this case refers to a case where a user is searching for explanatory variables (concentrations of additives C1 and C2) for manufacturing a battery in which the response variable (IV resistance value) falls within a desired range. In this case, it is preferable for the user to obtain an optimal (user-desired) response variable with as few experiments as possible. The second objective of the assistance device 100 of the present disclosure is "to suggest to the user explanatory variables for obtaining a desired range of a response variable with as few experiments as possible."

[0024] The support devices of the first embodiment and the second embodiment described below are devices that are primarily intended to achieve a first objective, and the support device of the third embodiment is a device that is primarily intended to achieve a second objective.

[0025] The support device 100 includes a CPU (Central Processing Unit) 181, a memory 182, and an interface (I / F) 183. The CPU 181 executes various processes. The interface 183 is a device for communicating with an external device of the support device 100. The external device is, for example, a display device 200.

[0026] The ROM stores programs executed by the CPU 181. The RAM can temporarily store data generated by the execution of programs in the CPU 181 and data input via the interface 183. The RAM can function as a temporary data memory used as a working area.

[0027] The program stored in ROM 162 may be stored in a recording medium and distributed as a program product. The recording medium is a non-transitory medium from which the program recorded therein can be read by a computer. Alternatively, the program may be provided by an information provider as a so-called product program that can be downloaded via the Internet or the like. The assistance device 100 reads the program provided from a storage medium or the Internet or the like. The assistance device 100 stores the read program in a predetermined storage area (e.g., ROM). The CPU 181 executes the program to perform a process of calculating a proposed value.

[0028] [Distribution parameters and initial data] Next, the distribution parameters and initial data shown in FIG. 1 will be described. First, the distribution parameters will be described. The distribution parameter A is a parameter determined by the user. The distribution parameter A is a parameter that defines the first distribution of each of M (M is an integer equal to or greater than 1) types of explanatory variables. In this embodiment, the first distribution is a normal distribution. The distribution parameter A is a parameter that defines the normal distribution, and the distribution parameter A has a mean μ and a standard deviation σ.

[0029] FIG. 2 is a diagram showing an example of the distribution parameter A. In this embodiment, the number of types of explanatory variables is four (M=4). The four types of explanatory variables are constituted by the concentrations of four types of additives. In the example of FIG. 2, the four types of additives are vinylene carbonate (VC), lithium bisoxalateborate (LiBOB), additive A, and additive B. Additive A and additive B are PF bond-containing lithium salt additives. Additive A and additive B differ in their decomposition in the electrolyte and their film formation behavior on the electrode.

[0030] In the example of Figure 2, the mean μs and standard deviation σs of each of the four explanatory variables are specified. For example, the mean μ1 of VC is 0.85, and the standard deviation σ1 of VC is 0.32. Furthermore, the normal distribution specified by the distribution parameter A in Figure 2 is a "multivariate normal distribution."

[0031] FIG. 3 is a diagram showing an example of initial data B. The initial data B is composed of N (N is an integer equal to or greater than 1) "initial data combinations." In the example of FIG. 3, N=18. The initial data combination is information indicating a combination of M types of explanatory variables and objective variables corresponding to the M types of explanatory variables. The objective variables corresponding to the M types of explanatory variables are variables derived in advance by a user through an experiment using the M types of explanatory variables. The objective variables corresponding to the M types of explanatory variables may also be variables predicted in advance by inputting the M types of explanatory variables into the prediction device 300.

[0032] In FIG. 3, the information surrounded by a bold line is one initial data combination. That is, the initial data in FIG. 3 includes 18 initial data combinations. In the example of FIG. 3, for example, the objective variable (IV resistance value) of the explanatory variables where VC, LiBOB, additive A, and additive B are 0% is specified to be 111.7 mΩ. The values ​​of the 72 (=18×4) explanatory variables in FIG. 3 correspond to the "multiple values" of the present disclosure.

[0033] [Functional block diagram of the support device] 4 is a functional block diagram of the support device 100. The support device 100 includes an acquisition unit 102, a candidate unit 104, a distribution unit 106, a distance unit 108, a probability unit 110, and a determination unit 112. A threshold unit 114 is indicated by a dashed line, and this threshold unit 114 will be described in the second embodiment.

[0034] The acquiring unit 102 acquires distribution parameters A (see FIG. 2) and initial data B (see FIG. 3) input by the user. The distribution parameters A acquired by the acquiring unit 102 are output to the candidate unit 104 and the distance unit 108.

[0035] The candidate unit 104 calculates L (L is an integer equal to or greater than 2) candidate value combinations of M types of explanatory variables (four types of explanatory variables in this embodiment). Here, a "candidate value combination" is a combination of candidate values ​​for each of the M types of explanatory variables. Also, a "candidate value" is a value that is a candidate for the proposed value (see FIG. 1). In this embodiment, L=1000.

[0036] FIG. 5 is a diagram for explaining candidate value combinations. In the example of FIG. 5, the numbers of the candidate value combinations and four types of explanatory variables are shown. As described above, since L=1000, the numbers 1 to 1000 are defined as the numbers of the candidate value combinations. In FIG. 5, "..." indicates a candidate value calculated by the candidate unit 104. In addition, information surrounded by a thick line in the example of FIG. 5 is one candidate value combination. In other words, the candidate unit 104 calculates 1000 candidate value combinations and 4000 (=4×1000) candidate values.

[0037] The candidate unit 104 calculates candidate values ​​using the distribution parameters. For example, the candidate unit 104 calculates candidate values ​​using uniform random numbers within a numerical range based on the mean μs and standard deviation σs corresponding to the explanatory variables in the distribution parameters. The numerical range is, for example, a range equal to or greater than μs-3σs and equal to or less than μs+3σs. For example, the candidate unit 104 calculates explanatory variables for VC (see FIG. 2) using uniform random numbers within a numerical range equal to or greater than μ1-3σ1 and equal to or less than μ1+3σ1. In this embodiment, the 1,000 candidate value combinations S are output to the distribution unit 106, the distance unit 108, and the probability unit 110.

[0038] The distribution unit 106 calculates the variance σ of the second distribution of each of the L candidate value combinations from the candidate unit 104 based on the initial data B (see FIG. 3) from the acquisition unit 102. In this embodiment, the second distribution is a normal distribution. The variance σ is calculated for each of the 1000 (L) candidate value combinations. The processing of the distribution unit 106 will be described in detail below.

[0039] Furthermore, the dispersion unit 106 calculates the variance σ of the second distribution using a Gaussian process regression model. First, the dispersion unit 106 updates (learns) the Gaussian process regression model using initial data B (both explanatory variables and target variables). Then, the dispersion unit 106 calculates the variance σ using a kernel function in the updated Gaussian process regression model. The kernel function k(x n , x m ) is expressed, for example, by the following formula (1):

[0040]

number

[0041] Here, x on the left side of equation (1) n and x m indicates a vector consisting of four explanatory variables. Also, n and m indicate variables that satisfy 1≦n≦N (=18) and 1≦m≦N, respectively.

[0042] γ on the right side of equation (1) is a predetermined real number. γ is, for example, a real number in the range of 0<γ≦2. In this embodiment, γ=2. t on the right side of equation (1) indicates a transposed matrix. σ(n, m) on the right side of equation (1) indicates Kronecker delta.

[0043] The hyperparameters θ0, θ1, θ2, and θ3 on the right side of equation (1) are the hyperparameters to be updated (optimized). The distribution unit 106 adjusts the hyperparameters θ0, θ1, θ2, and θ3 so that the probability expressed on the left side of equation (2) below best represents the initial data B.

[0044]

number

[0045] Here, X on the left side of equation (2) is x 1,..., x N In equation (2), y represents a vector consisting of the values ​​of N objective variables (IV resistance values) included in the initial data B. K represents a matrix with equation (1) as its (n, m) components.

[0046] Also, one candidate value combination is x * When expressed as above, the distribution unit 106 calculates the variance σ by the following equation (3).

[0047]

number

[0048] Here, K on the right side of equation (3) is the same as K in equation (2). * is expressed by equation (4).

[0049] As described above, distribution unit 106 updates the Gaussian process regression model based on equations (1) and (2). Then, distribution unit 106 calculates the variance σ for each of the L candidate value combinations using the updated Gaussian process regression model and equations (3) and (4). The calculated variance σ is output to determination unit 112.

[0050] Next, we will explain the processing of distance unit 108. Distance unit 108 calculates the Mahalanobis distance E for each combination of L candidate values ​​based on distribution parameter A. In a certain situation, the Mahalanobis distance E is the distance from the center of gravity of a data group consisting of L candidate values.

[0051] The processing of the distance unit 108 will be described in detail below. First, the distance unit 108 sets a correlation matrix C between M explanatory variables defined by the distribution parameter A through a predetermined calculation. A method for calculating the correlation coefficient r that constitutes the correlation matrix C will be described below. The distance unit 108 calculates the correlation coefficient r by substituting the numerical value included in the initial data B into the following equation (5).

[0052]

number

[0053] Here, j and k in equation (5) respectively represent two explanatory variables for calculating the correlation coefficient r. The two explanatory variables are explanatory variables included in the initial data, such as the concentration of VC and the concentration of LiBOB. Also, S in equation (5) jk indicates the covariance between explanatory variable j and explanatory variable k. j indicates the standard deviation of explanatory variable j. k indicates the standard deviation of explanatory variable k. N is the number of initial data combinations as described above. i is a variable and corresponds to the number in Figure 3. j i indicates the value of the i-th explanatory variable j. k iindicates the numerical value of the i-th explanatory variable k. javg indicates the average value of N explanatory variables j. kavg indicates the average value of N explanatory variables k. javg indicates the average value of N explanatory variables j. The correlation matrix C corresponds to "information indicating the correlation between multiple types of explanatory variables" in this disclosure.

[0054] As a modified example, the distance unit 108 may substitute the numerical value of the distribution parameter A (see FIG. 2) into equation (5) to calculate the correlation coefficient r. The distance unit 108 may substitute the average μs of two explanatory variables of the distribution parameter A into javg and kavg in equation (5), respectively. Furthermore, the distance unit 108 may substitute the standard deviation σs of two explanatory variables of the distribution parameter A into S in equation (5), respectively. j and S k may be substituted into

[0055] FIG. 6 is a diagram showing correlation coefficients of correlation matrix C. In the example of FIG. 6, for example, the correlation coefficient between VC and LiBOB is shown to be 0.44. The correlation matrix C is an M×M (4×4 in this embodiment) square matrix. Note that the correlation matrix C may be input by the user without being calculated.

[0056] If the distance unit 108 determines that there is no correlation between the explanatory variables, the distance unit 108 sets the correlation matrix C to a unit matrix. Various methods can be applied to determine whether there is a correlation. For example, if the total value of the correlation coefficients is less than a predetermined value, the distance unit 108 determines that there is no correlation. Furthermore, a configuration may be adopted in which the user can input information indicating the presence or absence of a correlation into the assistance device 100. In the case where such a configuration is adopted, if the user inputs information indicating that there is no correlation, the distance unit 108 determines that there is no correlation.

[0057] The distance unit 108 calculates the Mahalanobis distance E for each of the L candidate combinations using the following equations (6) and (7).

[0058] Σ=DCD (6)

[0059]

number

[0060] Σ on the left side of equation (6) represents the covariance matrix set for the explanatory variables. Matrix D on the right side of equation (6) is a diagonal matrix with σ1 to σ4 in FIG. 2 as diagonal components. Vector U on the right side of equation (7) is a vector with μ1 to μ4 in FIG. 2 as components. Vector X on the right side of equation (7) is a vector with the four explanatory variables defined in the candidate combination as components. The Mahalanobis distance E calculated by distance unit 108 is output to probability unit 110 and determination unit 112.

[0061] Next, the processing of the probability unit 110 will be described. The probability unit 110 determines an attribute probability P for each of the L candidate value combinations. Here, the attribute probability P is a probability value based on the first distribution described above. In other words, the attribute probability P is a degree of closeness between the "centroid of a data group assumed to be in a normal distribution (first distribution) defined by the distribution parameter A in FIG. 2" and the "candidate value combination corresponding to the attribute probability P." The attribute probability P corresponds to the "probability value" in this disclosure. The processing of the probability unit 110 will be described in detail below.

[0062] In this embodiment, it is assumed that the explanatory variables follow a normal distribution (see FIG. 2). In this case, the Mahalanobis distance follows a chi-square distribution expressed by the probability density function f(z) of the following equation (8). Furthermore, the probability unit 110 calculates the attribution probability P by the following equation (9).

[0063]

number

[0064] Here, γ() in equation (8) is a predetermined gamma function, and k in equation (8) is the degree of freedom. The probability value P calculated by probability unit 110 is input to determination unit 112.

[0065] As described above, the determination unit 112 receives as input the variance σ of each of the 1000 candidate combinations from the dispersion unit 106, the Mahalanobis distance E of each of the 1000 candidate combinations from the distance unit 108, and the attribute probability P of each of the 1000 candidate combinations from the probability unit 110.

[0066] The determining unit 112 calculates the evaluation value V of each of the 1000 candidate combinations based on the following formula (10).

[0067] Evaluation value V=σ a ×E b ×P c (10) Here, a, b, and c in formula (10) are predetermined real numbers. a, b, and c are, for example, real numbers in the range of -2 or more and 2 or less. In this embodiment, a, b, and c are assumed to be 1. Therefore, the determination unit 112 calculates a candidate combination evaluation value V by multiplying the variance σ, the Mahalanobis distance E, and the attribution probability P calculated for one candidate combination. Then, the determination unit 112 calculates the evaluation value V for each of the 1000 candidate combinations (all evaluation values ​​V for the 1000 candidate combinations).

[0068] Then, the determination unit 112 determines the candidate combination with the maximum evaluation value among the evaluation values ​​for each of the 1000 candidate combinations as the proposed candidate value combination. The determination unit 112 notifies the user of the proposed candidate value combination (see the description of the display device 200 in FIG. 1). The proposed candidate value combination corresponds to the "proposed value" in the present disclosure.

[0069] [Support device processing flow] 7 is a flowchart showing the flow of processing by the assistance device 100. The processing in FIG. 7 is executed every predetermined period (for example, every second).

[0070] First, in step S1, the support device 100 determines whether or not the distribution parameter A and the initial data B have been input to the support device 100. If the distribution parameter A and the initial data B have not been input (NO in step S1), the process ends. If the distribution parameter A and the initial data B have been input (YES in step S1), the process proceeds to step S2.

[0071] Next, in step S2, the support device 100 learns a Gaussian process regression model using the initial data B (see the above formulas (1) and (2)). Next, in step S4, the support device 100 calculates L candidate value combinations (candidate values) based on the distribution parameter A.

[0072] Next, in step S6, the support device 100 calculates the variance σ for each of the L candidate value combinations based on the trained Gaussian process regression model (see formulas (3) and (4) above). Next, in step S8, the support device 100 calculates the Mahalanobis distance E for each of the L candidate value combinations based on the distribution parameter A (see formulas (5) to (7) above). Next, in step S10, the support device 100 calculates the membership probability P for each of the L candidate value combinations based on the distribution parameter A (see formulas (8) and (9) above).

[0073] Next, in step S12, the support device 100 calculates an evaluation value V for each of the L candidate value combinations (see formula (10) above). Next, in step S14, the support device 100 outputs the candidate combination (candidate value) with the maximum evaluation value as a proposed candidate value combination (proposed value). The process by which the support device 100 outputs the proposed candidate value combination is also referred to as a "proposed process."

[0074] In addition, the user may wish to obtain multiple proposed candidate value combinations. In this case, a DCIR measurement is performed using the proposed candidate value combination to measure the IV resistance value. The user then adds the proposed candidate value combination and the resistance value to initial data and causes the support device 100 to execute a proposal process based on the initial data. The user can obtain multiple proposed candidate value combinations by causing the support device 100 to execute such a proposal process multiple times.

[0075] 8 is a flowchart showing updating of a prediction model. In step S20, the prediction device 300 updates the prediction model 350 based on training data (proposed candidate value combinations and objective variables corresponding to the proposed candidate value combinations) input by the user. The processing in FIG. 8 can be included in the support method of this embodiment.

[0076] [Actions and Effects of the Support Device of the Present Embodiment] The support device 100 of this embodiment calculates an evaluation value V for each of L candidate combinations. The evaluation value V is calculated using the variance σ and the attribution probability P. As described above, the variance σ is a value that indicates the degree of variation in the normal distribution of the candidate value combination. Therefore, a candidate value combination with a large variance σ is a combination of explanatory variables that can be expected to produce experimental results (objective variables) that cover a wide range. Therefore, a configuration that calculates an evaluation value using only the variance σ (hereinafter referred to as the "configuration of the comparative example") is conceivable.

[0077] However, in such a configuration, a candidate value combination with an extremely large variance σ may be selected as the proposed candidate value combination, and in this case, a combination outside the appropriate range (unrealistic) may be selected.

[0078] Therefore, the support device 100 of this embodiment determines a proposed value using not only the variance σ but also the attribution probability P. Specifically, the support device 100 calculates an evaluation value V based on the variance σ and the attribution probability P. As described above, the attribution probability P is a measure of proximity to the center of gravity of a data group assumed to be in a normal distribution (first distribution) defined by the distribution parameter A in FIG. 2. Therefore, a candidate value combination with a large attribution probability P is a candidate value combination with a high probability in the normal distribution defined by the user, and therefore tends to fall within an appropriate range. Therefore, a candidate value combination with a large evaluation value V calculated using the variance σ and the attribution probability P is a candidate value combination with a wide range, while tending to fall within the appropriate range. Therefore, a candidate value combination with a large evaluation value V (proposed candidate value combination) is an optimal combination of explanatory variables.

[0079] Fig. 9 is a diagram for explaining the effect of the support device 100 of this embodiment. In the example of Fig. 9, the number M of types of explanatory variables is 3, that is, the diagram shows the first explanatory variable, the second explanatory variable, and the third explanatory variable.

[0080] 9, the proposed candidate value combinations according to the configuration of the comparative example described above are indicated by black circles, and the proposed candidate value combinations according to the support device 100 of this embodiment are indicated by white circles. The hatched region R is a region defined by the multivariate normal distribution described above. Candidate value combinations with a large attribution probability P tend to be close to the center of gravity (center) of the region α.

[0081] In the configuration of the comparative example described above, a combination outside the appropriate range (unrealistic) may be selected, such as the proposed candidate value combinations indicated by the black circles in Fig. 9. On the other hand, according to the assistance device 100 of this embodiment, the proposed candidate value combinations are candidate value combinations within a wide range while still falling within the region α defined by the multivariate normal distribution (see the white circles in Fig. 9). Therefore, according to the assistance device 100 of this embodiment, it is possible to propose optimal and scattered explanatory variable values ​​to the user.

[0082] Furthermore, in this embodiment, there are multiple types of explanatory variables (four types in this embodiment). The probability section 110 performs calculations based on information indicating the correlation between the multiple types of explanatory variables (the correlation matrix in FIG. 6 in this embodiment). Therefore, even if there are multiple types of explanatory variables, it is possible to calculate the attribution probability P that reflects the multiple types of explanatory variables.

[0083] Furthermore, in this embodiment, the determination unit 112 calculates the evaluation value V by multiplying not only the variance σ and the attribute probability P but also the Mahalanobis distance E. As described above, the Mahalanobis distance E is the distance from the center of gravity of a data group consisting of L candidate values. Therefore, the assistance device 100 of this embodiment can propose to the user candidate value combinations that are appropriately scattered (away from the center of gravity) while remaining within an appropriate range.

[0084] 8 and other drawings, the prediction device 300 updates the prediction model 350 based on training data (proposed candidate value combinations and objective variables corresponding to the proposed candidate value combinations) input by the user. Therefore, the assistance device 100 can also assist in improving the prediction accuracy of the prediction device 300.

[0085] [Simulation Results] Next, a simulation result showing the advantageous effects of the support device 100 of this embodiment will be described. First, a test battery used in the simulation will be described. The positive electrode active material of the positive electrode of the test battery was Li(NiCoMn)O2. The conductive material of the positive electrode was acetylene black. The binder of the positive electrode was polyvinylidene difluoride (PVdF). The dispersion medium of the positive electrode was N-methyl-2-pyrrolidone (NMP). The positive electrode substrate of the positive electrode was Al foil. A positive electrode slurry with a mass blending ratio of positive electrode solids of "positive electrode active material / conductive material / binder = 92.0 / 7.1 / 0.9" was prepared. The slurry was applied to the surface (both front and back) of the positive electrode substrate and dried to form a positive electrode active material layer, which was then compressed. A positive electrode blank was produced as described above.

[0086] Next, the negative electrode of the test battery will be described. The negative electrode active material of the negative electrode is graphite. The negative electrode binder is CMC (carboxymethyl cellulose) and SBR (styrene butadiene rubber). The negative electrode dispersion medium is water. The negative electrode substrate is Cu foil. The mass blending ratio of the negative electrode solids is "negative electrode active material / CMC / SBR=98.3 / 1.0 / 0.7". The negative electrode slurry was applied to the surface (both the front and back) of the negative electrode substrate and dried to form a negative electrode active material layer. The negative electrode active material layer was then compressed. This produced a negative electrode blank.

[0087] Next, we will explain the electrolyte of the test battery. The volume ratio of the electrolyte solvents is EC / DMC / EMC = 3 / 3 / 4. The supporting electrolyte is LiPF6 (lithium hexafluorophosphate) with a concentration of 0.88 mol / L. The additives in the electrolyte are VC, LiBOB, Additive A, and Additive B, as shown in Figure 2. The component ratios of the solvents are based on the volume at 25°C and 1 atmosphere.

[0088] A member having a multilayer structure including a PP (polypropylene) layer and a PE (polyethylene) layer was used as the separator for the test battery, and the separator for the test battery was manufactured by cutting the member to a predetermined planar size.

[0089] 10 is a diagram showing the positive electrode 210 and negative electrode 220 used in the simulation. The positive electrode 210 is manufactured by cutting the above-mentioned positive electrode raw sheet. The negative electrode 220 is manufactured by cutting the above-mentioned negative electrode raw sheet.

[0090] The positive electrode 210 includes an Al tab 211 and a positive electrode active material layer 212. The positive electrode active material layer 212 has planar dimensions of 43 mm long and 29 mm wide. The Al tab 211 is ultrasonically bonded to the positive electrode active material layer 212. The Al tab 211 has planar dimensions of 7 mm long and 10 mm wide.

[0091] The negative electrode 220 includes a Cu tab 221 and a negative electrode active material layer 222. The negative electrode active material layer 222 has planar dimensions of 46 mm long and 30 mm wide. The Cu tab 221 is ultrasonically bonded to the positive electrode active material layer 212. The Cu tab 221 has planar dimensions of 8 mm long and 10 mm wide. Details of the manufacturing process for the positive and negative electrodes shown in FIG. 10 are disclosed, for example, in Japanese Patent Publication No. 7153701.

[0092] Furthermore, an electrode assembly was formed by stacking the positive electrode, separator, and negative electrode in this order. The electrode assembly was inserted into an exterior body made of aluminum laminate film in a dry environment to form a component. The component was then dried at 100°C under vacuum for 3 hours. After that, the component was cooled to 25°C, and the above-mentioned electrolyte solution was injected, and the exterior body was welded and sealed. This produced a test battery.

[0093] The test battery was subjected to the following aging process: charging the test battery at 400 mA to 4.1 V, discharging it at 400 mA to 2.5 V, and then storing it in an environment at 60°C for 12 hours. DCIR measurements were then performed by repeatedly charging and discharging the aged test battery at 200 mA to 3.7 V at 25°C and discharging it.

[0094] Fig. 11 is a diagram showing the simulation results. In the example of Fig. 11, the results of five comparative examples and five examples are shown. Fig. 11 shows the concentration of VC, the concentration of LiBOB, the concentration of additive A, the concentration of additive B, the variance σ, the attribution probability P, the Mahalanobis distance E, the evaluation value V, and the IV resistance value for these 10 results.

[0095] First, an example will be described. As described above, the support device 100 determines a proposed candidate value combination. Then, the user measures the IV resistance value (objective variable) by performing the above-mentioned DCIR measurement using the values ​​of multiple explanatory variables defined in the proposed candidate value combination. Then, the above-mentioned proposal process is repeated four times, and the results of five examples are obtained.

[0096] Next, a comparative example will be described. In the comparative example, the user checks the initial data and determines five combinations of explanatory variables based on the user's intuition. Here, it is assumed that the user determines the five combinations of explanatory variables described in the comparative example of FIG. 11. It is also assumed that the variance σ, the attribution probability P, the Mahalanobis distance E, the evaluation value V, and the IV resistance value are calculated for the five combinations of explanatory variables in the comparative example.

[0097] As is clear from Fig. 11, the variance σ of the example is larger than the variance σ of the comparative example. Therefore, the degree of dispersion of the candidate value combinations is greater in the example. This allows the user to conduct more efficient experiments, and as a result, the learning effect of the prediction model 350 (see Fig. 1) can be improved.

[0098] Next, a simulation result using root mean squared error (RMSE) for the accuracy of the prediction model 350 will be described. A method for calculating RMSE will be described below. Five sets of experimental data (combinations of four types of explanatory variables and a target variable) of the embodiment shown in FIG. 11 are used as the dataset DS1 of the embodiment. Three sets of experimental data randomly extracted from the dataset DS1 are combined with the initial data (see FIG. 3) to generate a training dataset Tr1 for the prediction model 350. The remaining two sets of experimental data in the dataset DS1 are used as the dataset Val for evaluating the prediction model 350.

[0099] A prediction model 350 was trained using a training dataset Tr1. In addition, in the training, explanatory variables were selected using a stepwise method. A dependent variable was predicted using the trained prediction model 350. Then, an RMSE was calculated as the difference between the predicted dependent variable and an experimentally measured dependent variable. This RMSE calculation was performed three times to calculate three RMSEs, and the average of the three RMSEs was then calculated. Similarly, an average of the three RMSEs was calculated using the above-mentioned RMSE calculation method using five sets of experimental data for the comparative example shown in FIG. 11.

[0100] Fig. 12 is a diagram showing the average value of RMSE for the comparative example and the average value of RMSE for the example. The example in Fig. 12 shows the average value of RMSE for the example when the average value of RMSE for the comparative example is normalized to be 1. As is clear from Fig. 12, the combination of experimental variables proposed by the support device 100 of this embodiment can improve the prediction accuracy of the prediction model 350.

[0101] As a modification of the first embodiment, the evaluation value V may be calculated without using the Mahalanobis distance E. For example, the evaluation value V may be calculated by multiplying the variance σ by the attribute probability P.

[0102] [Second embodiment] In the first embodiment, a configuration has been described in which the evaluation value V is calculated using the Mahalanobis distance E. In the second embodiment, a configuration will be described in which the Mahalanobis distance E is used by another method. The support device 100A of the second embodiment will be described with reference to FIG. 4.

[0103] The support device 100A of the second embodiment includes a threshold unit 114 indicated by a dashed line in Fig. 4. The threshold unit 114 changes the threshold Eth of the Mahalanobis distance E and outputs the changed threshold Eth to the determination unit 112. The threshold unit 114 randomly changes the threshold Eth. For example, the threshold unit 114 holds a probability density function for the threshold Eth, which is a normal distribution, and determines the threshold Eth based on the probability density function.

[0104] Fig. 13 is a flowchart showing the processing flow of the support device 100A of the second embodiment. In Fig. 13, steps S12 and S14 in Fig. 7 are replaced with steps S12A and S14A, and step S13A is added.

[0105] In step S12A, the determining unit 112 calculates an evaluation value V for each of the L candidate value combinations using the following equation (11).

[0106] V = σ × P (11) Next, in step S13A, the threshold unit 114 determines a threshold Eth based on the threshold probability density function and outputs the determined threshold Eth to the determination unit 112. Then, in step S14A, the determination unit 112 selects, from the L candidate value combinations, a candidate value combination whose Mahalanobis distance is greater than the threshold Eth determined in step S13A and whose evaluation value is the largest. The determination unit 112 then outputs the selected candidate value combination as a proposed candidate value combination. Note that the largest evaluation value is an example of the "evaluation value satisfies a criterion" in the present disclosure.

[0107] As described above, the support device 100A changes the threshold value Eth each time the above proposal process is executed. Fig. 14 is a diagram for explaining the advantageous effect of changing the threshold value Eth. Fig. 14 shows a case where the number of types of explanatory variables is two, that is, a case where the explanatory variables are a first explanatory variable and a second explanatory variable. Also, Fig. 14 shows a circle as an outline corresponding to the threshold value Eth. Also, Fig. 14 shows the determined proposal candidate value combination G.

[0108] Fig. 14(A) is a diagram showing a case where the threshold value Eth for determining the first proposed candidate value combination is determined as 19. Fig. 14(B) is a diagram showing a case where the threshold value Eth for determining the second proposed candidate value combination is determined as 30. Fig. 14(C) is a diagram showing a case where the threshold value Eth for determining the third proposed candidate value combination is determined as 24.

[0109] 14(A) to 14(C), a proposal candidate value combination whose Mahalanobis distance E is greater than the threshold value Eth is located outside the contour. Furthermore, since the attribute probability P of the proposal candidate value combination is large, the proposal candidate value combination tends to be located near the contour (threshold value Eth).

[0110] As shown in Fig. 14, the threshold value Eth is changed for each proposal process, and therefore the distance from the center of gravity of the proposed candidate value combinations can be changed. As a result, the degree of dispersion of the proposed candidate value combinations can be increased. Note that a range of the threshold value Eth may be set. This range is, for example, 10 or more and 30 or less.

[0111] Fig. 15 is a diagram showing the simulation results of this embodiment. Fig. 15 shows the results of the same simulation as the simulation described in Fig. 11. As is clear from Fig. 11 and Fig. 15, in the second embodiment, the variance σ and the evaluation value V are larger than in the first embodiment.

[0112] Fig. 16 is a diagram showing the RMSE of this embodiment. Fig. 16 shows the results of the same simulation as that described in Fig. 12. As is clear from Fig. 12 and Fig. 16, the RMSE of the second embodiment is improved compared to the first embodiment.

[0113] As a modification of the second embodiment, the threshold value Eth may be a fixed value. For example, the threshold value Eth may be a fixed value of 5 or more. Alternatively, the threshold value Eth may be a fixed value of 40 or less. Alternatively, the threshold value Eth may be a fixed value of 10 or more and 30 or less.

[0114] Third Embodiment In the first and second embodiments, the candidate unit 104 (see FIG. 4) is configured to calculate candidate values ​​using uniform random numbers. The method of determining candidate values ​​by the candidate unit 104 in the third embodiment is different from the method of determining candidate values ​​in the first and second embodiments.

[0115] Fig. 17 is a functional block diagram of a support device 100B according to the third embodiment. As shown in Fig. 17, a distribution parameter A, initial data B, and a desired range C (to be described later) are input to the support device 100B.

[0116] Next, the processing of the candidate unit 104B will be described. The candidate unit 104B determines L candidate values ​​based on the probability value defined by the probability density function g(x) shown in the following equation (12).

[0117]

number

[0118] Here, Σ in equation (12) is shown in equation (6) above, and E is the Mahalanobis distance. FIG. 18 is a diagram showing an example of a multivariate normal distribution when there are two explanatory variables. This multivariate normal distribution is a distribution showing the probability density function g(x) of equation (12). FIG. 18(A) is a diagram showing a case where there is no correlation between the explanatory variables, and FIG. 18(B) is a diagram showing a case where there is a correlation between the explanatory variables. The Z axis indicates the determination probability Q of the candidate value. The determination probability Q corresponds to the "determination probability of the explanatory variable" in this disclosure. The L candidate value combinations determined by the candidate unit 104B are output to the distribution unit 106B.

[0119] Next, the desired range C will be described. As described above, the desired range C is the range of the objective variable desired by the user. In this embodiment, the desired range is defined for the IV resistance value. The desired range is, for example, a range of 106 mΩ to 108 mΩ. The initial data B and the desired range C are input to the distribution unit 106B. The desired range C corresponds to the "range of the objective variable."

[0120] The dispersion unit 106B calculates the dispersion σ and the average value μ for each of the L candidate value combinations. First, the dispersion unit 106B defines a first objective variable and a second objective variable. Fig. 19 is a diagram for explaining the first objective variable and the second objective variable.

[0121] In the example of Fig. 19, the IV resistance value is shown as the first objective variable. In addition to the first objective variable, the example of Fig. 19 also shows a second objective variable. The second objective variable is determined, for example, by the following equation (13). Second objective variable = log(first objective variable - median of desired range) (13) The median of the desired range in equation (13) is 107. The distribution unit 106B calculates the second objective variable for each of the N initial data items using, for example, equation (13).

[0122] The distribution unit 106B updates the Gaussian process regression model using the above formulas (1) and (2). However, the objective variable (first objective variable or second objective variable) to which the desired range is applied is input to "y" in formula (2). Then, the distribution unit 106B calculates the variance σ using the above formulas (3) and (4).

[0123] Furthermore, the distribution unit 106B calculates the average μ of the second distribution for each candidate value combination using the following equation (14).

[0124]

number

[0125] The mean μ and variance σ for each candidate value combination calculated by the distribution unit 106B are input to the determination unit 112. The determination unit 112 calculates an evaluation value V based on the difference between the mean μ and the variance σ. Specifically, the determination unit 112 calculates the evaluation value V based on the following equation (15). Note that in this embodiment, the above equation (10) for calculating the evaluation value V is not used.

[0126] Evaluation value V = μ - σ (15) Here, since a candidate point with a small second objective variable is preferable, a candidate point with a small evaluation value V in equation (15) is a preferable candidate point. The determination unit 112 determines the candidate value combination with the smallest evaluation value V from among the L candidate value combinations as the proposed candidate value combination. Then, the determination unit 112 notifies the user of the proposed candidate value combination.

[0127] 20 is a flowchart showing the processing of the support device 100B of the third embodiment. First, in step S1C, the support device 100B determines whether or not the distribution parameter A, the initial data B, and the desired range C have been input to the support device 100. If the distribution parameter A, the initial data B, and the desired range C have not been input (NO in step S1C), the processing ends. If the distribution parameter A, the initial data B, and the desired range C have been input (YES in step S1C), the processing proceeds to step S2C.

[0128] Next, in step S2C, the assistance device 100 learns a Gaussian process regression model using the initial data B and the desired range C (see the above formulas (1) and (2)). As described above, the second objective variable is input to "y" in formula (2).

[0129] Next, in step S4C, the support device 100 determines L candidate value combinations based on a probability density function based on the predetermined distribution (multivariate normal distribution) of the above formula (12). Next, in step S6C, the support device 100B calculates the variance σ and the mean μ for each of the L candidate value combinations based on formulas (3), (4), and (14). Next, in step S30C, the support device 100B executes a user notification process.

[0130] Step S30C includes step S12C and step S14C. In step S12C, the support device 100B calculates an evaluation value V for each of the L candidate value combinations using equation (15) above. Next, in step S14C, the support device 100B selects the candidate value combination with the smallest evaluation value V from the L candidate value combinations. Then, the determination unit 112 outputs the selected candidate value combination as a proposed candidate value combination.

[0131] Fig. 21 shows the simulation results of the third embodiment. The example in Fig. 21 shows the results of a comparative example and an example. The comparative example is an example in which candidate values ​​are determined by the uniform random numbers described above, and the example is an example in which candidate values ​​are determined by the probability density function g(x) of equation (12).

[0132] As described above, the user conducts experiments using the proposed values ​​proposed by the assistance device. The number of experiments in FIG. 21 is the number of experiments conducted until the first objective variable falls within the desired range C. In the example of FIG. 21, the number of experiments in the comparative example is 18, while the number of experiments in the example is 16. Therefore, the number of experiments conducted until the first objective variable falls within the desired range C is fewer in the example than in the comparative example, which can reduce the burden of experimentation on the user. Note that the example of FIG. 21 shows that the attribution probability P in the example is higher than the attribution probability P in the comparative example.

[0133] As described above, the support device 100B of the third embodiment acquires distribution parameters (see FIG. 2) from the user. The predetermined distribution (multivariate normal distribution) indicated by these distribution parameters defines the determination probability Q of the explanatory variables (see FIG. 18). The support device 100B determines candidate values ​​based on the determination probability Q defined by this predetermined distribution. Therefore, the search range for candidate values ​​can be narrowed compared to the configuration of the comparative example in which candidate values ​​are determined using uniform random numbers. Therefore, the support device 100B can determine more appropriate candidate values.

[0134] Furthermore, the support device 100B calculates an evaluation value V based on the difference between the mean μ and the variance σ for each of the L candidate values. This improves the accuracy of proposing explanatory variables corresponding to objective variables that fall within the user's desired range C. Specifically, the support device 100B can reduce the number of experiments shown in FIG. 21.

[0135] Furthermore, in this embodiment, there are multiple types of explanatory variables (four types in this embodiment). The support device 100B determines L candidate value combinations using information indicating the correlation between the multiple types of explanatory variables (the correlation matrix in FIG. 6 in this embodiment). Therefore, even if there are multiple types of explanatory variables, it is possible to determine L candidate values ​​that reflect the multiple types of explanatory variables.

[0136] In this embodiment, it is assumed that the explanatory variables follow a normal distribution. However, if it is assumed that the explanatory variables follow a predetermined distribution other than the normal distribution, the candidate values ​​are determined based on the other distribution. Another predetermined distribution will be described below. FIG. 22 is an example of a predetermined distribution when there is one type of explanatory variable. Note that the vertical axis in FIG. 22 and FIGS. 23 and 24 described below indicates the determination probability Q, and the horizontal axis indicates the explanatory variable.

[0137] The predetermined distribution may be a normal distribution as shown in FIG. 22(A). Alternatively, the predetermined distribution may be a log-normal distribution as shown in FIG. 22(B). For example, when the assistance device of this embodiment is applied to an experiment in which a glass rod is dropped and the size of the broken pieces of the glass rod is measured, a log-normal distribution may be applied as the predetermined distribution. Alternatively, the predetermined distribution may be a distribution having multiple peaks as shown in FIG. 22(C) (two peaks in the example of FIG. 22(C)). Although not shown, when there are multiple types of explanatory variables, an integrated distribution obtained by integrating the multiple types of normal distributions may be applied as the predetermined distribution.

[0138] Fig. 23 is a diagram for explaining the conversion from the log-normal distribution in Fig. 22(B) to a normal distribution. As shown in Fig. 23, when the predetermined distribution is a log-normal distribution, the support device 100B may convert it to a normal distribution by converting it as y = logx. By converting it to a normal distribution in this way, the support device 100B can determine a proposed value by the above-mentioned method.

[0139] 24A and 24B are diagrams showing examples of discrete probability distributions, where Fig. 24A shows a binomial distribution and Fig. 24B shows a Poisson distribution.

[0140] It should be noted that, with regard to the above-mentioned embodiments and modified examples, it has been intended from the outset of the application that the configurations described in the embodiments may be appropriately combined, including combinations not mentioned in the specification, to the extent that no inconvenience or contradiction arises.

[0141] The embodiments disclosed herein should be considered to be illustrative in all respects and not restrictive. The scope of the present disclosure is defined by the claims, not by the above description, and is intended to include all modifications within the meaning and scope of the claims. [Explanation of symbols]

[0142] 100,100A,100B Support device, 102 Acquisition unit, 104 Candidate unit, 106 Variance unit, 108 Distance unit, 110 Probability unit, 112 Decision unit, 114 Threshold unit, 162 ROM, 182 Memory, 183 Interface, 200 Display device, 300 Prediction device, 350 Prediction model.

Claims

1. A method for assisting a search for explanatory variables by a computer, comprising: The process executed by the computer is obtaining distribution parameters indicating a first distribution that defines a determination probability of the explanatory variable; determining a plurality of candidate values ​​that are candidates for the explanatory variables based on the determination probability; obtaining a plurality of values ​​to be used as the explanatory variables; obtaining a range of a response variable corresponding to the explanatory variable; calculating a variance and a mean of a second distribution for each of the plurality of candidate values ​​based on the plurality of values ​​and the range of the response variable; determining a proposed value from the plurality of candidate values ​​based on a difference between a variance and an average of each of the plurality of candidate values, and notifying the user of the proposed value.

2. There are multiple types of explanatory variables, The support method according to claim 1 , wherein the first distribution is a multivariate normal distribution of the plurality of types of explanatory variables.

3. The explanatory variables are variables used in battery experiments, The support method further includes updating a prediction model that outputs a value as a dependent variable when an explanatory variable is input, based on the explanatory variable indicated by the proposed value and a dependent variable corresponding to the explanatory variable; the explanatory variables are variables related to materials of the battery, The support method according to claim 1 or 2, wherein the response variable is a variable related to a characteristic of the battery.

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