JP7730852B2 - Support method - Google Patents

Description

This disclosure relates to a support method.

In recent years, various experiments have been conducted for purposes such as manufacturing objects. In these experiments, observed values are obtained through experiments using parameter values determined by the user. These parameter values and observed values are then used as design values to manufacture the object. Japanese Patent No. 6919770 (Patent Document 1) discloses a technology that uses Bayesian optimization to search for optimal parameter values and notify the user of those parameters.

Patent No. 6919770

Hereinafter, the above parameter values will also be referred to as "explanatory variables," and the above observed values will also be referred to as "target variables." Generally, there is a realistic appropriate range for explanatory variables. However, in the invention described in Patent Document 1, there were cases where explanatory variables outside the appropriate range were proposed. Therefore, even if a user conducted an experiment using explanatory variables outside this appropriate range, they were unable to obtain the optimal target variable.

This disclosure has been made to solve the above-mentioned problem, and its purpose is to propose optimal explanatory variable values.

(1) The assistance method disclosed herein is a method for assisting in the search for explanatory variables. The assistance method includes acquiring a distribution parameter A indicating a first distribution that defines the determination probability of the explanatory variables. The assistance method includes determining multiple candidate values that are candidates for the explanatory variables based on the determination probability. The assistance method includes determining a proposed value from the multiple candidate values and notifying the user of the proposed value.

(2) The assistance method described in (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 the variance and 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 mean of each of the plurality of candidate values and notifying the user of the proposed value.

(3) In the support method described in (1) or (2), there are multiple types of explanatory variables. The first distribution is a multivariate normal distribution of the multiple types of explanatory variables.

(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 outputs a value as a response variable in response to input of the explanatory variables, based on the explanatory variables indicated by the proposed values and the response variables corresponding to the explanatory variables. The explanatory variables are variables related to the battery materials. The response variables are variables related to the battery characteristics.

This disclosure makes it possible to propose optimal explanatory variable values.

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. FIG. 10 is a diagram illustrating an example of distribution parameters. FIG. 10 is a diagram illustrating an example of initial data. FIG. 2 is a functional block diagram of the support device. FIG. 10 is a diagram illustrating a candidate value combination. FIG. 10 is a diagram illustrating correlation coefficients of a correlation matrix. 4 is a flowchart showing a flow of processing by the support device of the first embodiment. 10 is a flowchart illustrating a process of updating a prediction model. 10A and 10B are diagrams for explaining the effects of the support device of the first embodiment. FIG. 1 shows the positive and negative electrodes of a test battery. FIG. 10 is a diagram illustrating a simulation result of the first embodiment. FIG. 10 is a diagram illustrating a simulation result of the first embodiment. 10 is a flowchart showing a flow of processing by the support device of the second embodiment. FIG. 10 is a diagram for explaining advantageous effects obtained by changing the threshold value Eth. FIG. 10 is a diagram illustrating a simulation result of the second embodiment. FIG. 10 is a diagram illustrating a simulation result of the second embodiment. FIG. 10 is a functional block diagram of a support device according to a third embodiment. FIG. 10 is a diagram illustrating an example of a multivariate normal distribution when there are two explanatory variables. FIG. 2 is a diagram illustrating a first objective variable and a second objective variable. 11 is a flowchart showing a process of the support device according to the third embodiment. FIG. 10 is a diagram illustrating a simulation result of the third embodiment. FIG. 10 is a diagram illustrating an example of a predetermined distribution when there is one type of explanatory variable. FIG. 10 is a diagram for explaining conversion from a log-normal distribution to a normal distribution. FIG. 1 is a diagram illustrating an example of a discrete probability distribution.

Embodiments of the present disclosure will now be described in detail with reference to the drawings. Note that identical or equivalent parts in the drawings will be designated by the same reference numerals and their descriptions will not be repeated.

[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.

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).

The assistance device 100 and the prediction device 300 are, for example, computers such as a PC (personal computer), tablet, or 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) the proposed value output from the assistance device 100. The "proposed value" is the value of the explanatory variable proposed to the user.

The user inputs the initial data (see Figure 3 below) and distribution parameters (see Figure 2 below) to the assistance device 100. The assistance device 100 determines the proposed values by performing the calculations described below. The assistance device 100 then outputs the proposed values to the display device 200. The display device 200 displays the proposed values from the assistance device 100.

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

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

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 the user. For example, the prediction device 300 predicts a target variable (the IV resistance value of a battery) from an explanatory variable (the concentration of additives C1 and C2 in a battery) input by the 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.

The prediction device 300 may also predict explanatory variables (concentrations of battery additives C1 and C2) from a target variable (battery IV resistance value) input by the user based on the prediction model 350. This prediction allows the user to obtain the concentrations of battery additives C1 and C2 that will result in the desired IV resistance value.

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 while Figure 1 shows the support device 100 and the prediction device 300 as separate components, the support device 100 and the prediction device 300 may also be integrated.

The objectives of the assistance device 100 of the present disclosure include the following first and second objectives. First, the first objective will be explained. As explained in FIG. 1, the prediction device 300 is capable of making the above predictions. The first objective of this embodiment is to "improve the prediction accuracy of the prediction device 300."

Next, the second objective will be explained. For example, a user may search for explanatory variables to obtain a desired range of an objective variable through an experiment. More specifically, this is the case when the user is searching for explanatory variables (concentrations of additives C1 and C2) that will produce a battery with a desired range of objective variable (IV resistance value). In this case, it is preferable for the user to obtain the optimal objective variable (desired by the user) with as few experiments as possible. The second objective of the assistance device 100 disclosed herein is "to suggest to the user explanatory variables that will obtain a desired range of objective variable with as few experiments as possible."

The support devices of the first embodiment and the second embodiment described below are primarily devices for achieving the first objective, while the support device of the third embodiment is primarily a device for achieving the second objective.

The support device 100 includes a CPU (Central Processing Unit) 181, 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.

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

The program stored in ROM 162 may be stored on 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 product program that can be downloaded via the Internet or the like. The assistance device 100 reads the program provided from the storage medium or the Internet or the like. The assistance device 100 stores the read program in a specified storage area (e.g., ROM). The CPU 181 executes the program to perform processing to calculate the proposed value.

[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 of 1 or more) 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 includes a mean μ and a standard deviation σ.

Figure 2 shows an example of distribution parameter A. In this embodiment, there are four types of explanatory variables (M = 4). The four explanatory variables are composed of the concentrations of four types of additives. In the example of Figure 2, the four additives are vinylene carbonate (VC), lithium bisoxalateborate (LiBOB), additive A, and additive B. Additive A and additive B are P-F bond-containing lithium salt additives. Additive A and additive B differ in their decomposition behavior in the electrolyte and their film formation behavior on the electrode.

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

Figure 3 is a diagram showing an example of initial data B. Initial data B is composed of N (N is an integer greater than or equal to 1) "initial data combinations." In the example of Figure 3, N = 18. The initial data combinations are information indicating combinations 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 the user through experiments 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.

In Figure 3, the information surrounded by a bold line represents one initial data combination. In other words, the initial data in Figure 3 includes 18 initial data combinations. In the example of Figure 3, for example, the objective variable (IV resistance value) for 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 x 4) explanatory variables in Figure 3 correspond to the "multiple values" of this disclosure.

[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.

The acquisition unit 102 acquires distribution parameter A (see Figure 2) and initial data B (see Figure 3) input by the user. The distribution parameter A acquired by the acquisition unit 102 is output to the candidate unit 104 and distance unit 108.

The candidate unit 104 calculates L (L is an integer greater than or equal to 2) candidate value combinations for 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 Figure 1). In this embodiment, L = 1000.

Figure 5 is a diagram for explaining candidate value combinations. The example in Figure 5 shows the candidate value combination numbers and four types of explanatory variables. As mentioned above, since L = 1000, the candidate value combination numbers are specified as 1 to 1000. The "..." in Figure 5 indicates the candidate values calculated by the candidate unit 104. Furthermore, the information surrounded by a thick line in the example in Figure 5 is one candidate value combination. In other words, the candidate unit 104 calculates 1000 candidate value combinations, and 4000 (= 4 x 1000) candidate values.

The candidate unit 104 calculates candidate values using the distribution parameters. For example, the candidate unit 104 calculates them 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 variance unit 106, distance unit 108, and probability unit 110.

The distribution unit 106 calculates the variance σ of the second distribution for each of the L candidate value combinations from the candidate unit 104 based on the initial data B (see Figure 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 is described in detail below.

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 the explanatory variables and the target variable). 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 equation (1):

Here, _xn and _xm on the left side of equation (1) represent vectors consisting of four explanatory variables, where n and m represent variables satisfying 1≦n≦N (=18) and 1≦m≦N, respectively.

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

θ ₀ , θ ₁ , θ ₂ , and θ ₃ on the right-hand side of equation (1) are hyperparameters to be updated (optimized). The distribution unit 106 adjusts the hyperparameters θ ₀ , θ ₁ , θ ₂ , and θ ₃ so that the probability expressed on the left-hand side of equation (2) below best represents the initial data B.

Here, X on the left side of equation (2) represents a matrix consisting of x1 _{,..., xN} . y in equation (2) represents a vector consisting of the values of N objective variables (IV resistance values) included in initial data B. K represents a matrix with equation (1) as its (n, m) components.

Furthermore, when one candidate value combination is expressed as x ^* , the distribution unit 106 calculates the distribution σ by the following equation (3).

Here, K on the right side of equation (3) is the same as K in equation (2). Also, k _* in equation (3) is expressed by equation (4).

As described above, the distribution unit 106 updates the Gaussian process regression model based on equations (1) and (2). Then, the 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 the determination unit 112.

Next, the processing of the distance unit 108 will be described. The distance unit 108 calculates the Mahalanobis distance E for each combination of L candidate values based on the distribution parameter A. In some cases, the Mahalanobis distance E is the distance from the center of gravity of the data group consisting of the L candidate values.

The processing of the distance unit 108 is 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. The method for calculating the correlation coefficient r that constitutes the correlation matrix C is described below. The distance unit 108 calculates the correlation coefficient r by substituting the numerical values contained in the initial data B into the following equation (5).

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. Furthermore, S _jk in equation (5) represents the covariance between explanatory variable j and explanatory variable k. S _j in equation (5) represents the standard deviation of explanatory variable j. S _k in equation (5) represents the standard deviation of explanatory variable k. As described above, N is the number of initial data combinations. i is a variable and corresponds to the number described in FIG. 3. j _i represents the numerical value of the i-th explanatory variable j. _{k i} represents the numerical value of the i-th explanatory variable k. j avg represents the average value of N explanatory variables j. k avg represents the average value of N explanatory variables k. j avg represents 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 the present disclosure.

As a modified example, the distance unit 108 may calculate the correlation coefficient r by substituting the numerical value of the distribution parameter A (see FIG. 2) into equation (5). 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 _Sj and _Sk in equation (5), respectively.

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

If the distance unit 108 determines that there is no correlation between the explanatory variables, it sets the correlation matrix C to a unit matrix. Various methods can be used 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 employed in which the user can input information indicating the presence or absence of a correlation into the assistance device 100. When such a configuration is employed, if the user inputs information indicating that there is no correlation, the distance unit 108 determines that there is no correlation.

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

Σ=DCD (6)

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 Figure 2 as diagonal components. Vector U on the right side of equation (7) is a vector with μ1 to μ4 in Figure 2 as components. Vector X on the right side of equation (7) is a vector with the four explanatory variables specified in the candidate combination as components. The Mahalanobis distance E calculated by distance unit 108 is output to probability unit 110 and decision unit 112.

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 measure of the closeness between the "centroid of the data group assumed to be in a normal distribution (first distribution) defined by the distribution parameter A in Figure 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.

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

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 the probability unit 110 is input to the determination unit 112.

As described above, the determination unit 112 receives the variance σ of each of the 1,000 candidate combinations from the variance unit 106, the Mahalanobis distance E of each of the 1,000 candidate combinations from the distance unit 108, and the attribute probability P of each of the 1,000 candidate combinations from the probability unit 110.

The determination unit 112 calculates the evaluation value V for each of the 1,000 candidate combinations based on the following formula (10):

Evaluation value V=σ ^a ×E ^b ×P ^c (10)
Here, a, b, and c in formula (10) are predetermined real numbers. For example, a, b, and c are 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 the candidate combination evaluation value V by multiplying the variance σ, Mahalanobis distance E, and 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).

Then, the determination unit 112 determines the candidate combination with the maximum evaluation value among the evaluation values for each of the 1,000 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 Figure 1). The proposed candidate value combination corresponds to the "proposed value" in this disclosure.

[Processing flow of the support device]
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).

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

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

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 equations (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 equations (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 equations (8) and (9) above).

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 highest evaluation value as the 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 the "proposition process."

In some cases, a 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 the 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 having the support device 100 execute this proposal process multiple times.

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

[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 the 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") can be considered.

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

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

Figure 9 is a diagram illustrating the effect of the support device 100 of this embodiment. In the example of Figure 9, the number of types of explanatory variables, M, is 3, that is, the diagram shows the first explanatory variable, the second explanatory variable, and the third explanatory variable.

In the example of Figure 9, the candidate value combinations proposed by the configuration of the comparative example described above are shown as black circles, and the candidate value combinations proposed by the assistance device 100 of this embodiment are shown as white circles. Furthermore, the hatched region R is the region defined by the multivariate normal distribution described above. Candidate value combinations with a large attribution probability P described above tend to be closer to the center of gravity (center) of region α.

In the configuration of the comparative example described above, combinations outside the appropriate range (unrealistic) may be selected, such as the proposed candidate value combinations indicated by the black circles in Figure 9. On the other hand, with 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 Figure 9). Therefore, with the assistance device 100 of this embodiment, it is possible to propose optimal and scattered explanatory variable values to the user.

Furthermore, in this embodiment, there are multiple types of explanatory variables (four types in this embodiment). The probability unit 110 performs calculations based on information indicating the correlation between multiple types of explanatory variables (in this embodiment, the correlation matrix in Figure 6). 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.

In addition, in this embodiment, the determination unit 112 calculates the evaluation value V by multiplying not only the variance σ and the membership 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 support device 100 in this embodiment can propose to the user candidate value combinations that are appropriately scattered (away from the center of gravity) while still falling within an appropriate range.

Furthermore, as explained in FIG. 8 and elsewhere, the prediction device 300 updates the prediction model 350 based on the training data (proposed candidate value combinations and the 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.

[Simulation results]
Next, simulation results demonstrating the advantageous effects of the support device 100 of this embodiment will be described. First, the test battery used in the simulation will be described. The positive electrode active material of the test battery's positive electrode was Li(NiCoMn) _O2 . The positive electrode conductive material was acetylene black. The positive electrode binder was polyvinylidene difluoride (PVdF). The positive electrode dispersion medium was N-methyl-2-pyrrolidone (NMP). The positive electrode substrate was aluminum foil. A positive electrode slurry with a mass blend 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.

Next, the negative electrode of the test battery will be described. The negative electrode active material 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.

Next, the electrolyte of the test battery will be described. The volume ratio of the solvents in the electrolyte was EC/DMC/EMC = 3/3/4. The supporting electrolyte was LiPF ₆ (lithium hexafluorophosphate) with a concentration of 0.88 mol/L. The additives in the electrolyte were 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.

The separator for the test battery was a multilayered member containing a PP (polypropylene) layer and a PE (polyethylene) layer. The separator for the test battery was manufactured by cutting this member to a specified planar size.

Figure 10 shows 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 material. The negative electrode 220 is manufactured by cutting the above-mentioned negative electrode raw material.

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.

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 of positive and negative electrodes such as those shown in Figure 10 are disclosed, for example, in Japanese Patent Publication No. 7153701.

The positive electrode, separator, and negative electrode were then stacked in this order to form an electrode assembly. The electrode assembly was then inserted into an exterior body made of aluminum laminate film in a dry environment to form a component. This component was then dried at 100°C under vacuum for 3 hours. After this, the component was cooled to 25°C, after which the above-mentioned electrolyte solution was injected, and the exterior body was welded and sealed. This completed the production of a test battery.

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

Figure 11 shows the simulation results. In the example of Figure 11, the results of five comparative examples and five examples are shown. For these 10 results, Figure 11 shows the VC concentration, LiBOB concentration, additive A concentration, additive B concentration, variance σ, attribution probability P, Mahalanobis distance E, evaluation value V, and IV resistance value.

First, we will explain the working examples. As described above, the support device 100 determines a proposed candidate value combination. Then, the user performs the above-mentioned DCIR measurement using the values of multiple explanatory variables specified in the proposed candidate value combination, thereby measuring the IV resistance value (objective variable). The above proposal process was then repeated four times, resulting in five working example results.

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

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

Next, we will explain the results of a simulation using the root mean squared error (RMSE) to evaluate the accuracy of the prediction model 350. The method for calculating RMSE is explained below. The five sets of experimental data (combinations of four types of explanatory variables and a target variable) of the embodiment shown in Figure 11 are used as dataset DS1 of the embodiment. Three sets of experimental data randomly extracted from dataset DS1 are combined with the initial data (see Figure 3) to generate training dataset Tr1 for the prediction model 350. The remaining two sets of experimental data in dataset DS1 are used as dataset Val for evaluating the prediction model 350.

A prediction model 350 was trained using the training dataset Tr1. During this training, explanatory variables were selected using a stepwise method. The trained prediction model 350 was used to predict a dependent variable. The RMSE was then calculated as the difference between the predicted dependent variable and the dependent variable measured through experiments. This RMSE calculation was performed three times to calculate three RMSEs, and the average of the three RMSEs was then calculated. Similarly, the average of the three RMSEs was calculated using the above RMSE calculation method using five sets of experimental data for the comparative example shown in Figure 11.

Figure 12 is a diagram showing the average RMSE values of the comparative examples and the average RMSE values of the example examples. The example in Figure 12 shows the average RMSE values of the example examples when the average RMSE values of the comparative examples are normalized to be 1. As is clear from Figure 12, the combination of experimental variables proposed by the assistance device 100 of this embodiment can improve the prediction accuracy of the prediction model 350.

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 attribution probability P.

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 .

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, which is a normal distribution for the threshold Eth, and determines the threshold Eth based on the probability density function.

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

In step S12A, the determination unit 112 calculates an evaluation value V for each of the L candidate value combinations using the following formula (11):

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. Then, the determination unit 112 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.

As described above, the support device 100A changes the threshold Eth each time the above proposal process is executed. Figure 14 is a diagram for explaining the advantageous effects of changing the threshold Eth. Figure 14 shows a case where there are two types of explanatory variables, that is, a case where the explanatory variables are a first explanatory variable and a second explanatory variable. Also, in Figure 14, the outline corresponding to the threshold Eth is shown as a circle. Also, Figure 14 shows the determined proposed candidate value combination G.

Figure 14(A) is a diagram showing a case where the threshold value Eth for determining the first proposed candidate value combination is determined to be 19. Figure 14(B) is a diagram showing a case where the threshold value Eth for determining the second proposed candidate value combination is determined to be 30. Figure 14(C) is a diagram showing a case where the threshold value Eth for determining the third proposed candidate value combination is determined to be 24.

As shown in Figures 14(A) to 14(C), proposed candidate value combinations whose Mahalanobis distance E is greater than the threshold value Eth are located outside the contour. Furthermore, because the attribute probability P of the proposed candidate value combination is large, the proposed candidate value combination tends to be located near the contour (threshold value Eth).

As shown in FIG. 14, the threshold value Eth is changed for each proposal process, and therefore the distance of the proposed candidate value combination from the center of gravity can be changed. As a result, the degree of dispersion of the proposed candidate value combination can be increased. Note that a range for the threshold value Eth may be set. This range is, for example, greater than or equal to 10 and less than or equal to 30.

Figure 15 shows the simulation results for this embodiment. Figure 15 shows the results of the same simulation as that described in Figure 11. As is clear from Figures 11 and 15, the variance σ and evaluation value V are greater in the second embodiment than in the first embodiment.

Figure 16 shows the RMSE for this embodiment. Figure 16 shows the results of the same simulation as that described in Figure 12. As is clear from Figures 12 and 16, the RMSE for the second embodiment is improved compared to the first embodiment.

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 greater. Alternatively, the threshold value Eth may be a fixed value of 40 or less. The threshold value Eth may be a fixed value of 10 or greater and 30 or less.

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.

Figure 17 is a functional block diagram of the support device 100B of the third embodiment. As shown in Figure 17, in addition to distribution parameters A and initial data B, a desired range C (described below) is input to the support device 100B.

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

Here, Σ in equation (12) is shown in equation (6) above, and E is the Mahalanobis distance. Figure 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). Figure 18(A) is a diagram showing a case where there is no correlation between the explanatory variables, and Figure 18(B) is a diagram showing a case where there is a correlation between the explanatory variables. Note that 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.

Next, the desired range C will be explained. 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 IV resistance values. For example, the desired range is a range of 106 mΩ to 108 mΩ. Initial data B and the desired range C are input to the dispersion unit 106B. The desired range C corresponds to the "range of the objective variable."

The variance unit 106B calculates the variance σ and the mean value μ for each of the L candidate value combinations. First, the variance unit 106B defines a first objective variable and a second objective variable. Figure 19 is a diagram illustrating the first objective variable and the second objective variable.

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, for example, using equation (13).

The dispersion unit 106B updates the Gaussian process regression model using the above formulas (1) and (2). Note that the objective variable (first objective variable or second objective variable) to which the desired range has been applied is input as "y" in formula (2). The dispersion unit 106B then calculates the dispersion σ using the above formulas (3) and (4).

Furthermore, the distribution unit 106B calculates the mean μ of the second distribution for each candidate value combination using the following equation (14):

The mean μ and variance σ for each candidate value combination calculated by the variance unit 106B are input to the determination unit 112. The determination unit 112 calculates the 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 formula (15). Note that in this embodiment, the formula (10) above for calculating the evaluation value V is not used.

Evaluation value V = μ - σ (15)
Here, since candidate points with a small second objective variable are preferred, candidate points with a small evaluation value V in equation (15) are preferred. 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.

Figure 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 distribution parameter A, initial data B, and desired range C have been input to the support device 100. If distribution parameter A, initial data B, and desired range C have not been input (NO in step S1C), the processing ends. If distribution parameter A, initial data B, and desired range C have been input (YES in step S1C), the processing proceeds to step S2C.

Next, in step S2C, the assistance device 100 trains a Gaussian process regression model using the initial data B and the desired range C (see equations (1) and (2) above). As described above, the second objective variable is input as "y" in equation (2).

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 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 user notification processing.

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. The determination unit 112 then outputs the selected candidate value combination as a proposed candidate value combination.

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

As described above, the user conducts experiments using the proposed values proposed by the assistance device. The number of experiments in Figure 21 is the number of experiments conducted until the first objective variable falls within the desired range C. In the example of Figure 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 reduces the experimentation burden on the user. Note that the example of Figure 21 shows that the attribution probability P in the example is higher than the attribution probability P in the comparative example.

As described above, the support device 100B of the third embodiment acquires distribution parameters (see Figure 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 Figure 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.

The support device 100B also 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.

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 (in this embodiment, the correlation matrix in Figure 6). 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.

In this embodiment, the explanatory variables are assumed to follow a normal distribution. However, if the explanatory variables are assumed to follow a predetermined distribution other than a normal distribution, candidate values are determined based on that other distribution. Another predetermined distribution is described below. Figure 22 is an example of a predetermined distribution when there is one type of explanatory variable. Note that the vertical axis in Figure 22 and Figures 23 and 24 (described below) represents the determination probability Q, and the horizontal axis represents the explanatory variable.

The predetermined distribution may be a normal distribution as shown in Figure 22(A). Alternatively, the predetermined distribution may be a log-normal distribution as shown in Figure 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 with multiple peaks as shown in Figure 22(C) (two peaks in the example of Figure 22(C)). Although not specifically shown, when there are multiple types of explanatory variables, an integrated distribution obtained by integrating these multiple types of normal distributions may be applied as the predetermined distribution.

Figure 23 is a diagram illustrating the conversion from the log-normal distribution in Figure 22(B) to a normal distribution. As shown in Figure 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 using the method described above.

Figure 24 shows an example of a discrete probability distribution. Figure 24(A) shows a binomial distribution, and Figure 24(B) shows a Poisson distribution.

It is intended from the outset that the configurations described in the above-mentioned embodiments and modified examples may be combined as appropriate, including combinations not mentioned in the specification, to the extent that no inconvenience or contradiction arises.

The embodiments disclosed herein should be considered in all respects to be illustrative and not restrictive. The scope of the present disclosure is indicated by the claims, not the above description, and is intended to include all modifications that are equivalent in meaning to and within the scope of the claims.

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 (3)

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. 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. 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.