Apparatus and method for predicting failure rate for batteries

Abstract

The defect rate prediction device can include a data generation device that extracts two driving profiles from among a plurality of driving profiles that constitute original data, allowing overlap, combines the two extracted driving profiles to generate a plurality of extended driving profiles, and generates a plurality of extended weights corresponding to the plurality of extended driving profiles; an aging simulation device that performs a life analysis simulation applying a plurality of climatic conditions to the plurality of extended driving profiles to generate a plurality of capacity degradation degrees; and a PPM simulation device that generates a plurality of probability weights based on the plurality of extended weights and weights corresponding to the plurality of climatic conditions, and calculates a PPM value based on the plurality of capacity degradation degrees and the plurality of probability weights.

Description

[Technical field]

[0001] [CROSS REFERENCE TO RELATED APPLICATIONS] This application claims the benefit of priority based on Korean Patent Application No. 10-2022-0044656 dated April 11, 2022, and all contents disclosed in the documents of that Korean patent application are incorporated herein by reference.

[0002] The present disclosure relates to an apparatus and method for predicting a failure rate for a battery. [Background technology]

[0003] The main concerns of automakers regarding electric vehicle batteries are considered to be long life and minimization of defect rates, as these are quality factors that are directly related to the warranty period of electric vehicles. Automakers can analyze the life degradation of major vehicle parts and use it to inform potential customers, who are the end users, about warranty periods and mileage. To predict the life degradation of vehicle parts, automakers use statistical analysis methodologies in conjunction with simulations to determine defect rates, with the result value being in units of PPM.

[0004] It is important to note that the prerequisites for determining the defect rate are based on many years of reliability analysis experience for vehicle parts. Most of the vehicle parts of existing internal combustion engine vehicles are composed of mechanical devices including engines, while the core part of an electric vehicle is considered to be the battery, which is the main power source and main quality factor that replaces the engine of an internal combustion engine. Therefore, there is a limit to the application of existing statistical methodologies for mechanical reliability analysis to electric vehicle batteries that have electrochemical properties. Summary of the Invention [Problem to be solved by the invention]

[0005] The present invention provides an apparatus and method for predicting a failure rate of a battery based on capacity degradation data of the battery predicted by aging simulation. [Means for solving the problem]

[0006] A defect rate prediction device according to one feature of the present invention includes a data generation device that extracts at least two driving profiles from among a plurality of driving profiles that constitute original data, allowing overlap, combines the extracted at least two driving profiles to generate a plurality of extended driving profiles, and generates a plurality of extended weights corresponding to the plurality of extended driving profiles; an aging simulation device that performs a life analysis simulation applying a plurality of climatic conditions to the plurality of extended driving profiles to generate a plurality of capacity degradation degrees; and a PPM simulation device that generates a plurality of probability weights based on the plurality of extended weights and weights corresponding to the plurality of climatic conditions, and calculates a PPM value based on the plurality of capacity degradation degrees and the plurality of probability weights.

[0007] The aging simulation device may include an ECM module that applies an ECM to a battery to be subjected to an aging simulation for each of the multiple extended driving profiles to generate a voltage, current, SOC, C-rate, and heat generation amount of the battery corresponding to each of the multiple extended driving profiles, a thermal model module that generates an average temperature of the battery using the heat generation amount of the corresponding battery and the temperature of each extended driving profile for each of the multiple extended driving profiles, and an aging model module that calculates a capacity degradation degree of the battery based on the voltage, current, SOC, C-rate, driving state, average temperature, and number of cells of the corresponding battery for each of the multiple extended driving profiles.

[0008] The aging model module can calculate the degree of capacity degradation by distinguishing between cycle degradation according to a driving pattern, which is discharging and charging due to driving among the driving states, and calendar degradation in a battery rest state among the driving states.

[0009] The PPM simulation device can assign a corresponding probability weight from among the plurality of probability weights to each of the plurality of capacity degeneracy degrees, perform bootstrapping according to the plurality of probability weights assigned to the plurality of capacity degeneracy degrees, and calculate a PPM value for sample data extracted by the bootstrapping.

[0010] The PPM simulation device may include a probability weight generation unit that generates the plurality of probability weights using a result of multiplying the plurality of extension weights by weights for each of the plurality of weather conditions.

[0011] The probability weight generation unit can generate a plurality of overall weights by multiplying the plurality of extended weights by weights for each of the plurality of climatic conditions, calculate a weight sum by adding all of the plurality of overall weights belonging to each of the plurality of climatic conditions to calculate a probability weight by dividing each of the plurality of overall weights belonging to each of the climatic conditions by the weight sum.

[0012] The PPM simulation device may include a PPM prediction unit that assigns each of the plurality of probability weights to a corresponding one of the plurality of capacity degeneracy degrees, and repeats bootstrapping a predetermined number of times to restore and extract a predetermined number of capacity degeneracy degrees from the plurality of capacity degeneracy degrees in accordance with the plurality of probability weights assigned to the plurality of capacity degeneracy degrees.

[0013] The PPM prediction unit may calculate a PPM value by applying at least one probability distribution model to the predetermined number of capacity degradations extracted from each bootstrapping, and may generate a final PPM value by adding the PPM values ​​derived from the predetermined number of bootstrappings.

[0014] The PPM simulation device can extract a plurality of capacity degeneracy degrees according to the plurality of probability weights for the plurality of capacity degeneracy degrees, perform a plurality of PPM simulations by applying a plurality of probability distribution models to the extracted plurality of capacity degeneracy degrees, and determine at least one probability distribution model by applying at least one statistical modeling index to the plurality of PPM simulation results.

[0015] According to another feature of the present invention, a method for predicting a defect rate includes the steps of: restoring and extracting at least two driving profiles from among a plurality of driving profiles constituting original data, allowing overlaps, and combining the extracted at least two driving profiles to generate a plurality of extended driving profiles; generating a plurality of extended weights corresponding to the plurality of extended driving profiles; performing a life analysis simulation applying a plurality of climatic conditions to the plurality of extended driving profiles to generate a plurality of capacity degradation degrees; generating a plurality of probability weights based on the plurality of extended weights and weights corresponding to the plurality of climatic conditions; and calculating a final PPM value by assigning the plurality of probability weights to the plurality of capacity degradation degrees.

[0016] The step of calculating the final PPM value may include the steps of: assigning a corresponding probability weight from among the plurality of probability weights to each of the plurality of capacity degeneracy degrees; bootstrapping according to the plurality of probability weights assigned to the plurality of capacity degeneracy degrees; and calculating a PPM value for sample data extracted by the bootstrapping.

[0017] The bootstrapping step may include extracting a predetermined number of capacity degeneracy levels from among the plurality of capacity degeneracy levels according to the plurality of probability weights assigned to the plurality of capacity degeneracy levels.

[0018] The step of calculating the PPM value may include calculating the PPM value by applying at least one probability distribution model to a predetermined number of capacitance degradation degrees extracted from bootstrapping.

[0019] The step of calculating the final PPM value may further include adding PPM values ​​derived from a predetermined number of bootstrappings to generate the final PPM value.

[0020] The step of generating the plurality of probability weights may include a step of generating a plurality of overall weights by multiplying the plurality of extended weights by weights of the plurality of climatic conditions, a step of calculating a weight sum by adding all of the plurality of overall weights belonging to each of the plurality of climatic conditions to each of the plurality of climatic conditions, and a step of calculating a probability weight by dividing each of the plurality of overall weights belonging to each of the climatic conditions by the weight sum.

[0021] The method for predicting a failure rate may further include extracting a plurality of capacitance degeneracy degrees according to the plurality of probability weights for the plurality of capacitance degeneracy degrees, performing a plurality of PPM simulations by applying a plurality of probability distribution models to the extracted plurality of capacitance degeneracy degrees, and determining at least one probability distribution model by applying at least one statistical modeling index to results of the plurality of PPM simulations. Effect of the Invention

[0022] The present invention provides an apparatus and method for predicting a battery failure rate based on battery capacity degradation data predicted by aging simulation. [Brief description of the drawings]

[0023] [Figure 1] FIG. 1 is a diagram illustrating a defect rate prediction device according to an embodiment. [Diagram 2] 1 is a block diagram showing an aging simulation device according to an embodiment; [Diagram 3]FIG. 1 illustrates a PPM simulation device according to an embodiment. [Figure 4] FIG. 1 illustrates a PPM simulation device according to an embodiment. [Diagram 5] 1 is a graph showing cumulative distribution functions for multiple capacitance degeneracy degrees according to an embodiment and cumulative distribution functions for three probability distribution models with excellent model fit; [Figure 6] FIG. 13 is a diagram showing visualization results of cumulative distribution functions and histogram-based probability density functions for three probability denominator models according to one embodiment. [Figure 7] FIG. 13 is a diagram showing visualization results of cumulative distribution functions and histogram-based probability density functions for three probability denominator models according to one embodiment. [Figure 8] FIG. 13 is a diagram showing visualization results of cumulative distribution functions and histogram-based probability density functions for three probability denominator models according to one embodiment. [Figure 9] FIG. 13 shows the results of applying three probability denominator models to multiple capacity degeneracy degrees derived by bootstrapping based on probability weights. [Figure 10] FIG. 13 shows the results of applying three probability denominator models to multiple capacity degeneracy degrees derived by bootstrapping based on probability weights. [Figure 11] FIG. 13 shows the results of applying three probability denominator models to multiple capacity degeneracy degrees derived by bootstrapping based on probability weights. [Figure 12] This is a table showing the PPM values ​​for each model derived for each number of bootstrapping rounds. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0024] Hereinafter, the embodiments disclosed herein will be described in detail with reference to the attached drawings, and the same or similar components are denoted by the same or similar reference numerals, and the duplicated description thereof will be omitted. The suffixes "module" and / or "part" for components used in the following description are given or mixed for the sake of ease of specification writing only, and do not have any meaning or role that is different from each other. In addition, when describing the embodiments disclosed herein, if it is determined that a specific description of such known technology may obscure the gist of the embodiments disclosed herein, the detailed description thereof will be omitted. Furthermore, the attached drawings are merely for the purpose of making the embodiments disclosed herein easily understandable, and it should be understood that the attached drawings do not limit the technical ideas disclosed herein, and include all modifications, equivalents, or alternatives within the ideas and technical scope of the present invention.

[0025] Terms including ordinal numbers such as first, second, etc. are used to describe various components, but the components are not limited by the terms. The terms are used only to distinguish one component from another.

[0026] When a component is referred to as being "coupled" or "connected" to another component, it should be understood that it may be directly coupled or connected to the other component, but that there may be other components in between. In contrast, when a component is referred to as being "directly coupled" or "directly connected" to another component, it should be understood that there are no other components in between.

[0027] It should be understood that in this application, terms such as "comprise" or "have" are intended to specify the presence of features, numbers, steps, operations, components, parts, or combinations thereof described in the specification, but do not preclude the possibility of the presence or addition of one or more other features, numbers, steps, operations, components, parts, or combinations thereof.

[0028] In the following specification, a "cell" refers to a battery cell that makes up a battery pack, and a battery can include at least one battery pack.

[0029] FIG. 1 is a diagram illustrating a defect rate prediction device according to an embodiment.

[0030] As shown in FIG. 1, the defect rate prediction device 1 includes a data generating device 10, an aging simulation device 20, and a PPM simulation device 30.

[0031] The data generating device 10 can generate input data having more types of data distributions than the data distribution of the original data by combining the driving profiles of the original data.

[0032] The driving profile for the battery life analysis may include a power value, a temperature, and a driving mode. The power is a value (unit: Watt) for the battery power sampled at a predetermined sampling time interval, the temperature is a value obtained by recording the temperature condition for a predetermined period in a predetermined unit, and the driving mode means the driving mode of the vehicle. The driving mode is defined by three driving patterns, and may include, for example, driving / discharging (driving), charging (charging), and parking / rest (rest). In the driving profile, the driving pattern is configured to be synchronized with the battery power value, and is defined by a driving pattern value of 2 for - sign (discharging), 1 for + sign (charging), and 0 for 0 (parking) according to the direction and value of the power. The temperature value and the driving pattern value may be values ​​obtained at the same sampling interval as the power value.

[0033] The data generating device 10 can extract and restore at least two operation profiles from a plurality (Na, a natural number equal to or greater than 2) of operation profiles constituting the original data, and generate a plurality (Nb, a natural number equal to or greater than 2) of operation profiles (hereinafter, extended operation profiles) by combining the at least two extracted operation profiles. For ease of explanation, it will be explained below that the number of operation profiles extracted and restored from the plurality of operation profiles is two, Na may be 30, and Nb may be 900. However, the invention is not limited to this.

[0034] The data generating device 10 can select two operation profiles from the 30 operation profiles, allowing overlaps, and generate an extended operation profile with a total combination of 900 (=30×30) by adding the two selected operation profiles. This solves the problem that the operation patterns of the population cannot be adequately depicted with the 30 operation profiles, which are the original data.

[0035] For example, the multiple operation profiles input to the data generating device 10 may be divided into two groups according to region, including 15 operation profiles (A1, A2, A3, ..., A15) for region A and 15 operation profiles (B1, B2, B3, ..., B15) for region B, and each operation profile may be composed of operation pattern data based on power values ​​for about one month (30 days). Each of the 900 extended operation profiles C1, C2, C3, ..., C900 generated by the data generating device 10 is generated by adding two corresponding operation profiles as follows.

[0036] C1=A1+A1,..., C30=A1+B15,

[0037] C31=A2+A1,..., C60=A2+B15,

[0038] ............

[0039] C421=A15+A1,..., C450=A15+B15,

[0040] C451=B1+A1,..., C480=B1+B15,

[0041] ............

[0042] C871=B15+A1,..., C900=B15+B15

[0043] As described above, an extended driving profile (e.g., C451) to which two driving profiles are added includes a total of 60 days of power values, consisting of 30 days of power values ​​of the first profile (e.g., A15) used in the combination and 30 days of power values ​​of the second profile (e.g., A1) used in the combination.

[0044] The data generating device 10 can generate a weight (hereinafter, extended weight) corresponding to each of the multiple extended driving profiles. For example, the data generating device 10 can generate a corresponding extended weight by multiplying two driving profile weights of the original data constituting one of the 1,800 generated extended driving profiles.

[0045] The aging simulation device 20 can perform a life analysis simulation in which Nc (a natural number equal to or greater than 2) climate conditions are applied to a plurality of extended operation profiles to generate a plurality of capacity fades. The aging simulation device 20 can generate a plurality of (Nb×Nc) capacity fades, and each of the plurality of capacity fades may be a capacity fade for a corresponding one of the plurality of climate conditions and a corresponding one of the plurality of extended operation profiles. Hereinafter, for convenience of explanation, it will be explained that Nc is 2. For example, the aging simulation device 20 can perform a life analysis simulation for 900 extended operation profiles under two climate conditions to generate a total of 1800 capacity fades.

[0046] FIG. 2 is a block diagram showing an aging simulation device according to an embodiment.

[0047] The aging simulation device 20 includes an ECM (Equivalent Circuit Model) module 21, a thermal model module 22, and an aging model module .

[0048] The ECM module 21 can generate battery operation information for the multiple extended operation profiles by applying each of the multiple extended operation profiles to the ECM to generate battery operation information according to operation. The ECM is an electrical equivalent circuit model for a battery to be subjected to aging simulation, and can be realized by modeling an electrical circuit using internal parameters of the battery. Input parameters required for the ECM according to one embodiment may include a power value, an initial SOC (State of Charge), an average temperature, the number of cells constituting the battery, a driving mode, an initial OCV (Open Circuit Voltage), and a cell capacity. The power value and the driving state are obtained from the extended operation profile, and the average temperature can be received from the thermal model module 22.

[0049] The ECM module 21 can derive the battery cell current based on the power value recorded in the extended driving profile. The ECM module 21 can integrate the battery cell current and estimate the current SOC value based on the initial SOC value, the battery cell capacity, and the current integration result. For example, the ECM module 21 can estimate the current SOC by adding the SOC change amount obtained by dividing the result of integrating the current battery cell current based on the power value per unit time by the battery cell capacity to the previous SOC. The initial SOC value required at the time of the initial operation for estimating the SOC value may be set as an input parameter. The ECM module 21 can determine the battery current by considering the connection relationship of the battery cells constituting the battery to the battery cell current. For example, if all the battery cells constituting the battery are connected in series, the battery current may be the same as the battery cell current. Alternatively, if the battery cells are connected in series in units of two cells connected in parallel, the battery current may be a value obtained by multiplying the battery cell current by two.

[0050] The ECM module 21 can determine the SOC of one battery cell as the SOC of the battery, assuming that the characteristics of all cells constituting the battery are identical.

[0051] The ECM module 21 can estimate the OCV of the battery cell and the voltage across the battery cell (hereinafter, battery cell voltage) based on an RC equivalent circuit corresponding to the battery cell. Specifically, the ECM module 21 can determine the OCV voltage corresponding to the current SOC, calculate the series resistance voltage when the battery cell current flows through the series resistance in the RC equivalent circuit, and the polarization resistance voltage when the battery cell current flows through the polarization resistance in the RC equivalent circuit, and calculate the battery cell voltage by adding the OCV voltage, the series resistance voltage, and the polarization resistance voltage. The ECM module 21 can determine the battery voltage by considering the connection relationship of the battery cells constituting the battery from the battery cell voltage. For example, if all the cells constituting the battery are connected in series, the ECM module 21 can calculate the battery voltage by multiplying the battery cell voltage by the number of battery cells.

[0052] The ECM module 21 can calculate the C-rate based on the battery cell current. The C-rate (charge and discharge rate) is a value that indicates a ratio of the current value used to charge and discharge the battery. The ECM module 21 can calculate the C-rate by dividing the battery cell current by the battery cell capacity.

[0053] The ECM module 21 can calculate the heat generation of the battery by considering the battery cell current, cell voltage, average temperature, and number of cells. The average temperature can be received from the thermal model module 22. The heat generation is input to the thermal model module 22 and the aging model module 23. The average temperature is used as an important input value that affects the main battery parameters in the RC model-based ECM model. In fact, it can be seen that when the temperature increases, the electrochemical reaction inside the battery becomes active and the internal resistance decreases, and when the temperature decreases, the internal resistance increases. This can affect not only the voltage range availability of the battery but also the SOH, i.e., capacity degradation.

[0054] The thermal model module 22 may generate an average temperature of the battery in the vehicle for each of the multiple extended driving profiles using the heat amount from the ECM module 21 and the temperature of each extended driving profile. The thermal model module 22 may generate the average temperature by considering parameter values ​​such as the heat amount of the air considering the structure inside the vehicle as well as the heat amount and temperature. To this end, the thermal model module 22 may receive a cooling reference temperature, a thermal resistance coefficient of the battery, and the like. The cooling reference temperature may mean a reference temperature value for proceeding with cooling when the temperature of the battery rises to a certain level. The temperature of the extended driving profile may be a temperature outside the vehicle reflecting the climatic conditions of the area in which the vehicle is operated. The thermal model module 22 may consider the thermal resistance coefficient of the battery together with the amount of coolant in order to determine the effect of the heat amount transferred through the air on the temperature of the battery. The thermal model module 22 may calculate an average temperature value generated in the battery by considering the heat amount of the battery, the presence or absence of cooling progress according to the cooling reference temperature, and the amount of heat transferred to the battery through the air.

[0055] The aging model module 23 can receive the battery voltage, battery current, SOC, C-rate, operation state, average temperature, and number of cells for each of a plurality of extended operation profiles, and can calculate the capacity degradation degree of the battery. The aging model module 23 can calculate the life analysis value of the battery according to the capacity degradation degree, and can also calculate the battery power value, the power value of one cell, and the accumulated energy throughput of the battery based on the battery voltage, battery current, and number of cells. The aging model module 23 can derive the SOH value, that is, the capacity retention value of the battery, by applying the battery power value, the accumulated energy, the average temperature, C-rate, and SOC to an algorithm formula reflecting the degradation curve equation. The temperature and charge / discharge of the battery are important factors that determine the degradation degree of the battery. The degradation curve can be obtained by an actual degradation experiment of the battery.

[0056] The aging model module 23 may determine the degree of capacity degradation according to a specific operating state of the battery in consideration of the operating state. For example, in the operation process of an electric vehicle, driving corresponds to discharging the battery, and degradation according to an operation pattern consisting of discharging and charging due to driving among the operating states may be defined as cycle degradation. Another operating pattern is a parked state of the electric vehicle, which is a rest state of the battery, and degradation in the rest state may be defined as calendar degradation. In cycle degradation, the battery is repeatedly charged and discharged, accelerating the capacity degradation of the battery, and in calendar degradation, the use of the battery is minimized, and the capacity of the battery naturally degrades. The aging model module 23 may classify the deterioration process of the battery into one of the above two forms based on the operating state and calculate the capacity fade. The method of the aging model module 23 calculating the capacity fade is not limited to the above and may be realized by various known methods.

[0057] The aging model module 23 can also calculate the degree of capacity retention based on the degree of capacity degradation. For example, assuming that the initial capacity of the battery is 100%, the aging model module 23 can calculate the degree of capacity retention by subtracting the degree of capacity degradation from 100%. The aging model module 23 can also derive the degree of resistance increase of the battery based on an algorithm that reflects the degree of capacity degradation and a degradation curve equation.

[0058] The ECM module 21, the thermal model module 22, and the aging model module 23 described above are merely examples, and the invention is not limited thereto. For example, the aging model module 23 can be realized in various ways by each battery manufacturer, and since the input parameters required by the aging model module differ depending on the aging model module, the ECM model module and the thermal model module can also be appropriately designed to provide the input parameters of the aging model module.

[0059] The PPM simulation device will be described below with reference to FIG.

[0060] FIG. 3 is a diagram showing a PPM simulation device according to an embodiment.

[0061] The PPM simulation device 30 can generate a plurality of probability weights based on a plurality of extension weights and weights corresponding to a plurality of climate conditions, and calculate a PPM value based on a plurality of capacity degeneracy degrees and a plurality of probability weights. The PPM simulation device 30 can assign a corresponding probability weight from among a plurality of probability weights to each of a plurality of capacity degeneracy degrees, perform bootstrapping according to the plurality of probability weights assigned to the plurality of capacity degeneracy degrees, and calculate a PPM value for sample data extracted by bootstrapping.

[0062] The PPM simulation device 30 can receive a plurality of extended driving profiles and a plurality of weather conditions, and a plurality of capacity degradation degrees corresponding to the plurality of extended driving profiles and the plurality of weather conditions. The PPM simulation device 30 can receive a file name, an extended weight, and a driving period together with the extended driving profile.

[0063] The file name is a name that indicates each of the multiple extended driving profiles. When the file names of the 900 extended driving profiles are C1-C900, two climate conditions can be applied to each of the 900 extended driving profiles, such as climate condition 1 (C1, ..., C451, ..., C900) and climate condition 2 (C1, ..., C451, ..., C900).

[0064] The operation period can mean the period required to reach the target mileage for each operation profile. For example, the operation profile for A1 is defined as a 30-day operation record, and when the same operation record is repeated 100 times, it is defined that the target mileage of 160,000 km is reached after about 8 years. In this case, the number 8 years is considered to be the operation period of the profile A1. This can be expressed as A1 (8 years), A2 (10 years), A3 (4 years), ..., A15 (13 years).

[0065] The PPM simulation device 30 may include a probability weight generation unit 31 and a PPM prediction unit 32 .

[0066] The probability weight generating unit 31 can generate a plurality of probability weights by using the results of multiplying a plurality of extended weights by the weights of a plurality of weather conditions. First, the probability weight generating unit 31 can generate a plurality of overall weights by multiplying a plurality of extended weights by the weights of a plurality of weather conditions. The probability weight generating unit 31 can generate 900 overall weights by multiplying 900 extended driving profiles by the weights of two weather conditions.

[0067] When the weights of the 15 operation profiles in the A region are A1 (wa1), A2 (wa2), A3 (wa3), A4 (wa4), ..., A15 (wa15), and the weights of the 15 operation profiles in the B region are B1 (wb1), B2 (wb2), B3 (wb3), B4 (wb4), ..., B15 (wb15), the extended weight of each extended operation profile can be expressed as the product of the weights of the two corresponding operation profiles. The probability weight generation unit 31 can calculate the overall weight by multiplying the extended weight by the weight (cc1, cc2) of the corresponding climate condition among the climate conditions 1 and 2. The total weights of the 900 extended operational profiles for climate condition 1 can be expressed as cc1*wa1*A1wa1, ..., cc1*wa1*wb15, cc1*wa2*wa1, ..., cc1*wa2*wb15, ..., cc1*wa15*wa1, ..., cc1*wa15*wb15, cc1*wb1*wa1, ..., cc1*wb1*wb15, ..., cc1*wb15*wa1, ..., cc1*wb15*wb15, The total weights of the 900 extended operational profiles for climate condition 2 can be expressed as cc2*wa1*A1wa1, ..., cc2*wa1*wb15, cc2*wa2*wa1, ..., cc2*wa2*wb15, ..., cc2*wa15*wa1, ..., cc2*wa15*wb15, cc2*wb1*wa1, ..., cc2*wb1*wb15, ..., cc2*wb15*wa1, ..., cc2*wb15*wb15.

[0068] The above calculation of the overall weight is merely an example according to an embodiment, and the present invention is not limited thereto. Any calculation method that can generate a corresponding weight based on the distribution of a population can be applied to an embodiment.

[0069] The probability weight generation unit 31 can calculate a weight sum for each of the multiple climatic conditions by adding all of the multiple overall weights belonging to each climatic condition, and calculate a probability weight by dividing each of the multiple overall weights belonging to each climatic condition by the weight sum.

[0070] For example, the probability weight generation unit 31 can calculate the 900 probability weights (CW1-CW900) belonging to climate condition 1 by dividing each of the 900 overall weights for climate condition 1 by the sum (TW1) of all 900 overall weights for climate condition 1, as in equation (1), as shown in equation (2).

[0071] [Number 1] TW1=cc1*wa1*A1wa1+...+cc1*wa1*wb15+cc1*wa2*wa1+...+cc1*wa2*wb15+...+cc1*wa15*wa 1+...+cc1*wa15*wb15+cc1*wb1*wa1+...+cc1*wb1*wb15+...cc1*wb15*wa1+...+cc1*wb15*wb15

[0072] [Number 2] CW1=cc1*wa1*A1wa1 / TW1,...CW900=cc1*wb15*wb15 / TW1

[0073] The probability weight generation unit 31 can calculate 900 probability weights (CW901-CW1800) belonging to climate condition 2 by dividing each of the 900 overall weights for climate condition 2 by the sum (TW2) of all 900 overall weights for climate condition 2, as in equation (4), as shown in equation (3).

[0074] [Number 3] TW2=cc2*wa1*A1wa1+...+cc2*wa1*wb15+cc2*wa2*wa1+...+cc2*wa2*wb15+...+cc2*wa15*wa 1+...+cc2*wa15*wb15+cc2*wb1*wa1+...+cc2*wb1*wb15+...cc2*wb15*wa1+...+cc2*wb15*wb15

[0075] [Number 4] CW901=cc2*wa1*A1wa1 / TW1,...CW1800=cc2*wb15*wb15 / TW2

[0076] As shown in equation (5), the sum of the 900 probability weights belonging to each group is 1.

[0077] [Number 5] 1=CW1+...+CW900, 1=CW901+...+CW1800

[0078] The PPM prediction unit 32 assigns each of a plurality of probability weights to a corresponding capacity degeneracy degree among the plurality of capacity degeneracy degrees, and repeats an operation (hereinafter, referred to as bootstrapping) of restoring and extracting a predetermined number (Nr) of the plurality of capacity degeneracy degrees according to the plurality of probability weights assigned to the plurality of capacity degeneracy degrees a predetermined number (Nn). The probability weights corresponding to the plurality of capacity degeneracy degrees are preferentially assigned, the assigned weights are redefined as probability values ​​according to the ratios of the assigned weights to the total number of capacity degeneracy degrees, and the capacity degeneracy degrees are re-extracted according to the probability values ​​in the bootstrapping process, thereby improving the accuracy of the PPM result.

[0079] For example, the PPM prediction unit 32 can assign each of 1800 probability weights to a corresponding capacity degeneracy degree among the 1800 capacity degeneracy degrees. In each bootstrapping, the PPM prediction unit 32 can restore and extract 1800 capacity degeneracy degrees among the 1800 capacity degeneracy degrees according to a plurality of probability weights. The PPM prediction unit 32 can repeat the bootstrapping 30 times. In this way, the probability weights are preferentially assigned to the corresponding capacity degeneracy degrees, and random extraction is performed according to the probability weights.

[0080] The PPM prediction unit 32 can calculate a PPM value by applying at least one probability distribution model to a predetermined number (Nr) of capacitance degradation degrees extracted from each bootstrapping. The PPM prediction unit 32 can generate a final PPM value (hereinafter, final PPM value) by adding the PPM values ​​derived from a predetermined number (Nn) of bootstrappings. At this time, statistical modeling is used to determine the at least one probability distribution model.

[0081] First, a method for determining the probability distribution model used by the PPM prediction unit 32 will be described.

[0082] Statistical modeling is used as an index to check the goodness of fit of various probability distribution models. Statistical modeling allows the selection of a balanced probability distribution model by avoiding the problems of overfitting and underfitting that occur in the process of fitting the data and the model.

[0083] To determine the probability distribution model used by one embodiment, statistical modeling uses metrics such as Negative Log Likelihood (NLL), Akaike Information Criteria (AIC), AIC correction (AICc), Bayesian Information Criteria (BIC), and Root Mean Square Error (RMSE).

[0084] NLL is an index used in the Maximum Likelihood Estimation (MLE) method, and is used to determine whether or not there is a match between actual data and a probability distribution model using a statistical value. The method for calculating NLL is as shown in Equation 6.

[0085]

number

[0086] In equation (6), L means a likelihood function, and corresponds to the equation in the square brackets of the equation on the rightmost side, and has the following meaning. fk(xi|θ) is a probability density function, where i has a value from 1 to the number of data n, and is the resultant value obtained by multiplying all the probability values ​​obtained when applying the parameter θ (Q). This is a process of maximizing the L value of the resultant value, that is, the likelihood function, by the parameter θ. After taking the log of this L value, the process of applying a negative sign results in -ln(L), which is the NLL. Therefore, maximizing the L value means minimizing the NLL, and the minimized NLL value means that the fit between the actual data and the probability distribution model is high. However, when the number of actual data is smaller than the number of parameters of the probability distribution model, there is a limit in that there is a risk of overfitting.

[0087] AIC is a statistical modeling index that uses a likelihood function, similar to the NLL introduced earlier. The method for calculating AIC is as shown in Equation 7.

[0088]

number

[0089] In equation (7), L means the likelihood function, and the higher the degree of fit, the larger the L value, and the larger the logarithmic ln(L) value, the smaller the -2ln(L) value. Here, k is the number of parameters of the model that fit the AIC, or in other words, the independent variables. In other words, the k value becomes higher as the complexity of the model increases and the number of independent variables for fit increases. This is because the higher the model fit, the smaller the -2ln(L) value becomes, so a value is added, which is thought to play the role of a penalty to prevent overfitting. It is said that the AIC value can accurately predict the distribution of the population because the L value increases and the effect of the penalty is reduced when the number of actual data increases.

[0090] AICc is one of the statistical modeling indices that corrects the bias of the AIC described above. In contrast to AIC, AICc has a rather accurate predictive power when the number of data is relatively limited and small. The method for calculating AIC is as shown in (Equation 8).

[0091]

number

[0092] Equation (8) uses AIC as a basic framework, and 2k(k+1) / nk-1 is added as a correction term. k is the number of independent variables, as in AIC, and n is the number of data. At this time, the performance difference between AIC and AICc disappears as the value of n, that is, the number of data, increases infinitely. As can be seen from the equation, the principle of AIC is used as is, so the smaller the AICc value, the higher the model fitness is predicted. However, there is a difference in predictive power between AIC and AICc, and it has been mentioned in previous studies that using AICc is a method to increase accuracy when determining the model fitness using a simulation. In one embodiment, a probability distribution model selected using AICc as a main index based on a limited number of data and evidence from previous studies can be applied to the PPM prediction unit 32. (Previous study: E. Song, S. Won, and W. Lee, "Using the corrected akaike's information criterion for model selection," The Korean Journal of Applied Statistics, vol. 30, no. 1, pp. 119-133, 2017.)

[0093] Like AIC, BIC can induce the best model fitness based on the result value in which information loss is minimized from the maximum likelihood value. The method for calculating BIC is as shown in Equation 9.

[0094]

number

[0095] Equation (9) is similar to Equation (7), and it can be seen that there is a difference in the terms that assign the penalty value. Unlike AIC, the penalty in BIC is structured to increase as the n value, which is the number of data, increases. Therefore, it can be said to be a model suitable for analyzing distribution due to data differences.

[0096] RMSE is also a statistical modeling index, and is calculated by subtracting the predicted value from the actual data, squaring the values, adding them all together, dividing by n, and applying the root. The method for calculating RMSE is as shown in (Equation 10).

[0097]

number

[0098] In equation (10), i has a value ranging from 1 to the number of data n, yi is the ith data of the actual observed value, and yi is defined as the ith data of the predicted value. The value obtained by subtracting the predicted value from the actual data is called the residual, which, when squared, added together, and then divided by n, has the same meaning as the Mean Squared Error (MSE). RMSE can be said to be a statistical modeling index used to analyze MSE in units similar to the actual value by applying a root to it.

[0099] A PPM simulation is performed by applying 17 probability distribution models, such as Beta, Birnbaumsaunders, Exponential, Extreme Value, Gamma, Generalized Extreme Value, Generalized Pareto, Inverse Gaussian, Logistic, Loglogistic, Lognormal, Nakagami, Normal, Rayleigh, Rician, Tlocationscale, and Weibull, to a predetermined number (e.g., 1800) of capacity degeneracy degrees sampled according to the probability weight. When the main index AICc is applied to the PPM simulation results, the three probability distribution models, Extreme Value, Generalized Extreme Value, and Weibull, showed the best model fit. Based on this, at least one probability distribution model of the PPM prediction unit 32 according to one embodiment may be at least one of the three.

[0100] As described above, at least one probability distribution model can be set in the PPM prediction unit 32, but the invention is not limited to this. Alternatively, the PPM simulation device 30 can determine the probability distribution model.

[0101] FIG. 4 is a diagram showing a PPM simulation device according to an embodiment.

[0102] As shown in FIG. 4, the PPM simulation device 30 may further include a probability distribution model determination unit 33.

[0103] The probability distribution model determination unit 33 receives a plurality of probability weights and a plurality of capacity degeneracy degrees, extracts a plurality of capacity degeneracy degrees according to the plurality of probability weights for the plurality of capacity degeneracy degrees, and applies the above-mentioned 17 probability distribution models or the like to the extracted plurality of capacity degeneracy degrees to perform a PPM simulation.

[0104] The probability distribution model determination unit 33 can determine at least one probability distribution model by applying at least one of the above-mentioned statistical modeling indexes to a plurality of PPM simulation results using a plurality of probability denominator models. The probability distribution model determination unit 33 can determine at least one probability distribution model based on a model fitness calculated by applying the statistical modeling index to the plurality of PPM simulation results. The probability distribution model determination unit 33 can transmit the at least one probability distribution model to the PPM prediction unit 32.

[0105] FIG. 5 is a graph showing cumulative distribution functions for a number of capacitance degeneracy degrees according to one embodiment and cumulative distribution functions for three probability distribution models with excellent model fit.

[0106] The three probability distribution models with excellent model fit shown in Figure 5 are the first-order Extreme Value model, the second-order Generalized Extreme Value model, and the third-order Weibull model.

[0107] Cumulative distribution functions when multiple capacity degeneracy degrees sampled are applied to three probability distribution models, the Extreme Value model, the Generalized Extreme Value model, and the Weibull model, are shown in Fig. 5. As shown in Fig. 5, it can be seen that the cumulative distribution function (51) of multiple capacity degeneracy degrees sampled according to the probability weight is similar to the cumulative distribution functions (52-54) of the three probability distribution models. In Fig. 5, the cumulative distribution function for multiple capacity degeneracy degrees according to one embodiment is displayed as "51", the cumulative distribution function according to the Extreme Value model is displayed as "52", the cumulative distribution function according to the Generalized Extreme Value model is displayed as "53", and the cumulative distribution function according to the Weibull model is displayed as "54".

[0108] In this way, when PPM values ​​are calculated using probability distribution functions with similar model fit, the accuracy of PPM prediction can be improved.

[0109] 6 to 8 are diagrams showing visualization results of cumulative distribution functions and histogram-based probability density functions for three probability denominator models according to one embodiment.

[0110] As shown in Figure 6, it can be seen that the degree of fit between the curve (CV1) showing the cumulative distribution function corresponding to the result of applying the multiple capacity degeneracy degrees (hereinafter, sample data) obtained by one sampling according to the probability weight to the Extreme Value Distribution model and the curve (CV0) showing the cumulative distribution function of the sample data is very high. It can also be seen that the curve (CV11) showing the histogram-based probability density function for the sample data appears in a balanced form.

[0111] As shown in Figure 7, the fit between the curve (CV2) showing the cumulative distribution function of the result of applying the Generalized Extreme Value Distribution model to the sample data and the curve (CV0) showing the cumulative distribution function of the sample data is also high. The curve (CV21) showing the probability density function is also well-balanced, and compared to the curve (CV11) in Figure 6, it can be seen that it has a lower peak and a wider variance to the left and right.

[0112] As shown in Figure 8, the fit between the curve (CV3) showing the cumulative distribution function corresponding to the result of applying the Weibull Distribution model to the sample data and the curve (CV0) showing the cumulative distribution function of the sample data is also high. The curve (CV31) showing the probability density function has a lower peak and a downward sloping shape compared to the curve (CV11) in Figure 6.

[0113] In the cumulative distribution function and probability density function, the x-axis is the random variable, which is the capacity degeneracy, and the y-axis value of the cumulative distribution function refers to the cumulative probability, while the y-axis value of the probability density function refers to the probability density. When the threshold for the capacity degeneracy is 0.3 (30%), PPM values ​​that are not seen in the probability density functions of Figures 7 and 8 and the sample data may occur in the probability density function of Figure 8.

[0114] The PPM prediction unit 32 can calculate the PPM value by applying the above-mentioned three probability distribution models to a plurality of capacity degradation degrees derived by bootstrapping based on the probability weight.

[0115] 9 to 11 are diagrams showing the results of applying three probability denominator models to a plurality of capacity degeneracy degrees derived by bootstrapping based on the probability weights.

[0116] The PPM prediction unit 32 performs bootstrapping based on the probability weight 30 times to extract 1,800 capacity degeneracy degrees 30 times, and applies the 1,800 capacity degeneracy degrees extracted each time to the Extreme Value Distribution model, the Generalized Extreme Value Distribution model, and the Weibull Distribution model, respectively, to form a histogram based on the results, and a probability density function based on the histogram can be generated.

[0117] FIG. 9 shows a histogram and a probability density function according to the Extreme Value Distribution model for the capacity degeneracy derived by 30 times of bootstrapping. FIG. 10 shows a histogram and a probability density function according to the Generalized Extreme Value Distribution model for the capacity degeneracy derived by 30 times of bootstrapping. FIG. 11 shows a histogram and a probability density function according to the Weibull Distribution model for the capacity degeneracy derived by 30 times of bootstrapping. FIG. 9 to FIG. 11 show 30 curves showing the probability density functions for each of the 30 times of bootstrapping. As can be seen from FIG. 9 to FIG. 11, a data fluctuation range is formed for the capacity degeneracy. In other words, the accuracy of PPM prediction can be improved by forming a data range for the capacity degeneracy.

[0118] The PPM prediction unit 32 can calculate the PPM value by adding a value where the degree of capacitance degradation exceeds a threshold value (e.g., 30%) within a confidence interval of 75% (12.5% ​​to 87.5%) of the multiple probability density function curves shown in each of Figures 9 to 11.

[0119] Figure 12 is a table showing the PPM values ​​for each model derived for each bootstrapping round.

[0120] As shown in Fig. 12, among the Extreme Value Distribution, Generalized Extreme Value Distribution, and Weibull Distribution, the 30 PPM values ​​that are the 30 bootstrap results based on the probability distribution models Extreme Value Distribution (121 in Fig. 12) and Generalized Extreme Value Distribution (122 in Fig. 12) are 0. In contrast, the 30 PPM values ​​that are the 30 bootstrap results based on the probability distribution model Weibull Distribution (123 in Fig. 12) range from a minimum value of 0.0000000047 to a maximum value of 0.0000006. Therefore, the PPM prediction unit 32 can calculate the final PPM value by adding the 30 PPM values ​​generated based on the Weibull Distribution model.

[0121] In this way, the PPM simulation device according to the embodiment can obtain various data by drawing a smoothed cumulative distribution function in which the input data, i.e., the battery capacity degenerate data, has continuity. Also, model fitting can be achieved with a set of probability distribution models that are not overfitted. Since bootstrapping is performed according to the probability weight, a PPM result value that reflects the variability of the battery can be calculated.

[0122] In one embodiment, bootstrapping is used to overcome the condition that the fitness of the probability distribution is uncertain and the samples extracted from the population are insufficient. This solves the problem of it being difficult to obtain long-term driving data based on various driving types in practice. A life analysis simulation performed based on a short-term battery charge / discharge cycle data model can only generate limited degeneration prediction data. In one embodiment, various driving profiles can be obtained by generating an extended driving profile that combines driving profiles. This overcomes the limitation of having to simply and repeatedly amplify the number of limited degeneration prediction data and predict the PPM value using the amplified data.

[0123] In addition, in one embodiment, the problem of overfitting of PPM prediction results can be solved by selecting an appropriate probability distribution model from among multiple probability distribution models using statistical modeling indicators. At the same time, the diversity of sample data can be improved by bootstrapping using probability weights.

[0124] Although the embodiments of the present invention have been described in detail above, the scope of the present invention is not limited to these embodiments, and various modifications and improvements made by those having ordinary skill in the art to which the present invention pertains also fall within the scope of the present invention.

Claims

1. A battery defect rate prediction device, comprising: a data generating device that extracts at least two operation profiles from among a plurality of operation profiles constituting the original data, allowing overlapping, combines the extracted at least two operation profiles to generate a plurality of extended operation profiles, and generates a plurality of extended weights corresponding to the plurality of extended operation profiles; an aging simulation device that performs a life analysis simulation by applying a plurality of climatic conditions to the plurality of extended driving profiles to generate a plurality of capacity degradation degrees; a PPM simulation device that generates a plurality of probability weights based on the plurality of expansion weights and weights corresponding to the plurality of weather conditions, and calculates a PPM value based on the plurality of capacity degradation degrees and the plurality of probability weights; Defective rate prediction device.

2. The aging simulation device comprises: an ECM module that applies each of the plurality of extended driving profiles to an electrical equivalent circuit model (ECM) for a battery that is a target of an aging simulation to generate a voltage, a current, a SOC, a C-rate, and a heat generation amount of the battery corresponding to each extended driving profile; a thermal model module for generating an average temperature of the battery for each of the plurality of extended driving profiles using the heat generation amount of the corresponding battery and the temperature of each of the extended driving profiles; and an aging model module for calculating a capacity degradation degree of the battery based on a voltage, a current, a SOC, a C-rate, a driving state, an average temperature, and a number of cells of the corresponding battery for each of the plurality of extended driving profiles.

3. The aging model module includes:

3. The device according to claim 2, further comprising a step of calculating a capacity degradation degree by classifying cycle degradation according to a driving pattern in which the battery is discharged and charged during driving among the driving states, and calendar degradation in a battery resting state among the driving states.

4. The PPM simulation device comprises:

4. The defect rate prediction device according to claim 1, further comprising: a plurality of probability weights each corresponding to each of the plurality of capacitance degeneracy degrees; a bootstrapping process according to the plurality of probability weights each assigned to each of the plurality of capacitance degeneracy degrees; and a PPM value for sample data extracted by the bootstrapping process.

5. The PPM simulation device comprises:

5. The defect rate prediction device according to claim 4, further comprising a probability weight generation unit that generates the plurality of probability weights using a result of multiplying the plurality of extension weights by weights for each of the plurality of climatic conditions.

6. The probability weight generation unit multiplying the plurality of extended weights by weights for each of the plurality of weather conditions to generate a plurality of overall weights; 6. The defect rate prediction device according to claim 5, further comprising: a weight sum is calculated by adding all of a plurality of overall weights belonging to each of the plurality of climatic conditions for each of the plurality of climatic conditions; and a probability weight is calculated by dividing each of the plurality of overall weights belonging to each of the plurality of climatic conditions by the weight sum.

7. The PPM simulation device comprises:

5. The failure rate prediction device according to claim 4, further comprising a PPM prediction unit that assigns each of the plurality of probability weights to a corresponding one of the plurality of capacity degeneracy degrees, and repeats bootstrapping a predetermined number of times to restore and extract a predetermined number of capacity degeneracy degrees from the plurality of capacity degeneracy degrees in accordance with the plurality of probability weights assigned to the plurality of capacity degeneracy degrees.

8. The PPM prediction unit is 8. The failure rate prediction device of claim 7, further comprising: applying at least one probability distribution model to the predetermined number of capacitance degradations extracted from each bootstrapping to calculate a PPM value; and adding the PPM values ​​derived from the predetermined number of bootstrappings to generate a final PPM value.

9. The PPM simulation device comprises:

5. The failure rate prediction device according to claim 4, further comprising: extracting a plurality of capacitance degeneracy degrees according to the plurality of probability weights for the plurality of capacitance degeneracy degrees; performing a plurality of PPM simulations by applying a plurality of probability distribution models to the extracted plurality of capacitance degeneracy degrees; and determining at least one probability distribution model by applying at least one statistical modeling index to results of the plurality of PPM simulations.

10. A method for predicting a defect rate for a battery, comprising the steps of: extracting at least two driving profiles from among the plurality of driving profiles constituting the original data, allowing overlapping, and combining the at least two extracted driving profiles to generate a plurality of extended driving profiles; generating a plurality of expansion weights corresponding to the plurality of expansion driving profiles; performing a life analysis simulation by applying a plurality of climatic conditions to the plurality of extended driving profiles to generate a plurality of capacity degradation degrees; generating a plurality of probability weights based on the plurality of expansion weights and weights corresponding to the plurality of weather conditions; assigning the plurality of probability weights to the plurality of capacitive degradation degrees and calculating a final PPM value.

11. The step of calculating the final PPM value comprises: assigning a corresponding probability weight from among the plurality of probability weights to each of the plurality of capacity degeneracy degrees; bootstrapping according to the plurality of probability weights assigned to the plurality of capacity degeneracy degrees; and calculating a PPM value for the sample data extracted by the bootstrapping.

12. The bootstrapping step includes:

12. The method of claim 11, further comprising: restoring and extracting a predetermined number of capacitance degeneracy degrees from among the plurality of capacitance degeneracy degrees according to the plurality of probability weights assigned to the plurality of capacitance degeneracy degrees.

13. The step of calculating the PPM value comprises:

13. The method of claim 12, further comprising the step of calculating a PPM value by applying at least one probability distribution model to a predetermined number of capacitance degradations extracted from the bootstrapping.

14. The step of calculating the final PPM value comprises:

14. The method of claim 11, further comprising adding PPM values ​​derived from a predetermined number of bootstrappings to generate a final PPM value.

15. The step of generating the plurality of probability weights comprises: multiplying the plurality of extended weights by weights for each of the plurality of weather conditions to generate a plurality of overall weights; calculating a weight sum by adding all of a plurality of overall weights belonging to each of the plurality of climatic conditions; The method for predicting a failure rate according to claim 10 , further comprising: calculating a probability weight by dividing each of a plurality of overall weights belonging to each of the climatic conditions by the weight sum.

16. extracting a plurality of capacity degeneracy degrees according to the plurality of probability weights for the plurality of capacity degeneracy degrees; performing a plurality of PPM simulations by applying a plurality of probability distribution models to the extracted plurality of capacitance degradation degrees; The method for predicting a failure rate according to claim 10, further comprising: applying at least one statistical modeling index to results of the plurality of PPM simulations to determine at least one probability distribution model.

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