Apparatus and method for predicting failure rate

Abstract

Disclosed is an apparatus for predicting a failure rate, the apparatus including: data generation means for recovering and extracting two driving profiles by allowing repetition between a plurality of driving profiles configuring original data, generating a plurality of extended driving profiles by combining the extracted two driving profiles, and generating a plurality of extended weights corresponding to the plurality of extended driving profiles; aging simulation means for generating a plurality of capacity attenuations by performing a life analysis simulation applied with a plurality of climate conditions on the plurality of extended driving profiles; and PPM simulation means for generating a plurality of probability weights based on the plurality of extended weights and weights corresponding to the plurality of climate conditions, and for calculating a PPM value based on the plurality of capacity attenuations and the plurality of probability weights.

Description

[0001] Cross-references to related applications

[0002] This application claims priority and benefit to Korean Patent Application No. 10-2022-0044656, filed with the Korean Intellectual Property Office on April 11, 2022, the entire contents of which are incorporated herein by reference. Technical Field

[0003] This disclosure relates to an apparatus and method for predicting the failure rate of a battery. Background Technology

[0004] Long lifespan and minimized failure rates are key concerns for automakers interested in electric vehicle batteries. This is because long lifespan and minimized failure rates are quality factors directly related to the warranty period of electric vehicles, and automakers can analyze the lifespan degradation of critical vehicle components and use long lifespan and minimized failure rates to communicate warranty and mileage information to potential end-users. To predict the lifespan degradation of vehicle components, automakers are using statistical analysis methods combined with simulation to determine failure rates, which have a result value in PPM (parts per million).

[0005] It is important to note that the prerequisites used to determine failure rates are based on years of experience in reliability analysis of vehicle components. While most vehicle components in existing internal combustion engine vehicles consist of mechanical devices including the engine, the core component of electric vehicles is the battery, which is the primary power source and major quality factor replacing the internal combustion engine. Therefore, existing statistical methods used for mechanical reliability analysis are limited when applied to electric vehicle batteries with electrochemical characteristics. Summary of the Invention

[0006] Technical issues

[0007] This invention provides an apparatus and method for predicting battery failure rate based on battery capacity degradation data predicted through aging simulation.

[0008] Technical solution

[0009] According to a feature of the present invention, an apparatus for predicting failure rates includes: a data generation device for recovering and extracting at least two driving profiles by allowing repetition among multiple driving profiles configuring raw data, generating multiple extended driving profiles by combining the extracted at least two driving profiles, and generating multiple extended weights corresponding to the multiple extended driving profiles; an aging simulation device for generating multiple capacity decays by performing a lifetime analysis simulation on the multiple extended driving profiles applying multiple climatic conditions; and a PPM simulation device for generating multiple probability weights based on the multiple extended weights and weights corresponding to the multiple climatic conditions, and for calculating PPM values ​​based on the multiple capacity decays and the multiple probability weights.

[0010] The aging simulation device may include: an ECM module for applying each of the plurality of extended driving profiles to an electrical equivalent circuit model (ECM) of the battery undergoing aging simulation to generate voltage, current, SOC, C-rate, and heating amount of the battery corresponding to each of the plurality of extended driving profiles; a thermal model module for generating an average temperature of the battery for each of the plurality of extended driving profiles by using the heating amount of the corresponding battery and the temperature of each of the extended driving profiles; and an aging model module for calculating the capacity degradation of the battery for each of the plurality of extended driving profiles based on the voltage, current, SOC, C-rate, driving mode, average temperature, and number of cells of the corresponding battery.

[0011] The aging model module can calculate capacity degradation by distinguishing between cycle degradation caused by driving mode discharge and charging and calendar degradation caused by the battery resting state in driving mode.

[0012] The PPM simulation device can assign a corresponding probability weight from the plurality of probability weights to each of the plurality of capacity decays, perform bootstrap based on the plurality of probability weights assigned to the plurality of capacity decays, and calculate the PPM value of the sample data extracted through the bootstrap.

[0013] The PPM simulation apparatus may include a probability weight generation unit, which generates the plurality of probability weights by multiplying the plurality of extended weights by the weight of each of the plurality of climate conditions.

[0014] The probability weight generation unit can multiply the plurality of extended weights by the weight of each of the plurality of climate conditions to generate a plurality of composite weights, and for each of the plurality of climate conditions, calculate the weight sum by adding all the plurality of composite weights belonging to each climate condition, and calculate the probability weight by dividing each of the plurality of composite weights belonging to each climate condition by the weight sum.

[0015] The PPM simulation device may include a PPM derivation unit, which assigns each of the plurality of probability weights to a corresponding capacity decay among the plurality of capacity decays, and repeats bootstrapping a predetermined number of times based on the plurality of probability weights assigned to the plurality of capacity decays to recover and extract a predetermined number of capacity decays among the plurality of capacity decays.

[0016] The PPM derivation unit can calculate the PPM value by applying at least one probability distribution model to a predetermined number of capacity decays extracted from each bootstrap, and generate the final PPM value by adding the PPM values ​​obtained from a predetermined number of bootstraps.

[0017] The PPM simulation apparatus can extract the multiple capacity decays based on the multiple probability weights for the multiple capacity decays, perform multiple PPM simulations by applying multiple probability distribution models to the extracted multiple capacity decays, and determine at least one probability distribution model by applying at least one statistical modeling index to the multiple PPM simulation results.

[0018] According to another feature of the present invention, a method for predicting failure rates includes the following steps: recovering and extracting at least two driving profiles by allowing repetition among multiple driving profiles configured with original data; generating multiple extended driving profiles by combining the extracted at least two driving profiles; generating multiple extended weights corresponding to the multiple extended driving profiles; generating multiple capacity decays by performing lifetime analysis simulations on the multiple extended driving profiles applying multiple climatic conditions; generating multiple probability weights based on the multiple extended weights and weights corresponding to the multiple climatic conditions; and calculating a final PPM value by assigning the multiple probability weights to the multiple capacity decays.

[0019] The calculation of the final PPM value may include: assigning a corresponding probability weight from the plurality of probability weights to each of the plurality of capacity decays; performing bootstrapping based on the plurality of probability weights assigned to the plurality of capacity decays; and calculating the PPM value of the sample data extracted through bootstrapping.

[0020] Bootstrapping may include recovering and extracting a predetermined number of capacity decays based on multiple probability weights assigned to the multiple capacity decays.

[0021] The calculation of the PPM value may include applying at least one probability distribution model to a predetermined number of capacity decays extracted from the bootstrap.

[0022] The calculation of the final PPM value may also include generating the final PPM value by adding the PPM values ​​obtained from a predetermined number of bootstrapping operations.

[0023] The generation of multiple probability weights may include: multiplying the multiple extended weights by the weight of each of the multiple climate conditions to generate multiple composite weights; calculating a weight sum for each of the multiple climate conditions by adding all the multiple composite weights belonging to each climate condition; and calculating a probability weight by dividing each of the multiple composite weights belonging to each climate condition by the weight sum.

[0024] The method may further include: extracting multiple capacity decays based on the multiple probability weights of the multiple capacity decays; performing multiple PPM simulations by applying multiple probability distribution models to the extracted multiple capacity decays; and determining at least one probability distribution model by applying at least one statistical modeling index to the results of the multiple PPM simulations.

[0025] Beneficial effects

[0026] This invention provides an apparatus and method for predicting battery failure rate based on battery capacity degradation data predicted through aging simulation. Attached Figure Description

[0027] Figure 1 This is a diagram illustrating a failure rate prediction device according to an exemplary embodiment.

[0028] Figure 2 This is a block diagram illustrating an aging simulation apparatus according to an exemplary embodiment.

[0029] Figure 3 This is a diagram illustrating a PPM simulation device according to an exemplary embodiment.

[0030] Figure 4 This is a diagram illustrating a PPM simulation device according to an exemplary embodiment.

[0031] Figure 5 It is a graph showing the cumulative distribution function of multiple capacity decays according to an exemplary embodiment and the cumulative distribution function of three probability distribution models with excellent model fit.

[0032] Figures 6 to 8 Each of these is a graph illustrating the cumulative distribution function and histogram-based probability density function of three probability denominator models according to an exemplary implementation.

[0033] Figures 9 to 11 This is a graph showing the results of applying three probability denominator models based on probability weights to multiple capacity decays obtained from bootstrapping.

[0034] Figure 12 It is a table representing the PPM value for each model obtained for each bootstrap count. Detailed Implementation

[0035] In the following description, exemplary embodiments disclosed herein will be described in detail with reference to the accompanying drawings, and the same or similar reference numerals will denote the same or similar components, regardless of the reference numerals, and repeated descriptions will be omitted. The suffixes “module” and / or “unit” used for the components described below are given or combined only for ease of writing and do not have a distinguishing meaning or function in themselves. Furthermore, in describing the exemplary embodiments disclosed herein, detailed descriptions will be omitted where it is determined that a detailed description relating to a well-known function or configuration would unnecessarily obscure the subject matter of the exemplary embodiments disclosed herein. Moreover, the drawings are provided to aid in the easy understanding of the exemplary embodiments disclosed herein, and the technical spirit disclosed herein is not limited to the drawings; it should be understood that the invention includes all modifications, equivalents, and substitutions included within the spirit and scope of the invention.

[0036] Terms including ordinary ordinal numbers (such as first and second) are used to describe various constituent elements, but constituent elements are not limited by terms. Terms are only used to distinguish one constituent element from another.

[0037] It should be understood that when a component is referred to as "connected to" or "connected to" another component, a component can be directly connected to or connected to another component, but there may also be intermediate elements. Conversely, when a component is referred to as "directly connected to" or "directly connected to" another component, it should be understood that there are no intermediate elements.

[0038] In this application, it should be understood that the terms "comprising" and "having" are intended to indicate the presence of the features, quantities, steps, operations, components and parts or combinations thereof described in the specification, and do not preclude the possibility of the presence or addition of one or more other features, quantities, steps, operations, components and parts or combinations thereof.

[0039] In the following description, "cell" refers to a battery cell used to construct a battery pack, and a battery pack may include at least one battery pack.

[0040] Figure 1 This is a diagram illustrating a failure rate prediction device according to an exemplary embodiment.

[0041] like Figure 1 As shown, the failure rate prediction device 1 includes a data generation device 10, an aging simulation device 20, and a PPM simulation device 30.

[0042] The data generation device 10 can generate input data by combining the driving profile as raw data, which has more types of data distribution than the raw data.

[0043] A driving profile used for battery life analysis can include power values, temperature, and driving modes. Power is a value of the battery power (in watts) sampled at predetermined sampling intervals; temperature is a value recorded within a predetermined time period for specific temperature conditions; and driving mode refers to the vehicle's driving status. Driving modes can be defined in three ways, such as driving / discharging mode, charging mode, and parking / resting mode. In the driving profile, the driving mode is configured to synchronize with the battery's power value, depending on the direction of the power, and the value can be defined as 2 for a - sign (discharging), 1 for a + sign (charging), and 0 for parking. Temperature and driving mode values ​​can be values ​​acquired at the same sampling interval as the power values.

[0044] The data generation apparatus 10 can recover and extract at least two driving profiles from multiple driving profiles (Na, 2 or greater natural numbers) configured with original data, and generate multiple driving profiles (Nb, 2 or greater natural numbers) (hereinafter referred to as extended driving profiles) by combining the at least two extracted driving profiles. Hereinafter, for ease of explanation, the number of driving profiles recovered and extracted from the multiple driving profiles is described as 2, and Na can be 30, and Nb can be 900. However, the invention is not limited thereto.

[0045] The data generation device 10 can select two driving profiles by allowing repetition among 30 driving profiles, and add the two selected driving profiles together to generate a total of 900 (=30×30) extended driving profiles. This solves the problem that the raw data of 30 driving profiles is insufficient to describe the driving patterns of a population.

[0046] For example, multiple driving profiles input to the data generation device 10 can be divided into two groups according to region, including 15 driving profiles A1, A2, A3, ..., A15 for region A and 15 driving profiles B1, B2, B3, ..., B15 for region B, and each driving profile can include approximately one month (30 days) of driving mode data based on power values. Each of the 900 extended driving profiles C1, C2, C3, ..., C900 generated by the data generation device 10 is generated by adding two corresponding driving profiles as follows.

[0047] C1 = A1 + A1, …, C30 = A1 + B15, C31 = A2 + A1, …, C60 = A2 + B15, ………… C421=A15+A1, …, C450=A15+B15, C451=B1+A1, …, C480=B1+B15, ………… C871=B15+A1, …, C900=B15+B15 An extended driving profile (e.g., C451) having two driving profiles added together as described above includes a total of 60 days of power values, wherein the 30 days of power values ​​used in the combination are from the first profile (e.g., A15) followed by 30 days of power values ​​from the second profile (e.g., A1) used in the combination.

[0048] The data generation device 10 can generate weights (hereinafter referred to as extended weights) corresponding to each of the multiple extended driving profiles. For example, the data generation device 10 can multiply the weights of two driving profiles of the original data of one of the 1,800 extended driving profiles generated by the configuration to generate the corresponding extended weights.

[0049] The aging simulation device 20 can generate multiple capacity decays by performing lifetime analysis simulations on multiple extended driving profiles, applying Nc (2 or greater natural numbers) climatic conditions. The aging simulation device 20 can generate multiple (Nb×Nc) capacity decays, where each of the multiple capacity decays can be a capacity decay for a corresponding climatic condition and a corresponding extended driving profile among the multiple climatic conditions. For simplicity, Nc will hereby be described as 2. For example, the aging simulation device 20 can perform lifetime analysis simulations on 900 extended driving profiles under two climatic conditions to generate a total of 1800 capacity gains.

[0050] Figure 2 This is a block diagram illustrating an aging simulation apparatus according to an exemplary embodiment.

[0051] The aging simulation device 20 includes an equivalent circuit model (ECM) module 21, a thermal model module 22, and an aging model module 23.

[0052] ECM module 21 can apply each of multiple extended driving profiles to the ECM to generate driving-based battery operation information, and generate multiple battery operation information for multiple extended driving profiles. The ECM is an electrical equivalent circuit model of the battery as a target for aging simulation, and can be implemented by modeling the battery's internal parameters as circuits. Input parameters required for the ECM according to an exemplary embodiment may include power value, initial state of charge (SOC), average temperature, number of cells in the configured battery, driving mode, initial open-circuit voltage (OCV), and cell capacity. Power value and driving mode can be obtained from the extended driving profiles, and average temperature can be received from thermal model module 22.

[0053] ECM module 21 can obtain the battery cell current based on the power value recorded in the extended driving profile. ECM module 21 can accumulate the battery cell current and estimate the current SOC value based on the initial SOC value, battery cell capacity, and the result of current accumulation. For example, ECM module 21 can estimate the current SOC by adding the SOC change obtained by dividing the accumulated current of the current battery cell current per unit time based on the power value by the battery cell capacity to the previous SOC. The initial SOC value required for the first operation of estimating the SOC value can be set as an input parameter. ECM module 21 can determine the battery current by taking into account the connection relationship between the battery cells of the configured battery into the battery cell current. For example, when all the battery cells of the configured battery are connected in series, the battery current can be equal to the battery cell current. Alternatively, when battery cells are connected in series as a unit of two cells connected in parallel, the battery current can be a value obtained by multiplying the battery cell current by 2.

[0054] ECM module 21 can determine the SOC of a battery cell as the SOC of the battery by assuming that all cells in the battery configuration have the same characteristics.

[0055] ECM module 21 can estimate the OCV and the voltage across the battery cell (hereinafter referred to as the battery cell voltage) based on the RC equivalent circuit corresponding to the battery cell. Specifically, 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 resistor in the RC equivalent circuit, and calculate the polarization resistance voltage when the battery cell current flows through the polarization resistor in the RC equivalent circuit. The battery cell voltage is then calculated by adding the OCV voltage, the series resistance voltage, and the polarization resistance voltage. ECM module 21 can determine the battery voltage by taking into account the connection relationship between the battery cells in the configured battery configuration. For example, when all the cells in the configured battery configuration are connected in series, ECM module 21 can calculate the battery voltage by multiplying the battery cell voltage by the number of battery cells.

[0056] ECM module 21 can calculate the C-rate based on the battery cell current. The C-rate (charge and discharge rate) is a percentage of the current value used to charge and discharge the battery. ECM module 21 can calculate the C-rate by dividing the battery cell current by the battery cell capacity.

[0057] ECM module 21 can calculate the battery's heating by considering cell current, cell voltage, average temperature, and the number of cells. The average temperature can be received from thermal model module 22. The heating amount can be input to both thermal model module 22 and aging model module 23. The average temperature serves as an important input value affecting key battery parameters in the RC-based ECM model. Indeed, it can be confirmed that as temperature increases, the electrochemical reactions inside the battery are activated and the internal resistance decreases, while as temperature decreases, the internal resistance increases. This affects not only the availability of the battery's voltage range but also its state of equilibrium (SOH), i.e., capacity decay.

[0058] For each of the multiple extended driving profiles, the thermal model module 22 can generate the average temperature of the battery in the vehicle by using the amount of heat and temperature of each extended driving profile received from the ECM module 21. The thermal model module 22 can generate the average temperature by considering parameters such as the heat of the air within the vehicle's internal structure, as well as the amount of heat and temperature. For this purpose, the thermal model module 22 can receive inputs such as the battery's cooling reference temperature and thermal resistance coefficient. The cooling reference temperature can be a reference temperature value for continued cooling when the battery temperature reaches a certain level. The temperature in the extended driving profile can be the temperature outside the vehicle, reflecting the climatic conditions of the area where the vehicle operates. The thermal model module 22 can consider the battery's thermal resistance coefficient and the amount of coolant to determine the effect of heat transferred to the air on the battery temperature. The thermal model module 22 can calculate the average temperature value generated in the battery by considering the battery's heat, whether cooling is in progress based on the cooling reference temperature, and the heat transferred to the battery through the air.

[0059] For each of the multiple extended driving profiles, the aging model module 23 can receive battery voltage, battery current, SOC, C-rate, driving mode, average temperature, and number of cells, and calculate the battery capacity degradation. The aging model module 23 can calculate the battery's lifespan analysis value based on capacity degradation, and can also calculate the battery's power value, the power value of a single cell, and the battery's energy throughput based on the battery voltage, battery current, and number of cells. The aging model module 23 can obtain the SOH value, i.e., the battery's capacity retention value, by applying the battery's power value, energy throughput, average temperature, C-rate, and SOC to an algorithmic formula reflecting the degradation curve equation. Battery temperature and charge / discharge are important factors in determining the degree of battery degradation. The degradation curve can be obtained through actual battery degradation experiments.

[0060] The aging model module 23 can determine capacity degradation based on specific battery operating states, taking into account driving modes. For example, during the operation of an electric vehicle, driving corresponds to battery discharge, and the degradation caused by driving modes, which consist of discharge and charging during driving, can be defined as cyclic degradation. Another driving mode is the electric vehicle's parking mode, which is a resting state for the battery, and degradation from the resting state can be defined as calendar degradation. In cyclic degradation, the battery is repeatedly charged and discharged, accelerating capacity degradation, while in calendar degradation, the battery is used minimally, allowing its capacity to naturally degrade. The aging model module 23 can calculate capacity degradation by classifying the battery degradation process into one of these two types within driving modes. The method by which the aging model module 23 calculates capacity degradation is not limited to those methods and can be implemented using various publicly known methods.

[0061] The aging model module 23 can also calculate the degree of capacity retention based on capacity decay. For example, assuming the initial capacity of the battery is 100%, the aging model module 23 can subtract the capacity decay from 100% to calculate the degree of capacity retention. The aging model module 23 can also obtain the degree of increase in battery resistance based on an algorithm that reflects the equation of the capacity decay curve.

[0062] The ECM module 21, thermal model module 22, and aging model module 23 described herein are exemplary embodiments, and the invention is not limited thereto. For example, since the aging model module 23 can be implemented differently for each battery manufacturer, and the required input parameters can vary depending on the aging model module, the ECM module and thermal model module can also be appropriately designed to provide input parameters to the aging model module.

[0063] In the following text, reference will be made to Figure 3 Describe the PPM simulation device.

[0064] Figure 3 This is a diagram illustrating a PPM simulation device according to an exemplary embodiment.

[0065] The PPM simulation device 30 can generate multiple probability weights based on multiple extended weights and weights corresponding to multiple climatic conditions, and calculate PPM values ​​based on multiple capacity decays and multiple probability weights. The PPM simulation device 30 can assign the corresponding probability weights from the multiple probability weights to each of the multiple capacity decays, perform bootstrapping according to the multiple probability weights assigned to the multiple capacity decays, and calculate the PPM values ​​of the sample data extracted through bootstrapping.

[0066] The PPM simulation device 30 can receive multiple extended driving profiles and multiple climate conditions as input, as well as multiple capacity attenuations corresponding to the extended driving profiles and multiple climate conditions. The PPM simulation device 30 can receive extended driving profiles, file names, extended weights, and driving periods.

[0067] The filename refers to the name of each of the multiple extended driving profiles. If 900 extended driving profiles are named C1 to C900, then each of the 900 extended driving profiles can be subjected to two climate conditions, such as climate condition 1 (C1, ..., C451, ..., and C900) and climate condition 2 (C1, ..., C451, ..., and C900).

[0068] Driving time periods can refer to the amount of time spent reaching the target mileage for each driving profile. For example, when an A1 driving profile consists of 30 days of driving records, and the same driving records are repeated 100 times, it can be defined as reaching the target mileage of 160,000 kilometers in approximately 8 years. In this case, the 8-year value is the driving time period for the A1 profile. This can be represented as A1 (8 years), A2 (10 years), A3 (4 years), ..., and A15 (13 years).

[0069] The PPM simulation device 30 may include a probability weight generation unit 31 and a PPM prediction unit 32.

[0070] The probability weight generation unit 31 can generate multiple probability weights by multiplying multiple extended weights by the weight of each of multiple climate conditions. First, the probability weight generation unit 31 can generate multiple composite weights by multiplying multiple extended weights by the weight of each of multiple climate conditions. The probability weight generation unit 31 can generate 900 composite weights by multiplying 900 extended driving profiles by the weight of each of two climate conditions.

[0071] The corresponding weights of the 15 driving profiles in region A are A1 (wa1), A2 (wa2), A3 (w3), A4 (wa4), ... and A15 (wa15), and the corresponding weights of the 15 driving profiles in region B are B1 (wb1), B2 (wb2), B3 (wb3), B4 (wb4), ... and B15 (wb15). The extended weight of each extended driving profile can be expressed as the product of the weights of the corresponding two driving profiles. The probability weight generation unit 31 can multiply the weights (cc1, cc2) of the corresponding climate conditions between climate conditions 1 and 2 by the extended weights to calculate the composite weight. The composite weight of the 900 extended driving profiles for climate condition 1 is cc1. wa1 wa1, ..., 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, and the composite weight of the 900 extended driving profiles for climate condition 2 is cc2 wa1 wa1, ..., cc2 wa1 wb15, cc2 wa2 wa1, ... , cc2 wa2 wb15,..., cc2 wa15 wa1, ..., cc2 wa15 wb15, cc2 wb1 wa1, ...,cc2 wb1 wb15, ..., cc2 wb15 wa1, ..., and cc2 wb15 wb15.

[0072] The above calculation of the composite weights is an example based on an exemplary implementation, and the invention is not limited thereto. Any calculation method that can generate corresponding weights based on population distribution can be applied to the exemplary implementation.

[0073] For each of the multiple climate conditions, the probability weight generation unit 31 can calculate the weight sum by adding all the multiple composite weights belonging to each climate condition, and calculate the probability weight by dividing each of the multiple composite weights belonging to each climate condition by the weight sum.

[0074] For example, the probability weight generation unit 31 can divide each of the 900 composite weights of climate condition 1 as represented in Equation 2 by the value (TW1) obtained by summing all 900 composite weights of climate condition 1 as represented in Equation 1, to calculate the 900 probability weights CW1 to CW900 belonging to climate condition 1.

[0075] [Equation 1]

[0076] TW1 = cc1 wa1 wa1 + … + 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

[0077] [Equation 2]

[0078] CW1 = cc1 wa1 wa1 / TW1, … CW900 = cc1 wb15 wb15 / TW1

[0079] The probability weight generation unit 31 can divide each of the 900 composite weights of climate condition 2 as shown in Equation 4 by the value (TW2) obtained by summing all 900 composite weights of climate condition 2 as shown in Equation 3, to calculate the 900 probability weights CW901 to CW1800 belonging to climate condition 2.

[0080] [Equation 3]

[0081] TW2 = cc2 wa1 wa1 + … + 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

[0082] [Equation 4]

[0083] CW901 = cc2 wa1 wa1 / TW1, … CW1800 = cc2 wb15 wb15 / TW2

[0084] The sum of the 900 probability weights belonging to each group is 1, as shown in Equation 5.

[0085] [Equation 5]

[0086] 1 = CW1 + … + CW900, 1 = CW901 + … + CW1800

[0087] The PPM prediction unit 32 can assign each of a plurality of probability weights to a corresponding capacity decay among a plurality of capacity decays, and repeat the operation of recovering and extracting a predetermined number (Nr) of capacity decays among the plurality of capacity decays based on the plurality of probability weights assigned to the plurality of capacity decays (hereinafter referred to as bootstrapping) a predetermined number of times (Nn). Pre-assigning the corresponding probability weights to each of the plurality of capacity decays, with the assigned weights redefined by probability values ​​based on the proportion of the total capacity decays, and re-extracting the corresponding capacity decays based on the probability values ​​during the bootstrapping process, can improve the accuracy of the PPM results.

[0088] For example, the PPM prediction unit 32 can assign each of the 1800 probability weights to the corresponding capacity decay among the 1800 capacity decays. The PPM prediction unit 32 can recover and extract the 1800 capacity decays based on the multiple probability weights during each bootstrapping. The PPM prediction unit 32 can repeat the bootstrapping 30 times. As described above, the probability weights are pre-assigned to the corresponding capacity decays, allowing capacity decays to be randomly extracted based on the probability weights.

[0089] The PPM prediction unit 32 can calculate the PPM value by applying at least one probability distribution model to a predetermined number (Nr) of capacity decays extracted at each bootstrap. The PPM prediction unit 32 can sum the PPM values ​​obtained from a predetermined number (Nn) of bootstraps to generate a final PPM value (hereinafter referred to as the final PPM value). In this case, statistical modeling can be used to determine at least one probability distribution model.

[0090] First, the method for determining the probability distribution model used by the PPM prediction unit 32 will be described.

[0091] Statistical modeling can be used as a goodness-of-fit index for various probability distribution models. Through statistical modeling, a balanced probability distribution model can be selected by avoiding overfitting and underfitting problems that occur during the fitting of data and models.

[0092] To determine the probability distribution model used by the exemplary implementation, statistical modeling uses metrics such as negative log-likelihood ratio (NLL), Akaike Information Criteria (AIC), AIC correction (AICc), Bayesian Information Criteria (BIC), and root mean square error (RMSE).

[0093] NLL is an indicator used in a method called maximum likelihood estimation (MLE), which is used to statistically determine whether actual data matches a probability distribution model. The method for calculating NLL is shown in Equation 6.

[0094] [Equation 6]

[0095] In Equation 6, L represents the likelihood function, which matches the formula in square brackets on the right-hand side and has the following meaning: fk(xi|θ) is the probability density function and the result of multiplying (Q) by all probability values ​​obtained by applying the parameter θ, where i is a value from 1 to the number of data points n. This is the process of maximizing the obtained value L (i.e., the likelihood function) through the parameter θ. By taking the logarithm of the value of L and applying a negative sign, we obtain -ln(L), which becomes NLL. Therefore, maximizing the value of L is minimizing NLL, and minimizing the NLL value implies a high goodness of fit between the probability distribution model and the actual data. However, when the amount of actual data is less than the number of parameters in the probability distribution model, there is a risk of overfitting.

[0096] Similar to NLL introduced earlier, AIC is one of the statistical modeling metrics that uses the likelihood function. The method for calculating AIC is shown in Equation 7.

[0097] [Equation 7]

[0098] In Equation 7, L is the likelihood function, and the value of L increases with higher goodness of fit, while the value of -2ln(L) decreases with a larger logarithm of ln(L). Here, k is the number of parameters in the model to be fitted with AIC, also known as the independent variables. In other words, the value of k increases with increasing model complexity and the number of independent variables to be fitted, and this increase in value is significant when the value of -2ln(L) decreases with higher goodness of fit. Therefore, k can be considered as a penalty to prevent overfitting. As the amount of actual data increases, the value of L increases and the AIC value is unaffected by the penalty, thus allowing for accurate prediction of the population distribution.

[0099] AICc is one of the statistical modeling metrics used to correct the bias of AIC. Compared to AIC, AICc is more predictive when the amount of data is relatively limited and small. The method for calculating AIC is shown in Equation 8.

[0100] [Equation 8]

[0101] Equation 8 uses AIC as the framework, but adds 2k(k+1) / nk-1 as a correction term. Similar to AIC, k is the number of independent variables, and n is the number of data points. In this case, as the value of n (i.e., the number of data points) increases infinitely, the performance difference between AIC and AICc disappears. It can be seen from the equation that using AIC as is results in a higher predictive model fit due to a smaller value of AICc. However, there is a difference in predictive power between AIC and AICc, and previous studies have shown that using AICc to determine the goodness of fit of the simulated model is a way to improve accuracy. In an exemplary implementation, a probability distribution model can be applied to the PPM prediction unit 32, which is selected based on a limited amount of evidence and data from previous studies using AICc as a key indicator (previous study: E. Song, S. Won, and W. Lee, "Using the corrected akaike's informationcriterion for model selection," The Korean Journal of Applied Statistics, vol. 30, no. 1, pp. 119-133, 2017.).

[0102] Similar to AIC, BIC can be used to determine the best goodness of fit of a model based on the result that has the minimum information loss at the maximum likelihood value. The method for calculating BIC is expressed in Equation 9.

[0103] [Equation 9]

[0104] As can be seen, Equation 9 is similar in form to Equation 7, the difference being the term that assigns the penalty value. Unlike AIC, the penalty in BIC increases with the value of n (where n is the number of data points). Therefore, BIC can be considered a suitable model for analyzing distributions based on data variance.

[0105] RMSE is also a statistical modeling metric. It is calculated by squaring the values ​​obtained by subtracting the predicted values ​​from the actual data, summing all the values ​​together, dividing the sum by n, and placing the root. The method for calculating RMSE is shown in Equation 10.

[0106] [Equation 10]

[0107] In Equation 10, i is a numerical value from 1 to the number of data points n, yi can be defined as the i-th actual observation, and yi can be defined as the i-th predicted value. The value obtained by subtracting the predicted value from the actual data is called the residual, which has the same meaning as the mean squared error (MSE) obtained by squaring, summing, and dividing by n. RMSE is a statistical modeling metric used to find the root of MSE to provide an interpretation in units similar to the actual value.

[0108] Each of the 17 probability distribution models (such as Beta, Birnbaumunder, Exponential, Extremum, Gamma, Generalized Extremum, Generalized Pareto, Inverse Gaussian, Logistic, Loglogistic, Lognormal, Nakagami, Normal, Rayleigh, Rice, Tlocationscale, and Weibull) can be applied to perform PPM simulations by applying a predetermined number (e.g., 1800) of capacity decay samples based on probability weights. When the AICc (primary index) is applied to the PPM simulation results, three probability distribution models (Extremum, Generalized Extremum, and Weibull) show the best goodness of fit. Based on this, at least one probability distribution model of the PPM prediction unit 32 according to the exemplary embodiment can be at least one of the above three.

[0109] As described above, at least one probability distribution model can be set in the PPM prediction unit 32, but the present invention is not limited thereto. Instead, the PPM simulation device 30 can determine the probability distribution model.

[0110] Figure 4 This is a diagram illustrating a PPM simulation device according to an exemplary embodiment.

[0111] like Figure 4 As shown, the PPM simulation device 30 may also include a probability distribution model determination unit 33.

[0112] The probability distribution model determination unit 33 can receive multiple probability weights and multiple capacity decays as inputs, extract multiple capacity decays based on the multiple probability weights for the multiple capacity decays, and perform PPM simulation by applying the above 17 probability distribution models to the extracted multiple capacity decays.

[0113] The probability distribution model determination unit 33 can determine at least one probability distribution model by applying at least one of the previously described statistical modeling indices to the results of multiple PPM simulations using multiple probability denominator models. The probability distribution model determination unit 33 can determine at least one probability distribution model based on the goodness of fit of the model calculated by applying the statistical modeling indices to the results of multiple PPM simulations. The probability distribution model determination unit 33 can then send the at least one probability distribution model to the PPM prediction unit 32.

[0114] Figure 5 It is a graph showing the cumulative distribution function of multiple capacity decays according to an exemplary embodiment and the cumulative distribution function of three probability distribution models with excellent model fit.

[0115] Will Figure 5 The three probability distribution models shown, which have excellent model fit, are described as a first-order extremum model, a second-order generalized extremum model, and a third-order Weibull model.

[0116] exist Figure 5 The diagram shows the cumulative distribution function when multiple sampling capacity decays are applied to three probability distribution models (extreme value model, generalized extreme value model, and Weibull model). Figure 5 As shown, it can be seen that the cumulative distribution function 51 of the multiple capacity fading samples based on probability weights is similar to the cumulative distribution functions 52 to 54 of the three probability distribution models. Figure 5 In the example, the cumulative distribution function of multiple capacity decays according to the exemplary embodiment is represented by "51", the cumulative distribution function according to the extreme value model is represented by "52", the cumulative distribution function according to the generalized extreme value model is represented by "53", and another cumulative distribution function according to the Weibull model is represented by "54".

[0117] In this way, the accuracy of PPM prediction can be improved when PPM values ​​are calculated using probability distribution functions with similar model fit.

[0118] Figures 6 to 8 Each of these is a graph illustrating the cumulative distribution function and histogram-based probability density function of three probability denominator models according to an exemplary implementation.

[0119] like Figure 6 As shown, the goodness of fit between curves CV1 and CV0 is very high. Curve CV1 represents the cumulative distribution function obtained by applying multiple capacity decays (hereinafter referred to as sample data) obtained through a single extraction based on probability weights to the extreme value distribution model, while curve CV0 represents the cumulative distribution function of the sample data. Furthermore, it can be seen that curve CV11, representing the histogram-based probability density function of the sample data, is balanced.

[0120] like Figure 7 As shown, the goodness of fit between curves CV2 and CV0 is also high. Curve CV2 represents the cumulative distribution function obtained by applying the sample data to the generalized extreme value distribution model, while curve CV0 represents the cumulative distribution function of the sample data. It can be seen that... Figure 6 Compared to curve CV11, curve CV21, which represents the probability density function, is also balanced, with a lower peak and a wider distribution from one side to the other.

[0121] like Figure 8 As shown, the goodness of fit between curves CV3 and CV0 is also high. Curve CV3 represents the cumulative distribution function obtained by applying the sample data to the Weibull distribution model, while curve CV0 represents the cumulative distribution function of the sample data. Figure 6 Compared to curve CV11, curve CV31, which represents the probability density function, has a lower peak value and a rightward sloping shape.

[0122] In the cumulative distribution function and probability density function, the x-axis represents the probability variable and capacity decay, and the y-axis value of the cumulative distribution function describes the cumulative probability, while the y-axis value of the probability density function describes the probability density. When the capacity decay threshold is 0.3 (30%), there exists... Figure 7 and Figure 8 PPM values ​​not seen in the probability density function and in the sample data appear Figure 8 The probability density function in the equation represents the likelihood.

[0123] The PPM prediction unit 32 can apply the above three probability distribution models to multiple capacity decays obtained by bootstrapping based on probability weights to calculate the PPM value.

[0124] Figures 9 to 11 This is a graph showing the results of applying three probability denominator models to multiple capacity decays derived from bootstrapping based on probability weights.

[0125] The PPM prediction unit 32 can perform 30 bootstrapping operations based on probability weights to extract 1800 capacity decays 30 times. The results of applying each of the 1800 extracted capacity decays to each of the extreme value distribution model, the generalized extreme value distribution model, and the Weibull distribution model are organized into a histogram, and a probability density function is generated based on the histogram.

[0126] Figure 9 The histogram and probability density function of the extreme value distribution model of capacity decay obtained by bootstrapping 30 times are shown. Figure 10 The histogram and probability density function of the generalized extreme value distribution model of capacity decay obtained by bootstrapping 30 times are shown. Figure 11 The histogram and probability density function of the capacity decay model obtained by bootstrapping 30 times are shown. Figures 9 to 11 The diagram shows 30 curves representing the probability density functions of the corresponding 30 bootstraps. Figures 9 to 11 As can be seen, there are fluctuations in the data regarding capacity decay. In other words, establishing a data range for capacity decay can improve the accuracy of PPM prediction.

[0127] PPM prediction unit 32 can Figures 9 to 11 The PPM value is calculated by summing the values ​​at which the capacity decay exceeds a threshold (e.g., 30%) within the 75% (12.5% ​​to 87.5%) confidence interval of the multiple probability density function curves illustrated in each of them.

[0128] Figure 12 It is a table representing the PPM value for each model obtained for each bootstrap count.

[0129] like Figure 12 As shown, 30 PPM values ​​are zero, which is based on the extreme value distribution in probability distribution models (extreme value distribution, generalized extreme value distribution, and Weibull distribution). Figure 12 gumbel_l) and generalized extreme value distribution ( Figure 12 The result of 30 bootstrappings of genextreme (in the model). In contrast, as a probability distribution model (Weibull distribution) ( Figure 12 The 30 PPM values ​​resulting from the 30 bootstrappings of the exponweib model range from a minimum of 0.0000000047 to a maximum of 0.0000006. Therefore, the PPM prediction unit 32 can sum the 30 PPM values ​​generated based on the Weibull distribution model to calculate the final PPM value.

[0130] Thus, the PPM simulation apparatus according to the exemplary embodiment can obtain various data because the battery capacity decay data, as input data, is plotted as a continuous, smooth cumulative distribution function. Furthermore, model fit can be achieved using a set of probability distribution models without overfitting. Bootstrapping is performed based on probability weights, thus allowing the calculation of PPM results reflecting battery volatility.

[0131] In an exemplary implementation, the uncertainty of the goodness of fit of the probability distribution and the insufficient sample extraction from the population can be overcome by using bootstrapping. This addresses the problem of the difficulty in obtaining long-term driving data based on various actual driving types. Lifetime analysis simulations based on short-term battery charge and discharge cycle data models inevitably generate limited degradation prediction data. According to an exemplary implementation, an expanded driving profile including combinations of driving profiles is generated, thereby obtaining various driving profiles. This overcomes the limitations of simply iteratively amplifying a limited number of degradation prediction data and predicting PPM values ​​using amplified data.

[0132] Furthermore, according to the exemplary implementation, an appropriate probability distribution model is selected from multiple probability distribution models using statistical modeling metrics, thereby addressing the problem of overfitting PPM prediction results. Additionally, bootstrapping using probability weights can improve the diversity of the sample data.

[0133] Although the invention has been described in conjunction with exemplary embodiments now considered to be practical, it should be understood that the invention is not limited to the disclosed exemplary embodiments.

Claims

1. A device for predicting the failure rate of a battery, the device comprising: A data generation device is configured to recover and extract at least two driving profiles by allowing repetition among multiple driving profiles configured with original data, generate multiple extended driving profiles by combining the extracted at least two driving profiles, and generate multiple extended weights corresponding to the multiple extended driving profiles, wherein the driving profiles include power values, temperature and driving modes, and the data generation device multiplies the weights of the two driving profiles of the original data of one of the multiple extended driving profiles configured to generate the corresponding extended weights; An aging simulation device is used to generate multiple capacity degradations by performing a life analysis simulation with multiple climatic conditions on the multiple extended driving profiles. as well as A parts-per-million (PPM) simulation device is used to generate multiple probability weights based on the multiple extended weights and weights corresponding to the multiple climatic conditions, and to calculate a PPM value based on the multiple capacity decays and the multiple probability weights. The PPM simulation device includes a probability weight generation unit, which generates the plurality of probability weights by multiplying the plurality of extended weights by the weight of each of the plurality of climate conditions.

2. The device according to claim 1, wherein, The aging simulation device includes: An equivalent circuit model (ECM) module is used to apply each of the plurality of extended driving profiles to the electrical equivalent circuit model (ECM) of a battery undergoing aging simulation, in order to generate the battery voltage, current, state of charge (SOC), charge rate (C-rate), and heating amount corresponding to each of the extended driving profiles. A thermal model module, used to generate an average battery temperature for each of the plurality of extended driving profiles by using the battery's heating amount and the temperature of each extended driving profile; and An aging model module is used to calculate the capacity decay of the corresponding battery for each of the plurality of extended driving profiles, based on the battery's voltage, current, SOC, C-rate, driving mode, average temperature, and number of cells.

3. The device according to claim 2, wherein, The aging model module calculates capacity degradation by distinguishing between cyclic degradation caused by driving in driving mode and calendar degradation caused by the battery resting in the driving mode.

4. The device according to claim 1, wherein, The PPM simulation device assigns a corresponding probability weight from the plurality of probability weights to each of the plurality of capacity decays, performs bootstrapping based on the plurality of probability weights assigned to the plurality of capacity decays, and calculates the PPM value of the sample data extracted through the bootstrapping.

5. The device according to claim 1, wherein, The probability weight generation unit: The multiple extended weights are multiplied by the weight of each of the multiple climate conditions to generate multiple composite weights, and For each of the plurality of climate conditions, a weight sum is calculated by adding all the plurality of composite weights belonging to each climate condition, and the probability weight is calculated by dividing each of the plurality of composite weights belonging to each climate condition by the weight sum.

6. The device according to claim 4, wherein, The PPM simulation device includes: The PPM derivation unit assigns each of the plurality of probability weights to a corresponding capacity decay in the plurality of capacity decays, and repeats bootstrapping a predetermined number of times based on the plurality of probability weights assigned to the plurality of capacity decays to recover and extract a predetermined number of capacity decays from the plurality of capacity decays.

7. The device according to claim 6, wherein, The PPM derivation unit calculates the PPM value by applying at least one probability distribution model to a predetermined number of capacity decays extracted from each bootstrap, and generates the final PPM value by adding the PPM values ​​derived from a predetermined number of bootstraps.

8. The device according to claim 4, wherein, The PPM simulation device extracts the multiple capacity decays based on the multiple probability weights for the multiple capacity decays, performs multiple PPM simulations by applying multiple probability distribution models to the extracted multiple capacity decays, and determines at least one probability distribution model by applying at least one statistical modeling index to the multiple PPM simulation results.

9. A method for predicting the failure rate of a battery, the method comprising the following steps: At least two driving profiles are recovered and extracted by allowing duplication among multiple driving profiles of the original configuration data, and multiple extended driving profiles are generated by combining the extracted at least two driving profiles. Generate multiple extended weights corresponding to the multiple extended driving profiles; Multiple capacity decays are generated by performing lifetime analysis simulations under multiple climatic conditions on the multiple extended driving profiles. Multiple probability weights are generated based on the multiple extended weights and the weights corresponding to the multiple climate conditions; as well as The final parts-per-million (PPM) value is calculated by assigning multiple probability weights to the multiple capacity decays. The driving profile includes power rating, temperature, and driving mode. Specifically, the corresponding extended weight is generated by multiplying the weights of two driving profiles of the original data from one of the multiple extended driving profiles generated by the configuration. The step of generating the plurality of probability weights includes the following steps: The multiple extended weights are multiplied by the weight of each of the multiple climate conditions to generate multiple composite weights. For each of the plurality of climate conditions, a weight sum is calculated by adding all the plurality of composite weights belonging to each climate condition; and The probability weights are calculated by dividing each of the plurality of composite weights belonging to each climate condition by the sum of the weights.

10. The method according to claim 9, wherein, The steps for calculating the final parts per million (PPM) value include the following: For each of the plurality of capacity decays, assign the corresponding probability weight from the plurality of probability weights; Bootstrapping is performed based on multiple probability weights assigned to the multiple capacity decays; and Calculate the PPM value of the sample data extracted through bootstrapping.

11. The method according to claim 10, wherein, The steps involved in bootstrapping include the following: Based on multiple probability weights assigned to the multiple capacity decays, a predetermined number of capacity decays are recovered and extracted from the multiple capacity decays.

12. The method according to claim 11, wherein, The steps for calculating the PPM value include the following: The PPM value is calculated by applying at least one probability distribution model to a predetermined number of capacity decays extracted from the bootstrap.

13. The method according to claim 10, wherein, The steps for calculating the final parts per million (PPM) value also include the following steps: The final PPM value is generated by adding the PPM values ​​derived from a predetermined number of bootstrapping iterations.

14. The method according to claim 9, further comprising the step of: Multiple capacity decays are extracted based on the multiple probability weights for the multiple capacity decays; Multiple PPM simulations are performed by applying multiple probability distribution models to multiple extracted capacity decays; as well as At least one probability distribution model is determined by applying at least one statistical modeling indicator to multiple PPM simulation results.

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