Residual battery capacity prediction method

Abstract

To provide a residual battery capacity prediction method with which it is possible to predict a true value in a short time utilizing the discharge measurement of a battery.SOLUTION: Provided is a residual battery capacity prediction method that predicts the residual capacity of a battery that is repeatedly usable by recharging. This method includes: defining an objective variable for predicting a residual battery capacity; extracting a plurality of explanatory variables which has high importance as the element used for residual capacity prediction and has linearity; deriving a relational expression that indicates relationship between the objective variable and the explanatory variables, as a regression equation; predicts the passage in time of the discharge voltage value and / or the discharge current of the battery, using the regression equation; and predicting the residual capacity of the battery.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a method for predicting the remaining capacity of a battery that can be repeatedly used by charging, such as a rechargeable battery like a nickel-metal hydride battery, a nickel-cadmium battery, a nickel-zinc battery, a lithium-ion secondary battery, or a rechargeable alkaline battery. [Background technology]

[0002] In recent years, there has been a surge in efforts to regulate carbon dioxide emissions, which are considered a cause of global warming. As a result, vehicles, for example, are gradually shifting from drive systems using fossil fuels such as gasoline and diesel to hybrid systems, and even to drive systems using motors powered by rechargeable batteries.

[0003] With the increasing activity in recycling such as the reuse of secondary batteries, a battery information processing system has been proposed as one method to improve the accuracy of estimating the full charge capacity of modularized battery packs, for example (see, for example, Patent Document 1). This system is for processing information to estimate the full charge capacity of a module and comprises a memory device that stores a trained neural network model and an analysis device that uses the trained neural network model to estimate the full charge capacity of the secondary battery from the AC impedance measurement results of the module.

[0004] Furthermore, to improve the accuracy of estimating the full charge capacity of a battery, a pre-trained neural network model has also been proposed (see, for example, Patent Document 2). This neural network model is a model that has been trained based on Nyquist plots of multiple modules whose full charge capacity is within a reference range. In this processing system, discriminant analysis is performed using at least one feature extracted from the module's Nyquist plot as an explanatory variable to determine whether the module belongs to a first group whose full charge capacity is within a reference range or a second group whose full charge capacity is outside a reference range. Then, in this processing system, for example, if the module is determined to belong to the first group, the pre-trained neural network model is used to estimate the module's full charge capacity.

[0005] Furthermore, a system has been proposed that accurately predicts whether battery capacity can be recovered through a capacity recovery process (see, for example, Patent Document 3). Specifically, in this system, when a nickel-metal hydride battery module is subjected to a capacity recovery process, the system uses the Mahalanobis-Taguchi method (MT method) with multiple explanatory variables to determine whether the module belongs to a first group where the battery capacity is below a reference capacity, or a second group where the battery capacity is above a reference capacity. Incidentally, the feature quantities of the multiple explanatory variables include at least two real number components of AC impedance plotted in the semicircular portion, at least two imaginary number components of AC impedance plotted in the semicircular portion, and at least one imaginary number component of AC impedance plotted in the linear portion.

[0006] Furthermore, a control system for secondary batteries has been proposed that performs anomaly detection while also predicting other parameters (internal resistance, SOC (state of charge), SOH (state of health), etc.) with high accuracy (see, for example, Patent Document 4). This control system uses a Kalman filter to detect the difference between the observed value (voltage) at a certain point in time and the voltage estimated using prior state variables. A threshold voltage is set in advance, and sudden anomalies, specifically micro-shorts, are detected based on the detected difference voltage. Patent Document 4 also states that it is preferable to use a neural network to learn time-series data of the difference voltage and to determine and detect whether it is abnormal or normal. [Prior art documents] [Patent Documents]

[0007] [Patent Document 1] Japanese Patent Publication No. 2020-20604 [Patent Document 2] Japanese Patent Publication No. 2020-21592 [Patent Document 3] Japanese Patent Publication No. 2020-24153 [Patent Document 4] WO2019 / 138286 publication [Overview of the project] [Problems that the invention aims to solve]

[0008] In the models and systems described in such patent documents, even methods such as measuring the internal resistance and voltage of a battery and using machine learning to predict the remaining charge are inaccurate, and measuring the true value takes a long time.

[0009] Given these circumstances, the present invention aims to provide a method for predicting the remaining battery capacity that can predict the true value in a short time by utilizing battery discharge measurement. [Means for solving the problem]

[0010] The first method for predicting the remaining battery capacity of the present invention is a method for predicting the remaining capacity of a battery that can be repeatedly used by charging, defining an objective variable for predicting the remaining amount of the battery, extracting a plurality of explanatory variables having high importance and linearity as elements used for predicting the remaining amount, deriving a relational expression showing the relationship between the objective variable and the explanatory variables as a regression equation, using the regression equation to predict the temporal progress of at least one of the discharge voltage value and the discharge current of the battery, and predicting the remaining amount of the battery capacity is what it is.

[0011] In the second method for predicting the remaining battery capacity of the present invention, for each of the explanatory variables, the decreasing slope ([dV / dt] or [dA / dt]) of the discharge voltage or the discharge current with respect to the entire measurement time, the rate of decrease per unit time within a specified time within the range excluding the initial value with respect to at least one of the discharge voltage value and the discharge current, and the step difference which is the amount of decrease per predetermined time interval are used, In addition, the initial voltage is used as a constant (intercept) in the regression equation, is what it is.

[0012] In the third method for predicting the remaining battery capacity of the present invention, each of the explanatory variables is regularized to calculate a partial regression coefficient, and the partial regression coefficient is used as each coefficient in each objective variable in the regression equation.

[0013] In the third method for predicting the remaining battery capacity of the present invention, the regression equation includes, in addition to the plurality of explanatory variables, either an initial voltage value or an initial current value as a constant term.

Brief Description of the Drawings

[0014] [Figure 1]It is a flowchart showing a method for predicting the remaining amount of battery capacity when predicting the remaining amount of battery capacity using the method for predicting the remaining amount of battery capacity according to an embodiment of the present invention. [Figure 2A] It is a flowchart showing a method for deriving a regression equation according to an embodiment of the present invention. [Figure 2B] It is an explanatory diagram showing the relationship between the explanatory variables and the objective variable constituting the regression equation according to an embodiment of the present invention. [Figure 3A] It is a graph showing the modes of the transient states of good batteries and defective batteries to be determined by the remaining amount prediction method according to an embodiment of the present invention. [Figure 3B] It is a demand graph used as a material for selecting explanatory variables used in the remaining amount prediction method according to an embodiment of the present invention. [Figure 3C] (A) is a graph showing the standardized partial regression coefficients for the extracted explanatory variables that are elements used in the remaining amount prediction method according to an embodiment of the present invention, and (B) is a graph showing the analysis behavior of each element that is a judgment material for extracting each element used in the remaining amount prediction method according to an embodiment of the present invention. [Figure 3D] It is a table showing data such as partial regression coefficients used as a material for selecting explanatory variables used in the remaining amount prediction method according to an embodiment of the present invention. [Figure 3E] They are graphs plotting the data used when calculating the explanatory variables and their coefficients in the regression equation used in the remaining amount prediction method according to an embodiment of the present invention. [Figure 3F] It is an explanatory diagram showing the overall slope among the explanatory variables in the regression equation used in the remaining amount prediction method according to an embodiment of the present invention. [Figure 3G] It is an explanatory diagram showing the step difference among the explanatory variables in the regression equation used in the remaining amount prediction method according to an embodiment of the present invention. [Figure 3H] It is an explanatory diagram showing the reduction rate among the explanatory variables in the regression equation used in the remaining amount prediction method according to an embodiment of the present invention. [Figure 3I] It is an explanatory diagram showing the change in the defective rate before and after using the remaining amount prediction method according to an embodiment of the present invention. [Figure 4]This graph shows that the defect rate could be reduced to 10% or less by using the remaining quantity prediction method according to one embodiment of the present invention. [Modes for carrying out the invention]

[0015] Hereinafter, one embodiment of the present invention and one example thereof (a specific example) will be described in detail with reference to the attached drawings.

[0016] <1. One Embodiment> Figure 1 shows a method for predicting remaining battery capacity, including the steps required to perform the battery capacity prediction method according to one embodiment of the present invention. In this embodiment, the battery targeted for remaining charge prediction is a HEV (Hybrid-Electric Vehicle) battery (hereinafter simply referred to as "battery"), but the battery targeted by the remaining charge prediction method of the present invention is, of course, not limited to this. That is, various types of batteries are compatible, such as rechargeable batteries like nickel-metal hydride (NiH) batteries, nickel-cadmium batteries, and nickel-zinc batteries, as well as lithium-ion secondary batteries and rechargeable alkaline batteries that can be used repeatedly by charging.

[0017] [Steps for configuring the method for predicting remaining battery capacity] The battery capacity remaining prediction method of this embodiment consists of steps 1 S1 to 5 S5, as shown in Figure 1, and predicts the remaining capacity using a regression equation, which will be described later.

[0018] In subsequent embodiments, the remaining quantity prediction method of the present invention uses the terms "explanatory variable" and "objective variable (or response variable)". While these technical terms can be considered synonymous with "explanatory factor" and "objective factor," respectively, in mathematical terms, a "factor" is generally understood to be one of the constituent elements expressed in the form of a product for a single "term". However, in the present invention, considering that the functional form in the regression equation described later is polynomial, and each "explanatory variable" corresponds to each "term," the term "factor" is avoided, and the former technical term "variable" is used instead.

[0019] The general flow of regression analysis related to one embodiment of the present invention will be explained below using Figure 1, but here we will first explain how to determine the "regression equation". In one embodiment of the present invention, a "regression analysis" method is used to implement the method for predicting the remaining battery level. A general method for obtaining the "regression equation" used in this regression analysis will be explained in detail with reference to Figure 2 as appropriate. Incidentally, in this regression analysis, since multiple elements as shown in Figure 2B are used as explanatory variables, it is configured to perform a "multiple regression analysis".

[0020] In other words, in this multiple regression analysis, the dependent variable, which is the objective variable, is predicted and explained using multiple independent variables, which are the explanatory variables.

[0021] As shown in Figure 2A, this multiple regression analysis generally consists of the following steps T1 through T4, which are used to determine the appropriate regression equation.

[0022] Step 1, T1, determines the dependent variable (OV) and the explanatory variables (EV) that are likely to be related to it. In this regression analysis, the degree of influence that the explanatory variables have on the dependent variable is quantified, and their relationship is represented by an equation such as a straight line. The relationship between these two types of eigenvariates, namely the explanatory variables (EV1, EV2, ...) and the dependent variable (OV), is shown in Figure 2B.

[0023] In this embodiment, Elastic Net regression is used to determine the explanatory variables, which are elements of the data, from pre-obtained data, and this will be explained later.

[0024] Step 2, T2, involves estimating the regression equation. This regression equation is the equation obtained as a result of the regression analysis, and specifically, it is a functional form as shown in equation (1) below. This regression equation summarizes the relationship between the dependent variable and the independent variables into a single equation by estimating the values ​​of the "coefficients" and "intercept" of the equation. Details will be explained later. Note that the coefficients here are sometimes called "regression coefficients."

[0025] Furthermore, the coefficients in the multiple regression equation, which will be discussed later, are sometimes called "partial regression coefficients." Since these partial regression coefficients depend on the magnitude and units of the explanatory variables, comparing the coefficients of each explanatory variable directly is meaningless. To compare these coefficients, standardization is performed using a method called standard deviation regression, which yields "standardized partial regression coefficients." Using these standardized partial regression coefficients, it becomes possible to compare the relative magnitudes of the coefficients even if the magnitudes and units of the explanatory variables are different, thus allowing for a comparison of their influence on the dependent variable (see Figure 3D).

[0026] Furthermore, this regression analysis allows us to determine the coefficients of the explanatory variables (i.e., regression coefficients) and the constant term (i.e., intercept) from previously obtained data. For example, the Ordinary Least Squares (OLS) method can be used to find the "partial regression coefficients" and the "regression constant" (sometimes simply called the "constant") that minimize the sum of squares of the errors between the observed and predicted values ​​of the dependent variable.

[0027] Step 3, T3, evaluates the regression equation obtained (estimated) in Step 2, T2. Indicators used for this evaluation include the precision of the regression equation (corrected value R²), coefficients (P-value), statistical significance (i.e., significance of the regression equation: significance value F), or impact (t-value).

[0028] In multiple regression analysis, the coefficients of each explanatory variable in the regression equation are sometimes called "partial regression coefficients." The definitions of each are omitted here, but The "correction value R²" takes on a value between 0 and 1, and the closer it is to 1, the more accurate the regression equation is considered to be. Generally, a p-value of less than 0.05 indicates that the explanatory variable has a strong relationship with the dependent variable. • If the "F-score" is less than 0.05, it can be determined that the regression equation is significant. The "t-value" indicates that the larger the absolute value, the stronger the influence. As a guideline, if the absolute value of t is less than 2, it is judged that the explanatory variable does not influence the dependent variable.

[0029] In addition to calculating the coefficient of determination in multiple regression analysis, another method for evaluating regression equations is "residual analysis," which examines the variability of the "residuals." It is known that if the regression equation is valid for the measured data, the residuals will be appropriately distributed (uniformity of variance). To check this, one can create a graph called a "residual plot," which arranges the residuals of each data point in order, and manually verify it (in this graph, for example, the horizontal axis can be set to the data number and the vertical axis to the residual value). In this residual plot, one can check how the residuals on the horizontal axis are distributed relative to "0" on the vertical axis. Incidentally, if the residuals are uniformly distributed relative to "0" on the vertical axis, there is generally no major problem.

[0030] In the fourth step T4, the regression equation obtained in the third step T3 is evaluated, and the one with the highest accuracy is selected and used as the regression equation in the battery capacity remaining prediction method of this embodiment.

[0031] [Method for predicting remaining battery level] Next, a method for predicting the remaining battery capacity will be described, which includes steps necessary to perform the battery capacity prediction method according to one embodiment of the present invention. This remaining capacity prediction method consists of the first step S1 to the fifth step S5, as shown in Figure 1.

[0032] In the first step, S1, multiple "explanatory variables" and "constants" (these elements will be described in detail in the second step, S2), such as equation (1) described later, are added together into a single equation and defined as the "objective variable (OV)". Here, the "objective variable" refers to the variable that is the result of the cause that is the subject of the "explanatory variables".

[0033] In the second step S2, several "explanatory variables (EV)" are extracted. Here, "explanatory variables EV" are also called "independent variables," and refer to variables that are the cause of something. In this invention, as shown in Figure 3C(B), explanatory variables that have high cross-validation results in Elastic Net regression and stable analytical behavior are extracted. That is, in this embodiment, the definitions and other details will be explained in the examples described later, but as shown in Figure 3C(A), (30sec) Decrease rate ·(120sec) floor difference • Overall tilt S (tilt OCV) These three elements were extracted as explanatory variables.

[0034] Furthermore, it is necessary and important to select elements with high linearity, in order to define them in relation to the dependent variable, as will be discussed later; in other words, in order to enable the application of the superposition principle. Here, "Elastic Net" refers to "ridge regression" and "LASSO". This refers to a method that combines "[...]. Like LASSO (least angle regression), Elastic Net can generate dimensionality-reduced models by generating zero-value coefficients. Empirical studies suggest that the Elastic Net method performs better than LASSO because it uses data with highly correlated predictors. Furthermore, "cross-validation results" refer to a method for evaluating the generalization performance of individual models.

[0035] In this embodiment, the "Elastic Net" method can solve the "regularization" problem more accurately than other methods. In other words, it can calculate partial regression coefficients with high accuracy. The mathematical definition of Elastic Net is that it is a method that provides a solution to the following equation Z (the problem), which is written using a norm α that is strictly defined between 0 and 1, and a non-negative normalization parameter λ. Z≡min[(1 / 2N)Σ N i=1 (y i -β0-x i T β) 2 +λP α (β)] where N is the number of measurements y i : response data of the i-th measurement value x i : data (vector of P-values of the i-th measurement value, x i T is a tensor) λ: a positive hyperparameter corresponding to one value of Lambda (e.g., a coefficient representing the influence degree of the regularization term, etc.), also called a regularization parameter β0: a scalar β: a vector α: a hyperparameter that adjusts the relative contributions of the L1 norm (Manhattan distance) and the L2 norm (Euclidean distance) and the domain is 0 ≤ α ≤ 1 P α (β): penalty term (regularization term)

[0036] Here, the penalty term (regularization term) P α (β) omits the mathematical definition of its specific details, but can be evaluated using a norm related to β, etc. Incidentally, when α = 1, Elastic Net becomes the same as LASSO. On the other hand, as α shrinks towards 0, Elastic Net approaches ridge regression. Incidentally, this "Ridge regression" is a method for estimating the coefficients of a multiple regression model when the independent variables are strongly correlated. Also, this ridge regression is for solving the problem that the least squares estimator becomes inaccurate when there is multicollinearity (strongly correlated independent variables) in a linear regression model, and the ridge regression estimator is more accurate than the least squares estimator

[0037] Furthermore, the normalization term is introduced as a parameter to adjust the degree of penalty, because if the coefficient becomes too large, the graph will behave in a way that causes it to jump ("penalty applied").

[0038] (Regarding explanatory variables) In this embodiment, since multiple explanatory variables are combined to form the objective variable, it is necessary to extract linear functions for each explanatory variable. Therefore, from among the major elements that are expected to be the causes of the explanatory variables described later, the following three elements were extracted as important and linear elements, and in particular those that have a significant influence on the objective variable. In other words, 1) The "overall slope S (=dv / dt)" refers to the "temporal slope of the entire initial voltage or open-circuit voltage (OCV (Open Circuit Voltage: rest potential))," and hereafter, this "overall slope S" may be referred to as "slope OCV." That is, it is defined as the rate of change of voltage over the entire time from the initial time (t=0) when the (initial voltage or) open-circuit voltage (OCV) is given to a specific measurement time range, i.e., the voltage change over the entire time interval up to the specific measurement time range, i.e., the voltage slope over the entire time. Furthermore, this is defined as the "first explanatory variable: x1." 2) "Difference" This is defined as "Second explanatory variable: x2". 3) "Percentage decrease (=dv' / dt')" This is defined as "the third explanatory variable: x3".

[0039] As will be explained in more detail later, the dependent variable y obtained using these explanatory variables x, that is, the regression equation, can be expressed as follows (1). y=[(k1)·(x1)]+[(k2)·(x2)]+[(k3)·(x3)]+c ...(1) However, x1, x2, x3: explanatory variables, k1, k2, k3: coefficients c: constant (intercept)

[0040] Furthermore, it is generally necessary to exclude any (multi)collinearity between these extracted explanatory variables. Here, (multi)collinearity refers to a linear relationship between two explanatory variables. In other words, in a multiple regression model, it refers to the existence of combinations of explanatory variables with high correlation coefficients.

[0041] Regarding the method for extracting these explanatory variables, for example, multiple regression analysis is used to determine the elements of the explanatory variables and to evaluate the resulting regression equation (regression model). Furthermore, as an extension of multiple regression analysis, regularization (Lasso regression) is also an important technique as it can improve the accuracy of the regression equation. In other words, this "regularized regression" is a method that multiplies factors with strong multicollinearity together by coefficients, as explained above, so that they can be expressed as partial regression coefficients. As a result, the overall multiplication of coefficients pulls on each other, causing a reduction in the coefficients of the regression equation (this is why regularized regression is also called reduced estimation). Therefore, although a detailed explanation is omitted here, based on the knowledge and experience gained by the inventors of this application over many years, the embodiment employs a technique of first deriving the explanatory variables and then subjecting them to multiple regression analysis again to return to a regression equation without reduction.

[0042] For example, in this embodiment, the method used to derive this regression equation is a method consisting of the first step T1 to the fourth step T4, as explained with reference to Figure 2A.

[0043] The purpose of performing this multiple regression analysis is to predict and explain the dependent variable (y in the regression equation described later) using the dependent variable (x in the regression equation described later). The predictive and explanatory power of the explanatory variables can be considered as the magnitude of their influence on the dependent variable. Therefore, using the least squares method (OLS) described above, we can find the partial regression coefficients and regression constants described above that minimize the sum of the squares of the errors between the observed and predicted values ​​of the dependent variable.

[0044] (i) "Overall slope S": First explanatory variable In other words, this overall slope S (slope OCV) (=dv / dt) is defined as the overall slope (over the entire time axis) in the graph relating the measurement time [sec] to the discharge voltage [V], as shown in Figure 3, and mathematically it is a linear first-order function.

[0045] Note that "the whole" here refers to, for example, as shown in Figure 2A, the discharge voltage V from the discharge voltage value V0 at the initial time t0 to a specific value V S (Hereafter referred to as "Minimum Effective Discharge Voltage V") S The specific time t when descending to (which is called ") S This refers to the change in discharge voltage [V] over a specific time range T up to a certain point.

[0046] In each battery used in this embodiment, once this specific time Δt is set (specified), the temporal progression (change) of the discharge voltage drop phenomenon is uniquely determined within that specific time. In other words, the discharge voltage drop curve (hereinafter sometimes referred to as the "drop function") within the specific time can be uniquely depicted (determined). In this way, once the discharge voltage drop curve can be uniquely depicted (determined), the overall slope S (=dv / dt) described above is determined by a linear first-order function, regardless of how far the specific time range T is set, and regardless of the functional form (drop curve) of the drop function. In other words, the discharge voltage value V0 at the initial time, i.e., the discharge start time (t=0), the specific time range T, and the discharge voltage value V after the end of the specific time range T have elapsed. S Therefore, the overall slope S (=dv / dt) is uniquely determined. That is, S = dv / dt =(V0-V S ) / T ···(2)

[0047] (ii) "Difference D": Second explanatory variable This difference D is an explanatory variable added because the inventors of this invention discovered that the element showing the decrease in discharge voltage per predetermined time (for example, the number of seconds required each time) in a graph measuring the time course of discharge voltage is a major contributing factor in predicting the remaining battery capacity, and is a particularly important element in nickel-metal hydride (NiH) batteries. In this embodiment, for example, data is used that includes the voltage value (Vmes) at the measurement time (referred to as the "measurement point") and the voltage value (Vmes-30) at a measurement time 30 seconds prior to this measurement point. That is, D = (Vmes - 30) - (Vmes) ... (3) It can be defined as follows.

[0048] (iii) "Percentage of decrease": The third explanatory variable This "decrease rate (=dv' / dt')" is a unique time domain T' (=T-t0) that remains after subtracting a specific time (hereinafter referred to as "initial time t0") from the discharge start time, i.e., the initial time (t=0), and is effective for predictive sampling. The temporal progression (change) of the discharge voltage drop phenomenon is uniquely determined for each individual battery.

[0049] In other words, this third element, the rate of decrease (=dv' / dt'), also uniquely depicts (determines) the discharge voltage drop curve (drop function) within the time domain T', just as in the case of the overall slope S mentioned above. Since the discharge voltage drop curve (drop function) can be uniquely depicted (determined) in this way, just as in the case of the first element, the overall slope S (=dv / dt) mentioned above, this second element, the rate of decrease (=dv' / dt'), is determined by a linear function for the overall slope within the time domain T', regardless of the extent of the time domain T' or the functional form (drop curve) of its drop function. In other words, the rate of decrease of the third element is uniquely determined from the charge / discharge voltage V within a specific time range T' in an arbitrary domain obtained by subtracting a specific initial time t0 from the initial time, and the specific time domain T' (=T-t0). That is, Percentage decrease = dv' / dt' =(V0-V0´-Vs) / (TT´) ··· (4)

[0050] Furthermore, the reason for excluding the initial time t0 from the second element's rate of decrease is that the voltage drop is more pronounced during the first 10 seconds of discharge than thereafter, making it undesirable to use this time for predicting remaining capacity.

[0051] The above are the three elements used as explanatory variables, but in addition, a constant c is also used. In this embodiment, the explanatory variables that make up these three elements are the overall slope, difference, and decrease rate mentioned above, but depending on the type of battery used for remaining charge prediction, the explanatory variables are not necessarily limited to the above, and any explanatory variables that can provide a better remaining charge prediction may be adopted.

[0052] In the third step, S3, we derive the regression equation. As mentioned earlier, this regression equation uses explanatory variables that have a large influence on the dependent variable, and each of these explanatory variables must have linear elements. The dependent variable is defined as the sum of these explanatory variables.

[0053] In other words, by utilizing the linearity of each explanatory variable (x1, x2, x3, ..., xn) and defining the dependent variable as y, which is the sum (combination) of these variables, the following relationship (regression equation) holds. y≡[(k1)·(x1)]+[(k2)·(x2)]+[(k3)·(x3)] ····+[(kn)·(xn)]+c However, x1, x2, x3, ..., xn: explanatory variables, k1, k2, k3, ..., kn: coefficients c: constant (intercept)

[0054] In this embodiment, since there are three explanatory variables, the relational equation (regression equation) in this embodiment is as described above. y=[(k1)·(x1)]+[(k2)·(x2)]+[(k3)·(x3)]+c ...(1) However, x1, x2, x3: explanatory variables, k1, k2, k3: coefficients c: constant (intercept) This is the result.

[0055] Furthermore, as mentioned above, it is required to derive a highly accurate regression equation (1), so the estimated regression equations are evaluated in advance to select a highly accurate one. The method for deriving this regression equation has already been explained with reference to Figure 2, so the explanation will be omitted here, but a specific example will be explained in the example described later.

[0056] In the fourth step, S4, a regression equation is used to predict the remaining battery capacity over time. For this prediction, for example, for each nickel-metal hydride (NiH) battery with a rated voltage of 8V, the regression equation (1) obtained in step S3 is used to predict the current capacity due to discharge for each nickel-metal hydride (NiH) battery.

[0057] In other words, in this embodiment, by performing a DC discharge for about 3 minutes, for example, a constant current is applied to each nickel-metal hydride (NiH) battery for about 3 minutes, and the voltage value of its battery capacity is monitored. Then, by using the voltage value obtained at this time, various data can be collected from detecting the transient phenomenon of the remaining capacity over this 3-minute period for each nickel-metal hydride (NiH) battery, and by using the regression equation (1) described above, it is possible to predict the temporal progression of the remaining capacity thereafter.

[0058] In the fifth step, S5, based on the prediction of the time course of the battery capacity of each nickel-metal hydride (NiH) battery using a regression equation in the fourth step, S4, the usable time until the voltage drops to within the effective voltage range (sometimes called the "end voltage") of each nickel-metal hydride (NiH) battery is predicted, and the quality of the nickel-metal hydride (NiH) battery is determined.

[0059] [effect] Therefore, conventionally, when determining the quality of batteries, the AC-IR method, which measures internal resistance, was used for sorting. However, this method required a considerable amount of measurement time to reduce the defect rate in the sorting process to a certain level. In other words, with short measurement times, the prediction of quality was inaccurate, resulting in a large number of defective products being included.

[0060] On the other hand, according to this embodiment of the present invention, it has been found that by selecting a regression equation (1) and performing a current discharge for about 2 minutes (120 seconds) to 3 minutes (180 seconds) using this regression equation (1), a waveform graph (function) suitable for predicting the remaining battery charge can be obtained. Therefore, by using this regression equation (1), it becomes possible to determine whether a battery is good or bad by performing a current discharge for only about 2 or 3 minutes. As a result, this leads to the rapid selection and effective use of reusable batteries such as secondary batteries, and ultimately contributes to the promotion of carbon neutrality.

[0061] <One Example (Specific Example)> Next, we will describe in detail below an actual example (a specific example) of a method for predicting the remaining battery capacity by performing the battery capacity prediction method described in the previous embodiment of the present invention.

[0062] According to this embodiment, although the details will be described later, by using the remaining capacity prediction method of the previous embodiment, we were able to obtain a regression equation suitable for predicting the time course of the battery capacity of a nickel-metal hydride (NiH) battery. This will be explained in detail below.

[0063] In this embodiment, when estimating the explanatory variables, DC discharge is performed to show a transient state in which the voltage (V) of the nickel-metal hydride (NiH) battery decreases from the rated voltage of 8V to the current capacity value required for actual use (for example, 6.3Ah or more). In Figure 3A, those judged as good products that meet the above requirements are indicated by symbols A to D. On the other hand, those judged as defective products are indicated by symbols E to H.

[0064] (Derivation of the regression equation) Next, explanatory variables are determined using waveform graphs with codes A to D indicating good products. In this case, one possible method for deriving these explanatory variables is, as mentioned above, to extract those with high cross-validation results using R / F (Random Forest). Alternatively, methods such as K-fold cross-validation can be used. Furthermore, when deriving these explanatory variables, it is necessary and important to select those with high linearity in order to define them in relation to the objective variable. It should be noted that in this invention, the estimation and derivation of these explanatory variables is not limited to the methods and techniques described above, and various methods can be employed. For example, as an accurate estimation method, Elastic Net can be used, as will be specifically described below.

[0065] In other words, in this embodiment, multiple explanatory variables are estimated and derived using this Elastic Net method, and these derived explanatory variables and constants are used to obtain a regression equation (1)' as in the embodiment described above. For example, as explained in the embodiment described above, that is, as explained in the third step S3, if we utilize the linearity of each explanatory variable (x1, x2, x3, ..., xn) and define the dependent variable y as the sum (combination) of these, the following relationship holds. y≡[(k1)·(x1)]+[(k2)·(x2)]+[(k3)·(x3)] ···+[(kn)·(xn)]+c However, k1, k2, k3, ..., kn: coefficients c: constant (intercept)

[0066] In this embodiment, since there are three explanatory variables, the relationship in this embodiment is: y=[(k1)·(x1)]+[(k2)·(x2)]+[(k3)·(x3)]+c ...(1) However, x1, x2, x3: explanatory variables, k1, k2, k3: coefficients c: constant (intercept) This is the result.

[0067] Incidentally, if we were to extract those with high cross-validation results using R / F (Random Forest), for example, in this embodiment, the demand graph shown in Figure 3B shows that the following factors contribute to demand in that order: difference 180, 120s▲%, overall slope OCV, difference 120, 180s▲%, △30, difference 60, 30s▲%, △120. However, in this prediction method, among the elements that contribute highly to demand, the overall slope OCV and difference 120 are preferable to adopt as explanatory variables, but other elements that contribute highly to demand, namely difference 180, 120s▲%, 180s▲%, △30, difference 60, △120, etc., are not preferable as explanatory variables and result in poor accuracy. The reason for this will be explained later, referring to Figure 3(C)B and Figure 3D. Furthermore, the definitions of symbols that may cause ambiguity among those described above will be explained below. 1) 120s▲%: Percentage decrease in discharge voltage [V] over 120 seconds from any given time. (Except for the first 10 seconds) 2) Slope OCV: Overall slope (=dv / dt), 3) 180s▲%: Percentage decrease in discharge voltage [V] over 180 seconds from any given time. (Except for the first 10 seconds) 4) 30s▲%: Percentage decrease in discharge voltage [V] over a 30-second period starting from any given time. (Except for the first 10 seconds) 5) △30: Total percentage of the measurement taken from the initial time to 30 seconds later. 6) △120: Total percentage of the measurement taken from the initial time to 120 seconds.

[0068] On the other hand, in this embodiment, based on the accumulated knowledge and insights gained from the inventor's years of experience related to this application, it was found that using the slope OVC for x1, the difference of 120 (120-second difference) for x2, and the decrease rate of 30 seconds (30-second decrease rate) for x3 as explanatory variables, as shown in Figure 3C(A), by analyzing the data in Figure 3C(B) and Figure 3D, for example using the Elastic Net method, yields good accuracy in predicting the remaining battery capacity.

[0069] In other words, to explain this in more detail, for example, we introduced a squared error function (cost function), and in order to minimize this squared error function, we analyzed each element in the vicinity of the normalization parameter λ being 0.01000 in Figure 3C (B). We regularized the explanatory factors, extracted the partial regression coefficients, and selected the elements with the highest influence from them. For example, to avoid multicollinearity and extract the relative influence, we used the relational formula, i.e., Standardized partial regression coefficient (β) = Partial regression coefficient (B) × Standard deviation of independent variable ÷ Standard deviation of dependent variable From this, I calculated the standardized partial regression coefficients. By selecting the most significant contributors from the standardized partial regression coefficients, the following elements were extracted. ·No.11:30s▲%(30sec reduction rate) • No. 20: Difference 120 (120-second difference) No. 25: Tilting OCV

[0070] Incidentally, as shown in Figure 3D, the tolerance (likelihood) values ​​obtained were 0.902, 0.776, and 0.823, respectively. Furthermore, the linearity of these explanatory variables was confirmed, as shown in Figure 3E.

[0071] Next, we calculate the coefficients (partial regression coefficients) k1, k2, and k3 of the explanatory variables, as shown in the table in Figure 3E. As mentioned earlier, we can use methods such as the least squares method (OLS) to find the partial regression coefficients and even the regression constant that minimize the sum of the squares of the errors between the observed and predicted values ​​of the dependent variable.

[0072] (Specific methods for determining partial regression coefficients and constants) Next, we will explain the method for determining the coefficients k1, k2, and k3 for each explanatory variable. For example, in this embodiment, the partial regression coefficients (k1~k3) and the regression constant (C) will be explained with reference to Figure 3E. Note that the coefficient values ​​shown here are merely examples used for predicting the remaining charge of nickel-metal hydride (NiH) batteries, and these explanatory variables and coefficients may vary considerably depending on the type of battery used for prediction and the measuring instruments used.

[0073] (i) The first partial regression coefficient k1 (a coefficient related to the slope "Slope OVC (overall slope S)" shown in Figure 3F): This coefficient k1 is the partial regression coefficient of the first explanatory variable x1. In this embodiment, we approximated it by roughly reading the numerical values ​​on the graph in Figure 3E(C), and found that k1 = 0.30 - (-1.0) / 0.04 - (-0.11) =8.66 ≒8.7 This was the result. In this embodiment, the actual accurate coefficient k1 was calculated based on precise data, yielding a value of k1 = 8.731.

[0074] (ii) Second partial regression coefficient k2 (coefficient at the 120-second difference D shown in Figure 3G (in this figure, the difference from 30 seconds ago): This coefficient k2 is the partial regression coefficient of the second explanatory variable x2. In this embodiment, we approximated it by roughly reading the numerical values ​​on the graph in Figure 3E(B), and found that k2=-[0.80-(-0.47)] / [0.01-(-0.02)] = -1.27 / 0.03 ≈-42.3 This was the result. In this embodiment, the actual accurate coefficient k2 was calculated based on precise data, yielding a value of k2 = -42.449.

[0075] (iii) Third partial regression coefficient k3 (coefficient for the decrease rate of 30s▲% shown in Figure 3H): This coefficient k3 is the partial regression coefficient of the third explanatory variable x3. In this embodiment, we approximated it by roughly reading the numerical values ​​on the graph in Figure 3E (A), and found that k3=1.7-(-1.5) / [0.002-(―0.002)] =3.2 / 0.004 ≒800 This was the result. In this embodiment, the actual accurate coefficient k3 was calculated based on precise data, yielding a value of k3 = 802.946.

[0076] (iv) Regarding the constant (intercept) k: Furthermore, regarding the constant (intercept) k, if we approximate it by reading the data shown in the graph in Figure 3E, for example, y ≈ c + (8.7 × 25) + (-42.5 × 20) + (803 × 1) =120 However, if we set the initial time to 3 minutes and discard the intrinsic time from the start time that is unsuitable for remaining quantity prediction (e.g., 120 seconds), then y=120, c ≈ -50.5 This was the result. In this embodiment, the actual precise constant (intercept) was calculated based on rigorous data, yielding the value c = -57.617.

[0077] This allows the regression equation used in this embodiment to be uniquely determined, as shown in the following equation. y=[(8.7)·(x1)]+[(-42.5)·(x2)] +[(802.9)·(x3)]-57.6···(1)´ However, y: dependent variable x1~x3: explanatory variables It should be noted that this regression equation (1)' is merely one applied in this embodiment, and it goes without saying that the battery capacity prediction method of the present invention is not limited to this formula or coefficient.

[0078] (action) Therefore, when we investigated the correlation between predicted current capacity and measured current capacity [Ah] using regression equation (1)' in this embodiment, as shown in the experimental data in Figure 3I, we found that for the predicted residual capacity of N (=130) batteries, the failure rate using the conventional simple measurement method by AC-IR was 34%, but when we used regression equation (1)' to make predictions, the failure rate could be reduced to about 7%.

[0079] Furthermore, according to this embodiment, the measurement time for residual capacity when the defect rate is reduced to 7% using the regression equation (1)' is approximately 2 minutes, which is a significant reduction in time compared to conventional methods. In addition, in this embodiment, the remaining capacity was predicted based on the discharge current of the nickel-metal hydride (NiH) battery, but in the present invention, the remaining capacity of any of the target batteries can be predicted from the temporal prediction of at least one of the discharge voltage (V) and discharge current (I).

[0080] (effect) Thus, in this embodiment, as shown in Figure 4, while conventional methods required approximately 20 minutes of discharge voltage measurement to achieve a defect rate of 34%, this method allows for a defect rate of 7%, significantly below the 10% target, with a discharge voltage measurement of approximately 2 minutes. In other words, while conventional prediction methods resulted in a defect rate of 34%, the prediction method of the present invention can reduce this to 7%, achieving a 27% reduction in the defect rate. Moreover, this method significantly reduces the time required for battery quality determination work for battery reuse, from 20 minutes to approximately 2 minutes, eliminating wasted time in quality determination work and greatly improving the efficiency of the determination process.

[0081] An embodiment and examples of the present invention have been described above. Finally, the above-described embodiment and examples are merely examples of the present invention, and the present invention is not limited to the above-described embodiment and examples. For this reason, various modifications are possible depending on the design, etc., even for embodiments and examples other than those described above, as long as they do not depart from the technical idea of ​​the present invention. Furthermore, the effects described herein are merely examples and are not limiting. Other effects may also exist.

[0082] It should be noted that the drawings and data in the above-described embodiments and examples are illustrative and conceptual in nature, and depending on the battery used, there may be discrepancies between the components in these embodiments and examples and the actual batteries used. Furthermore, the numerical values ​​in the drawings and data will naturally vary significantly depending on the battery used. However, if the effects described in the above-described embodiments and examples are similar to those described above, then those various effects can be expected. [Explanation of Symbols]

[0083] c...constant (intercept) EV... Explanatory variable (independent variable) k1...Overall slope S (slope OCV) (=dv / dt) (coefficient of the first explanatory variable) k²···Difference D (coefficient of the second explanatory variable) k3...decrease rate (=dv' / dt') (coefficient of the third explanatory variable) OV... Objective variable (or response variable) OLS (Least Squares Method) OCV... Initial voltage or open circuit voltage P-value...coefficient R2... Accuracy (correction value) T'...Specific time domain (=T-t0) V...Charge / Discharge Voltage F-score... Significance value: Statistical significance (i.e., the significance of the regression equation) t-value...influence t0...Initial time ts...specific time t=0...Initial time (discharge start time) T...Specific time range T´...time domain V0...Discharge voltage value at initial time V...Discharge voltage Vs...Specific value (minimum effective discharge voltage value)

Claims

1. A method for predicting the remaining capacity of a battery that can be repeatedly used by charging, comprising: defining a response variable for predicting the remaining capacity of the battery; extracting a plurality of explanatory variables that are highly important as factors to be used for the remaining amount prediction and have linearity; deriving a relational expression indicating a relationship between the objective variable and the explanatory variable as a regression equation; Using the regression equation, a time course prediction is made for at least one of a discharge voltage value and a discharge current value of the battery; predicting the remaining capacity of the battery; A method for predicting remaining battery capacity.

2. The explanatory variables are the gradient of decrease ([dV / dt] or [dA / dt]) of the discharge voltage or discharge current over the entire measurement time, the rate of decrease per unit time within a specified time within a range excluding the initial value for at least one of the discharge voltage value and the discharge current, and the difference which is the amount of decrease per predetermined time interval, In addition, the initial voltage is used as a constant (intercept) in the regression equation.

2. The method for predicting remaining battery capacity according to claim 1.

3. Regularizing each of the explanatory variables to calculate partial regression coefficients; The partial regression coefficients are used as coefficients for the respective response variables in the regression equation.

3. The method for predicting remaining battery capacity according to claim 1 or 2.

4. The regression equation includes, in addition to the plurality of explanatory variables, either an initial voltage value or an initial current value as a constant term.

4. The method for predicting remaining battery capacity according to claim 1.

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