CN113868831A - Battery capacity consistency estimation method and system - Google Patents

Battery capacity consistency estimation method and system Download PDF

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CN113868831A
CN113868831A CN202110956930.4A CN202110956930A CN113868831A CN 113868831 A CN113868831 A CN 113868831A CN 202110956930 A CN202110956930 A CN 202110956930A CN 113868831 A CN113868831 A CN 113868831A
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battery capacity
weibull
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probability
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王琳舒
张杭
黄倩
方彦彦
云凤玲
赵挺
高敏
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China Automotive Battery Research Institute Co Ltd
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Abstract

The invention provides a method and a system for estimating consistency of battery capacity, which comprises the steps of inputting a plurality of battery capacity observed values into a consistency statistical model to obtain a battery capacity distribution statistical characteristic and an abnormal value identification result; verifying the estimation result of the consistency statistical model, and judging whether the battery capacity distribution statistical characteristics described by the estimation result of the consistency statistical model are consistent with the distribution statistical characteristics of the actual battery capacity observation value or not based on the detection result; the estimation result of the consistency statistical model is used for evaluating the consistency of the battery capacity and identifying abnormal values of the battery capacity distribution. The consistency statistical model is established based on the three-parameter Weibull model, the estimation result of the Weibull characteristic parameters is obtained by adopting an improved Weibull parameter estimation method, the Weibull parameter estimation method is used for evaluating the consistency of the battery capacity and identifying the abnormal value of the battery capacity distribution, the calculated amount of the model can be greatly reduced, the observation precision is improved, and the influence of abnormal variables on the estimation result is avoided.

Description

Battery capacity consistency estimation method and system
Technical Field
The invention relates to the technical field of battery detection, in particular to a method and a system for estimating battery capacity consistency.
Background
The large consistent difference in battery capacity occurs due to manufacturing variations and different battery performance decay rates during use of the battery. Under the conventional manufacturing condition, the battery capacity follows normal distribution, namely, the two sides of the probability peak value present symmetrical distribution, and the consistency characteristic of the battery capacity distribution can be obtained through Gaussian probability model parameters. However, when the battery is abnormal in the preparation process or the use process, the battery capacity distribution is not symmetrical any more, the normal distribution is converted into the skewed distribution, and the Gaussian probability model cannot acquire the asymmetrical distribution statistical characteristics of the battery capacity, so that the battery capacity consistency information is difficult to acquire. In general, the Weibull probability model can acquire the asymmetric characteristics of random variables, and the dispersion and symmetry characteristics of the distribution of the random variables are analyzed through the size parameter A and the shape parameter B respectively.
In the prior art, a scheme is applied to 'wind speed probability distribution parameter estimation', an explicit calculation relational expression of shape parameters is drawn up by utilizing a rogowski curve through the interchange of a dependent variable and an independent variable, and a three-parameter solving relational expression of wind speed three-parameter Weibull distribution parameter estimation with higher precision is obtained; the method is also applied to multi-quantile estimation of sea clutter amplitude distribution parameters, three sample accumulated probabilities are selected to obtain three quantile equations, the incremental sequence is utilized to calculate the estimation value of each quantile, and the values of Weibull shape parameters and size parameters are obtained through solution, so that the influence of abnormal scattering units with large amplitude values on the right sides of the quantiles can be effectively avoided, the parameter estimation performance is greatly improved, and the steady estimation of the shape parameters and the scale parameters is obtained; the method is also applied to scene illumination estimation, a Weibull cumulative probability density function is converted into a unitary linear function to be solved, a numerical mathematical expression of the size parameter and the shape parameter with the position parameter as an independent variable is determined, the position parameter is calculated based on the maximum correlation coefficient, and the size parameter and the shape parameter are calculated by the position parameter; in addition, Rockette, H and the like adopt a maximum likelihood estimation method to estimate and calculate three parameters of Weibull, and the estimation method can be known according to the derivation process, and when the shape parameters are known, the size parameters and the position parameters have unique solutions; when the three parameters are unknown, the situation that the optimal solution of the three parameters cannot be obtained may occur when the position parameters meet the condition that the numerical values of the position parameters are smaller than the minimum value of the random variable.
Obviously, the above solution has the following drawbacks: due to the existence of the position parameter C, the Weibull model parameter estimation is more complex, if the C value cannot be accurately estimated, the estimation results of the size parameter A value and the shape parameter B value are influenced, and the identification error of the statistical characteristics of random variables is caused. In practical application, when an abnormal variable which is too small exists in a random variable, the Weibull parameter estimation result generates a large deviation due to the fact that the estimation value of the position parameter C is too small, and therefore the distribution statistical characteristics of the random variable cannot be accurately predicted. At present, the existing Weibull distribution estimation method cannot eliminate the interference of abnormal variables on parameter estimation results, the reliability of the estimation results is low, and the accuracy requirements in practical application are difficult to meet.
Disclosure of Invention
The invention provides a method and a system for estimating consistency of battery capacity, which are used for overcoming the defects in the prior art.
In a first aspect, the present invention provides a method for estimating battery capacity consistency, including:
randomly extracting a plurality of battery samples and determining a plurality of battery capacity observed values;
inputting the plurality of battery capacity observed values into a consistency statistical model to obtain battery capacity distribution statistical characteristics and abnormal value identification results; the consistency statistical model is established based on a three-parameter Weibull probability model, and distribution statistical characteristics and abnormal values of the battery capacity are obtained by estimating three characteristic parameters of the Weibull model of the capacity distribution;
verifying the estimation result of the consistency statistical model, and judging whether the battery capacity distribution statistical characteristics described by the estimation result of the consistency statistical model are consistent with the distribution statistical characteristics of the actual battery capacity observation value or not based on the detection result;
and using the estimation result of the consistency statistical model for evaluating the consistency of the battery capacity and identifying abnormal values of the battery capacity distribution.
In one embodiment, the consistency statistical model is obtained by:
establishing a consistency statistical model based on a Weibull probability model;
determining three Weibull characteristic parameters of the Weibull probability model based on the Weibull probability model;
determining a mathematical expression of the secondary characteristic parameters related to the Weibull characteristic parameters based on the three Weibull characteristic parameters of the Weibull probability model;
estimating the secondary characteristic parameters based on statistical characteristics of the battery capacity observation value distribution;
estimating three Weibull characteristic parameters of the Weibull probability model based on a secondary characteristic parameter expression;
and obtaining the statistical characteristics and abnormal values of the consistency distribution of the battery capacity based on the three Weibull characteristic parameters.
In one embodiment, the building a consistency statistical model based on the Weibull probability model includes:
determining three Weibull characteristic parameters of a Weibull probability model, wherein the three Weibull characteristic parameters comprise a size parameter, a shape parameter and a position parameter;
constructing a cumulative probability function, a probability density function and a derivative function of the probability density function of the Weibull distribution based on the size parameter, the shape parameter and the position parameter;
wherein the size parameter is used for reflecting the discrete characteristic of the distribution, the shape parameter is used for reflecting the symmetrical characteristic of the distribution, and the position parameter is used for reflecting the minimum numerical range of the distribution.
In one embodiment, the determining a mathematical expression about the Weibull characteristic parameter of the quadratic characteristic parameter based on three Weibull characteristic parameters of the Weibull probability model includes:
the Weibull secondary characteristic parameters comprise Weibull probability density peak values, Weibull probability density peak value position values and distribution cumulative probability ratio values;
acquiring a mathematical expression of the Weibull probability density peak position value relative to Weibull characteristic parameters according to the derivative function of the Weibull probability density function;
obtaining the cumulative probability on the left side of the Weibull probability density peak value and the cumulative probability on the right side of the Weibull probability density peak value based on the Weibull probability density peak value and the Weibull cumulative probability function;
and obtaining a mathematical expression of the distribution cumulative probability ratio function on the Weibull characteristic parameter according to the ratio of the left cumulative probability of the Weibull probability density peak position value and the right part cumulative probability of the Weibull probability density peak position value.
In one embodiment, estimating the secondary characteristic parameter based on the statistical characteristics of the battery capacity observation distribution includes:
obtaining a plurality of equidistant subintervals in the distribution interval and corresponding subinterval distribution probabilities based on the distribution interval and the distribution probability of the battery capacity observation value, replacing the equidistant subintervals by a median value of each subinterval, and dividing the subinterval distribution probabilities by the subinterval spacing values to obtain distribution probability densities corresponding to the median values of the subintervals;
respectively obtaining the maximum value of the probability density of the preset number from the probability density of the battery capacity distribution subintervals, and obtaining the position value of the maximum value of the probability density of the preset number of battery capacity distribution on the basis of the maximum value of the probability density of the preset number of battery capacity distribution and the median of the preset number distribution subintervals;
obtaining the cumulative probability at the maximum value of the distribution probability density of the preset number of the battery capacities based on the position value of the maximum value of the distribution probability density of the preset number of the battery capacities;
calculating a weighted mean value of the position of the peak value of the probability density according to the position values of the maximum values of the distribution probability densities of the preset number of the battery capacities, and taking the distribution probability at the position of the peak value of the distribution probability density as a weighting coefficient to obtain an estimated mean value of the position of the peak value of the distribution probability density of the battery capacities;
establishing a linear equation set between the position value of the maximum value of the distribution probability density of the battery capacity of the preset number and the cumulative probability at the maximum value of the distribution probability density of the battery capacity of the preset number based on the characteristic that the Weibull cumulative probability function is approximately linear near the position value of the peak value of the probability density, and establishing a linear function expression of the Weibull cumulative probability density function of the battery capacity distribution at the peak value of the distribution probability density through the slope average value and the intercept average value of the linear function obtained by solving two equations in the equation set;
substituting the estimated mean value of the battery capacity distribution probability peak value position value into a linear function expression of the Weibull cumulative probability density function of the battery capacity at the distribution probability density peak value to obtain an estimated value of the cumulative probability at the battery capacity distribution probability density peak value;
obtaining an estimated value of a battery capacity distribution probability density peak value at the position value of the distribution probability density peak value according to the average value of the maximum values of the probability densities of the preset number;
and obtaining the ratio of the cumulative probabilities of the battery capacity distribution on the left and right sides of the probability density peak according to the cumulative probabilities on the left and right sides of the battery capacity distribution probability density peak.
In one embodiment, estimating three Weibull characteristic parameters of the battery capacity distribution based on a secondary characteristic parameter expression and a secondary characteristic parameter estimated based on statistical characteristics of the battery capacity observation distribution includes:
establishing an equation based on a mathematical expression of the battery capacity distribution cumulative probability ratio function about Weibull characteristic parameters and the ratio of the cumulative probabilities of the battery capacity distribution on the left side and the right side of the probability density peak value to obtain shape parameters of the battery capacity Weibull distribution;
substituting the shape parameters of the battery capacity Weibull distribution into a mathematical expression of the probability density peak value about Weibull characteristic parameters, and establishing an equation with the estimation peak value at the battery capacity distribution probability peak value to obtain the size parameters of the battery capacity Weibull distribution;
substituting the shape parameter of the battery capacity Weibull distribution and the size parameter of the battery capacity Weibull distribution into a mathematical expression of the distribution probability density peak position value and the Weibull characteristic parameter, and establishing an equation with an estimated value of the battery capacity distribution probability peak position value to obtain the position parameter of the battery capacity Weibull distribution.
In one embodiment, verifying the estimation results of the three characteristic parameters of the Weibull model, and determining whether the statistical distribution characteristics of the battery capacity described by the estimation results of the three characteristic parameters of the Weibull model are consistent with the statistical distribution characteristics of the actual battery capacity based on the verification results includes:
and judging based on a preset hypothesis test method, if the capacity distribution described by the three characteristic parameter estimation results of the Weibull model of the battery capacity distribution and the actual observation value distribution accord with the difference range under a preset confidence coefficient, determining that the parameter estimation results are the actual distribution statistical characteristics capable of reflecting the battery capacity, otherwise, determining that the parameter estimation results cannot reflect the actual distribution statistical characteristics of the battery capacity.
In one embodiment, the using three characteristic parameters of the Weibull model for battery capacity consistency evaluation and abnormal value identification of battery capacity distribution includes:
evaluating the statistical characteristics of the consistency of the battery capacity distribution based on the three characteristic parameters of the Weibull model obtained by estimation, evaluating the discreteness of the battery capacity distribution based on the size parameters, and evaluating the symmetry of the battery distribution based on the shape parameters; determining a minimum value range of the battery capacity distribution based on the position parameter;
comparing the Weibull position parameter obtained by estimation with the distribution range of the actual battery capacity observed value, determining the capacity value of the Weibull position parameter obtained by estimation, which is smaller than the actual battery capacity observed value, as the abnormal value of the battery capacity distribution, determining the capacity observed value of the Weibull position parameter obtained by estimation as the abnormal value of the battery capacity, and determining the battery with the capacity value smaller than the Weibull position parameter as the abnormal value of the battery capacity.
In a second aspect, the present invention also provides a battery capacity consistency estimation system, including:
the determining module is used for randomly extracting a plurality of battery samples and determining a plurality of battery capacity observed values;
the detection module is used for inputting the battery capacity observed values into a battery capacity consistency statistical model to obtain battery capacity distribution statistical characteristics and abnormal value identification results; the battery capacity consistency statistical model is established based on a three-parameter Weibull probability model, and the distribution statistical characteristics and abnormal values of the battery capacity are obtained by estimating three characteristic parameters of the Weibull model of the capacity distribution;
the consistency testing module is used for verifying the estimation result of the consistency statistical model and judging whether the battery capacity distribution statistical characteristics described by the estimation result of the consistency statistical model are consistent with the distribution statistical characteristics of the actual battery capacity observation value or not based on the testing result;
and the consistency evaluation module is used for evaluating the consistency of the battery capacity and identifying abnormal values of the battery capacity distribution according to the estimation result of the consistency statistical model.
In a third aspect, the present invention further provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the battery capacity consistency estimation method according to any one of the above.
In a fourth aspect, the present invention also provides a non-transitory computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the battery capacity consistency estimation method as described in any one of the above.
According to the method and the system for estimating the consistency of the battery capacity, the battery capacity is detected by adopting the improved Weibull parameter estimation method, compared with the traditional parameter estimation method, the model calculation amount can be greatly reduced, the estimation precision is improved, and the influence of the existence of abnormal variables on the overall distribution symmetry characteristic is avoided.
Drawings
In order to more clearly illustrate the technical solutions of the present invention or the prior art, the drawings needed for the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and those skilled in the art can also obtain other drawings according to the drawings without creative efforts.
FIG. 1 is a schematic flow chart of a method for estimating consistency of battery capacity according to the present invention;
FIG. 2 is a schematic diagram of a statistical analysis process of statistical characteristics of random variable distribution according to the present invention;
FIG. 3 is a schematic diagram of a three-parameter Weibull probability density function provided by the present invention;
FIG. 4 is a schematic diagram of a calculation process for estimating Weibull three parameters according to the present invention;
FIG. 5 is a probability histogram of the capacity distribution provided by the present invention;
FIG. 6 is a graph of the cumulative probability at the peak of the probability of the capacity distribution provided by the present invention
Figure BDA0003220768030000081
About
Figure BDA0003220768030000082
A linear regression graph of (a);
FIG. 7 is a graph comparing the cell capacity distribution provided by the present invention with the Weibull probability density function;
FIG. 8 is a schematic diagram of a battery capacity consistency estimation system provided by the present invention;
fig. 9 is a schematic structural diagram of an electronic device provided by the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is obvious that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Aiming at the defects of the prior art, the invention provides an abnormal battery capacity detection method by taking the test battery capacity as an application scene, the battery capacity is detected by adopting an improved Weibull parameter estimation method, and the method is based on the symmetry characteristics of random variable distribution to three related parameters: the size parameter, the shape parameter and the position parameter are accurately estimated, and a Weibull parameter estimation value is obtained through a display solving process, so that the estimation result precision is effectively improved, the calculated amount is reduced, the accurate identification of the overall distribution statistical characteristics of the sample is realized, and the interference of abnormal variables on the distribution statistical characteristics is avoided.
Fig. 1 is a schematic flow chart of a battery capacity consistency estimation method provided by the present invention, as shown in fig. 1, including:
s1, randomly extracting a plurality of battery samples and determining a plurality of battery capacity observation values;
s2, inputting the battery capacity observed values into a consistency statistical model to obtain battery capacity distribution statistical characteristics and abnormal value identification results; the consistency statistical model is established based on a three-parameter Weibull probability model, and distribution statistical characteristics and abnormal values of the battery capacity are obtained by estimating three characteristic parameters of the Weibull model of the capacity distribution;
s3, verifying the estimation result of the consistency statistical model, and judging whether the battery capacity distribution statistical characteristics described by the estimation result of the consistency statistical model are consistent with the distribution statistical characteristics of the actual battery capacity observation value based on the test result;
and S4, using the estimation result of the consistency statistical model for evaluating the consistency of the battery capacity and identifying the abnormal value of the battery capacity distribution.
Specifically, the invention aims at testing the battery capacity, and a plurality of batteries to be detected (generally more than 100 batteries) are input into the well-established battery capacity consistency statistical model, so that the battery capacity distribution consistency evaluation and abnormal value identification results can be obtained.
The statistical model for the consistency of the battery capacity is obtained by obtaining statistical characteristics of the battery capacity distribution through a three-parameter Weibull model and estimating three characteristic parameters in the three-parameter Weibull model based on the statistical characteristics of the battery capacity distribution.
According to the invention, the improved Weibull parameter estimation method is adopted to detect the battery capacity, compared with the traditional parameter estimation method, the model calculation amount can be greatly reduced, the estimation precision is improved, and the influence of the existence of abnormal variables on the overall distribution symmetry characteristic is avoided.
Based on the above embodiment, the consistency statistical model is obtained by the following steps:
establishing a consistency statistical model based on a Weibull probability model;
determining three Weibull characteristic parameters of the Weibull probability model based on the Weibull probability model;
determining a mathematical expression of the secondary characteristic parameters related to the Weibull characteristic parameters based on the three Weibull characteristic parameters of the Weibull probability model;
estimating the secondary characteristic parameters based on statistical characteristics of the battery capacity observation value distribution;
estimating three Weibull characteristic parameters of the Weibull probability model based on a secondary characteristic parameter expression;
and obtaining the statistical characteristics and abnormal values of the consistency distribution of the battery capacity based on the three Weibull characteristic parameters.
Wherein, the consistency statistic model is established based on the Weibull probability model, and the consistency statistic model comprises the following steps:
determining three Weibull characteristic parameters of a Weibull probability model, wherein the three Weibull characteristic parameters comprise a size parameter, a shape parameter and a position parameter;
constructing a cumulative probability function, a probability density function and a derivative function of the probability density function of the Weibull distribution based on the size parameter, the shape parameter and the position parameter;
wherein the size parameter is used for reflecting the discrete characteristic of the distribution, the shape parameter is used for reflecting the symmetrical characteristic of the distribution, and the position parameter is used for reflecting the minimum numerical range of the distribution.
Wherein, the determining a mathematical expression about the Weibull characteristic parameter of the quadratic characteristic parameter based on the three Weibull characteristic parameters of the Weibull probability model includes:
the Weibull secondary characteristic parameters comprise Weibull probability density peak values, Weibull probability density peak value position values and distribution cumulative probability ratio values;
acquiring a mathematical expression of the Weibull probability density peak position value relative to Weibull characteristic parameters according to the derivative function of the Weibull probability density function;
obtaining the cumulative probability on the left side of the Weibull probability density peak value and the cumulative probability on the right side of the Weibull probability density peak value based on the Weibull probability density peak value and the Weibull cumulative probability function;
and obtaining a mathematical expression of the distribution cumulative probability ratio function on the Weibull characteristic parameter according to the ratio of the left cumulative probability of the Weibull probability density peak position value and the right part cumulative probability of the Weibull probability density peak position value.
Wherein estimating the secondary characteristic parameter based on the statistical characteristics of the battery capacity observation distribution comprises:
obtaining a plurality of equidistant subintervals in the distribution interval and corresponding subinterval distribution probabilities based on the distribution interval and the distribution probability of the battery capacity observation value, replacing the equidistant subintervals by a median value of each subinterval, and dividing the subinterval distribution probabilities by the subinterval spacing values to obtain distribution probability densities corresponding to the median values of the subintervals;
respectively obtaining the maximum value of the probability density of the preset number from the probability density of the battery capacity distribution subintervals, and obtaining the position value of the maximum value of the probability density of the preset number of battery capacity distribution on the basis of the maximum value of the probability density of the preset number of battery capacity distribution and the median of the preset number distribution subintervals;
obtaining the cumulative probability at the maximum value of the distribution probability density of the preset number of the battery capacities based on the position value of the maximum value of the distribution probability density of the preset number of the battery capacities;
calculating a weighted mean value of the position of the peak value of the probability density according to the position values of the maximum values of the distribution probability densities of the preset number of the battery capacities, and taking the distribution probability at the position of the peak value of the distribution probability density as a weighting coefficient to obtain an estimated mean value of the position of the peak value of the distribution probability density of the battery capacities;
establishing a linear equation set between the position value of the maximum value of the distribution probability density of the battery capacity of the preset number and the cumulative probability at the maximum value of the distribution probability density of the battery capacity of the preset number based on the characteristic that the Weibull cumulative probability function is approximately linear near the position value of the peak value of the probability density, and establishing a linear function expression of the Weibull cumulative probability density function of the battery capacity distribution at the peak value of the distribution probability density through the slope average value and the intercept average value of the linear function obtained by solving two equations in the equation set;
substituting the estimated mean value of the battery capacity distribution probability peak value position value into a linear function expression of the Weibull cumulative probability density function of the battery capacity at the distribution probability density peak value to obtain an estimated value of the cumulative probability at the battery capacity distribution probability density peak value;
obtaining an estimated value of a battery capacity distribution probability density peak value at the position value of the distribution probability density peak value according to the average value of the maximum values of the probability densities of the preset number;
and obtaining the ratio of the cumulative probabilities of the battery capacity distribution on the left and right sides of the probability density peak according to the cumulative probabilities on the left and right sides of the battery capacity distribution probability density peak.
Wherein, estimating three Weibull characteristic parameters of the battery capacity distribution based on a secondary characteristic parameter expression and a secondary characteristic parameter estimated based on statistical characteristics of the battery capacity observation value distribution comprises:
establishing an equation based on a mathematical expression of the battery capacity distribution cumulative probability ratio function about Weibull characteristic parameters and the ratio of the cumulative probabilities of the battery capacity distribution on the left side and the right side of the probability density peak value to obtain shape parameters of the battery capacity Weibull distribution;
substituting the shape parameters of the battery capacity Weibull distribution into a mathematical expression of the probability density peak value about Weibull characteristic parameters, and establishing an equation with the estimation peak value at the battery capacity distribution probability peak value to obtain the size parameters of the battery capacity Weibull distribution;
substituting the shape parameter of the battery capacity Weibull distribution and the size parameter of the battery capacity Weibull distribution into a mathematical expression of the distribution probability density peak position value and the Weibull characteristic parameter, and establishing an equation with an estimated value of the battery capacity distribution probability peak position value to obtain the position parameter of the battery capacity Weibull distribution.
Specifically, the core-battery capacity detection model of the present invention is obtained by the following steps, as shown in fig. 2:
firstly, establishing a Weibull probability model
Cumulative probability function of a three-parameter Weibull probability model, as in equation (1):
Figure BDA0003220768030000121
probability density function of a three-parameter Weibull probability model, as in equation (2):
Figure BDA0003220768030000122
the derivative of the probability density function of a three-parameter Weibull probability model, as in equation (3):
Figure BDA0003220768030000123
wherein the size parameter a reflects the dispersion of the distribution; the shape parameter B reflects the symmetry of the distribution; the positional parameter C reflects the minimum numerical range of the distribution.
Secondly, determining characteristic parameter expression
Estimating Weibull parameters according to the distribution symmetry, firstly determining the distribution symmetry characteristics, and determining the distribution symmetry by the method: distributing the random variable value x at the peak of the probability density with the random variablepAs a boundary point, comparing the cumulative probability of distribution intervals on the left and right sides of the boundary point to determine the distribution symmetry characteristic, as shown in fig. 3, when the distribution probability on the left side is high, the random variable is distributed in a right state; when the right side distribution probability is high, the random variable is distributed in a left state; when the left and right distribution probabilities are equal, the random variables are symmetrically distributed.
The probability density peak location value is determined by equation (3), i.e.:
Figure BDA0003220768030000131
finding x at the peak of the probability densitypThe value:
Figure BDA0003220768030000132
xpand (4) processing the probability density value:
Figure BDA0003220768030000133
random variable is in xpDistribution probability of the left and right sides:
xpleft side distribution probability:
Figure BDA0003220768030000134
xpright distribution probability:
Figure BDA0003220768030000135
xpratio of distribution probability of left and right sides:
Figure BDA0003220768030000136
identifying a distribution symmetry feature according to equation (9):
when η > 1 in formula (9), x is distributed to the right, when η < 1, x is distributed to the left, and when η is 1, x is distributed to the leftpThe distribution probability of the left side and the right side is equal, namely symmetrical distribution, the value B of the shape parameter is 3.2598, and the distribution symmetry is judged according to the value B:
b <3.2598, left-biased distribution;
b is 3.2598, symmetrically distributed;
b >3.2598, biased to right state distribution.
Parameter estimation
As shown in FIG. 4, first, the distribution interval and the distribution probability of a given random variable are counted to obtain n equally spaced subintervals { (x)1,x2],(x2,x3]…,(xn,xn+1]Distribution probability p1,p2...pnAnd probability density
Figure BDA0003220768030000141
N distribution subintervals are given by the median { x ] of the interval1,x2,...,xnReplacing, wherein:
Figure BDA0003220768030000142
wherein i is 1,2,3.
Second, find the three with the highest probability densityAn
Figure BDA0003220768030000143
Values and their corresponding distribution probabilities, probability densities:
Figure BDA0003220768030000144
and
Figure BDA0003220768030000145
for estimating distribution peak position
Figure BDA0003220768030000146
And peak probability density
Figure BDA0003220768030000147
Will be provided with
Figure BDA0003220768030000148
As
Figure BDA0003220768030000149
The weighting coefficients of (1), calculating
Figure BDA00032207680300001410
Weighted mean of
Figure BDA00032207680300001411
I.e., the peak of the distribution probability density, is solved as follows:
Figure BDA00032207680300001412
calculating three according to formula (1)
Figure BDA00032207680300001413
Cumulative probability function of
Figure BDA00032207680300001414
The following were used:
Figure BDA0003220768030000151
Figure BDA00032207680300001515
distribution probability density of (a):
Figure BDA0003220768030000152
since the cumulative probability density function is at xpApproximately linear near point, i.e.:
Figure BDA0003220768030000153
will be provided with
Figure BDA0003220768030000154
And
Figure BDA0003220768030000155
substituting into equation (14), a system of linear equations is established in the form of equation (15):
Figure BDA0003220768030000156
three equations in the formula (15) are combined in pairs to obtain three groups of (a, b) values, and then the average value of the three groups of (a, b) values is obtained
Figure BDA0003220768030000157
As a solution to the system of equations, will be finally calculated from equation (11)
Figure BDA0003220768030000158
And
Figure BDA0003220768030000159
substituted into the formula (14) to obtain the product
Figure BDA00032207680300001510
Cumulative probability of (c)
Figure BDA00032207680300001511
Thus, eta can be obtained according to the formula (9), and the value B can be obtained;
Figure BDA00032207680300001512
according to the formula (6), obtaining the value of the size parameter A:
Figure BDA00032207680300001513
and (5) obtaining the value of the position parameter C according to the formula (5):
Figure BDA00032207680300001514
based on any of the above embodiments, verifying the estimation results of the three characteristic parameters of the Weibull model, and determining whether the statistical distribution statistical characteristics of the battery capacity described by the estimation results of the three characteristic parameters of the Weibull model are consistent with the statistical distribution statistical characteristics of the actual battery capacity based on the test results, includes:
and judging based on a preset hypothesis test method, if the capacity distribution described by the three characteristic parameter estimation results of the Weibull model of the battery capacity distribution and the actual observation value distribution accord with the difference range under a preset confidence coefficient, determining that the parameter estimation results are the actual distribution statistical characteristics capable of reflecting the battery capacity, otherwise, determining that the parameter estimation results cannot reflect the actual distribution statistical characteristics of the battery capacity.
Wherein, the application of the three characteristic parameters of the Weibull model to the evaluation of the consistency of the battery capacity and the identification of abnormal values of the battery capacity distribution comprises the following steps:
evaluating the statistical characteristics of the consistency of the battery capacity distribution based on the three characteristic parameters of the Weibull model obtained by estimation, evaluating the discreteness of the battery capacity distribution based on the size parameters, and evaluating the symmetry of the battery distribution based on the shape parameters; determining a minimum value range of the battery capacity distribution based on the position parameter;
comparing the Weibull position parameter obtained by estimation with the distribution range of the actual battery capacity observed value, determining the capacity value of the Weibull position parameter obtained by estimation, which is smaller than the actual battery capacity observed value, as the abnormal value of the battery capacity distribution, determining the capacity observed value of the Weibull position parameter obtained by estimation as the abnormal value of the battery capacity, and determining the battery with the capacity value smaller than the Weibull position parameter as the abnormal value of the battery capacity.
Specifically, based on the above-described embodiment, pearson x is used2Distribution versus size parameter
Figure BDA0003220768030000161
Shape parameter
Figure BDA0003220768030000162
And location parameters
Figure BDA0003220768030000163
The Weibull distribution of (D) was subjected to hypothesis testing. Assuming that the distribution type of the parent X of the random variable is known, as in equation (19):
H0:F(x)＝F(x；θ1,θ2,θ3) (19)
and (3) observing the weighted square sum of the theoretical frequency of the subsample and the actual frequency deviation, wherein the weighted square sum is shown as the formula (20):
Figure BDA0003220768030000164
wherein i represents a sample grouping; m represents the actual sample frequency; n represents the number of samples; p is a radical ofiRepresenting the model estimation probability.
From Pearson's theorem, as the sample size approaches + ∞, χ2Approximately obey χ with degree of freedom l-12And (4) distribution. When in useWhen the estimated parameters are known, χ2The degree of freedom of (2) is required to take the number k of estimated parameters into account for discriminating χ of hypothesis test2Is x2(l-k-1). From this, as formula (21):
if it is not
χ2≥χa 2(l-k-1) (21)
Rejection of original hypothesis H0Consider the sample population as F of the original hypothesis0There is a significant difference, as in equation (22):
if it is not
χ2≤χa 2(l-k-1) (22)
Accepting the original hypothesis H0Consider the sample population as F of the original hypothesis0There was no significant difference.
Grouping the observation value ranges according to the number of samples, wherein the degree of freedom is the number of groups minus l, the k value in a three-parameter Weibull distribution model is 3, and the degree of freedom is according to x2The table of critical values of distribution indicates the% at a significant level of 5%a 2And (l-k-1) a critical value, thereby judging whether the parameter estimation result can reflect the actual distribution statistical characteristics of the observed value.
Based on any of the above embodiments, the present invention takes a statistical analysis process of battery capacity of a certain batch as an example, 3427 batteries in a batch are randomly extracted from the 3427 batteries, and a three-parameter Weibull model is used to perform statistical analysis on the capacity of the extracted battery samples. Analyzing the discrete characteristic of the battery capacity distribution through the size parameter A, analyzing the symmetrical characteristic of the battery capacity distribution through the shape parameter B and analyzing the minimum numerical range of the battery capacity distribution through the position parameter C.
Basic information of the sample cell capacity distribution is shown in table 1:
TABLE 1
Statistical value Maximum value/Ah Minimum value/Ah Mean value/Ah Standard deviation/Ah
Numerical value 27.7966 26.9097 27.3181 0.1516
The Weibull distribution of the battery capacity distribution is subjected to parameter estimation by adopting the parameter estimation method based on the distribution symmetry characteristics. The calculation process is as follows:
assuming that n is 20, that is, the capacity distribution is 20 equally spaced intervals, the distribution probability histogram is as shown in fig. 5, and three intervals with the maximum distribution probability are determined according to the distribution probability of the battery capacity in 20 intervals, and the result is shown in table 2:
TABLE 2
Figure BDA0003220768030000181
The capacity value at the position of the probability peak is calculated according to equation (11):
Figure BDA0003220768030000182
the probability density peak is calculated according to equation (13):
Figure BDA0003220768030000183
solving a linear equation set according to the formula (15), and substituting the calculation result into the formula (14) to obtain
Figure BDA0003220768030000184
Cumulative distribution probability of (2):
Figure BDA0003220768030000185
as shown in fig. 6.
According to the formulas (7) to (9), calculation is made
Figure BDA0003220768030000186
Left and right sides distribution cumulative probability ratio:
p-＝F(xp)＝0.4146 (23)
p+＝1-F(xp)＝0.5854
(24)
Figure BDA0003220768030000191
calculating shape parameters according to equation (16)
Figure BDA0003220768030000192
Figure BDA0003220768030000193
Calculating the dimensional parameter according to equation (17)
Figure BDA0003220768030000194
Figure BDA0003220768030000195
Calculating a position parameter according to equation (18)
Figure BDA0003220768030000196
Figure BDA0003220768030000197
Parameters obtained by the estimation algorithm
Figure BDA0003220768030000198
And
Figure BDA0003220768030000199
and obtained by maximum likelihood estimation
Figure BDA00032207680300001910
And
Figure BDA00032207680300001911
the values were compared and passed through Pearson's chi2Distribution hypothesis testing was performed on the results of the Weibull three-parameter estimation, as shown in table 3:
TABLE 3
Figure BDA00032207680300001912
According to table 3, three parameters Weibull obtained based on distribution symmetry feature estimation and maximum likelihood estimation are compared. Weibull three parameters obtained by two estimation methods meet Pearson's X2Test conditions, χ based on the estimation results of the present invention2The smaller value indicates that the Weibull function curve calculated by the method has higher fitting degree with the actual battery capacity distribution. The size parameter and the shape parameter obtained based on the distribution symmetry characteristic estimation are both smaller than the maximum likelihood estimation result, which shows that the dispersion of the battery capacity distribution of the batch estimated based on the distribution symmetry characteristic is smaller; two estimation methods to obtain shape parameters
Figure BDA0003220768030000201
The values are all less than 3.2598, which indicates that the battery capacity distribution of the batch is biased to the left, and the position parameter estimated based on the distribution symmetry characteristic is greater than the maximum likelihood estimation result, which indicates that the battery capacity distribution of the batch is estimated based on the distribution symmetry characteristicThe left state distribution statistical characteristics are more obvious.
The probability distribution histogram of the battery capacity is compared with the Weibull probability density function curve obtained by two estimation methods, as shown in FIG. 7. As can be seen from fig. 7, the Weibull probability model obtained based on the distribution symmetry feature estimation ignores the samples with smaller capacity in the battery samples, thereby improving the fitting degree of the Weibull function curve and the capacity distribution statistical feature. According to the battery consistency characteristics estimated by the method, the batteries with the capacity distribution within the range of 26.88-26.97 Ah in the batch of battery samples are abnormal batteries, the normal battery capacity distribution is biased-left distribution, the minimum value of the distribution is about 27.0593Ah, and the size parameter characterization distribution dispersion is 0.3115 Ah. From this, it was found that the size parameter 0.4541 and the shape parameter 2.7259 obtained by the maximum likelihood estimation method had an estimation deviation due to the influence of the abnormal battery, and the battery having the batch capacity of less than 27Ah was the abnormal battery.
The abnormal battery capacity detection system provided by the present invention is described below, and the abnormal battery capacity detection system described below and the abnormal battery capacity detection method described above may be referred to in correspondence with each other.
Fig. 8 is a schematic structural diagram of a battery capacity consistency estimation system provided by the present invention, as shown in fig. 8, including: a determination module 81, a detection module 82, a consistency check module 83, and a consistency evaluation module 84, wherein:
the determining module 81 is configured to randomly extract a plurality of battery samples and determine a plurality of battery capacity observation values; the detection module 82 is configured to input the battery capacity observation values into a consistency statistical model, and obtain a battery capacity distribution statistical characteristic and an abnormal value identification result; the consistency statistical model is established based on a three-parameter Weibull probability model, and distribution statistical characteristics and abnormal values of the battery capacity are obtained by estimating three characteristic parameters of the Weibull model of the capacity distribution; the consistency test module 83 is configured to verify the estimation result of the consistency statistical model, and determine whether the statistical characteristics of the battery capacity distribution described by the estimation result of the consistency statistical model are consistent with the statistical characteristics of the distribution of the actual battery capacity observation value based on the test result; the consistency evaluation module 84 is configured to use the estimation result of the consistency statistical model to evaluate consistency of the battery capacity and identify an abnormal value of the battery capacity distribution.
According to the invention, the improved Weibull parameter estimation method is adopted to detect the battery capacity, compared with the traditional parameter estimation method, the model calculation amount can be greatly reduced, the estimation precision is improved, and the influence of the existence of abnormal variables on the overall distribution symmetry characteristic is avoided.
Fig. 9 illustrates a physical structure diagram of an electronic device, and as shown in fig. 9, the electronic device may include: a processor (processor)910, a communication Interface (Communications Interface)920, a memory (memory)930, and a communication bus 940, wherein the processor 910, the communication Interface 920, and the memory 930 communicate with each other via the communication bus 940. Processor 910 may invoke logic instructions in memory 930 to perform a battery capacity consistency estimation method comprising: randomly extracting a plurality of battery samples and determining a plurality of battery capacity observed values; inputting the plurality of battery capacity observed values into a consistency statistical model to obtain battery capacity distribution statistical characteristics and abnormal value identification results; the consistency statistical model is established based on a three-parameter Weibull probability model, and distribution statistical characteristics and abnormal values of the battery capacity are obtained by estimating three characteristic parameters of the Weibull model of the capacity distribution; verifying the estimation result of the consistency statistical model, and judging whether the battery capacity distribution statistical characteristics described by the estimation result of the consistency statistical model are consistent with the distribution statistical characteristics of the actual battery capacity observation value or not based on the detection result; and using the estimation result of the consistency statistical model for evaluating the consistency of the battery capacity and identifying abnormal values of the battery capacity distribution.
Furthermore, the logic instructions in the memory 930 may be implemented in software functional units and stored in a computer readable storage medium when the logic instructions are sold or used as independent products. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
In another aspect, the present invention also provides a computer program product comprising a computer program stored on a non-transitory computer-readable storage medium, the computer program comprising program instructions which, when executed by a computer, enable the computer to perform the battery capacity consistency estimation method provided by the above methods, the method comprising:
in yet another aspect, the present invention also provides a non-transitory computer-readable storage medium having stored thereon a computer program, which when executed by a processor, is implemented to perform the battery capacity consistency estimation methods provided above, the method comprising: randomly extracting a plurality of battery samples and determining a plurality of battery capacity observed values; inputting the plurality of battery capacity observed values into a consistency statistical model to obtain battery capacity distribution statistical characteristics and abnormal value identification results; the consistency statistical model is established based on a three-parameter Weibull probability model, and distribution statistical characteristics and abnormal values of the battery capacity are obtained by estimating three characteristic parameters of the Weibull model of the capacity distribution; verifying the estimation result of the consistency statistical model, and judging whether the battery capacity distribution statistical characteristics described by the estimation result of the consistency statistical model are consistent with the distribution statistical characteristics of the actual battery capacity observation value or not based on the detection result; and using the estimation result of the consistency statistical model for evaluating the consistency of the battery capacity and identifying abnormal values of the battery capacity distribution.
The above-described embodiments of the apparatus are merely illustrative, and the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware. With this understanding in mind, the above-described technical solutions may be embodied in the form of a software product, which can be stored in a computer-readable storage medium such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the methods described in the embodiments or some parts of the embodiments.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (10)

1. A method for estimating consistency of battery capacities, comprising:
randomly extracting a plurality of battery samples and determining a plurality of battery capacity observed values;
inputting the plurality of battery capacity observed values into a consistency statistical model to obtain battery capacity distribution statistical characteristics and abnormal value identification results; the consistency statistical model is established based on a three-parameter Weibull probability model, and distribution statistical characteristics and abnormal values of the battery capacity are obtained by estimating three characteristic parameters of the Weibull model of the capacity distribution;
verifying the estimation result of the consistency statistical model, and judging whether the battery capacity distribution statistical characteristics described by the estimation result of the consistency statistical model are consistent with the distribution statistical characteristics of the actual battery capacity observation value or not based on the detection result;
and using the estimation result of the consistency statistical model for evaluating the consistency of the battery capacity and identifying abnormal values of the battery capacity distribution.
2. The battery capacity consistency estimation method according to claim 1, wherein the consistency statistical model is obtained by:
establishing a consistency statistical model based on a Weibull probability model;
determining three Weibull characteristic parameters of the Weibull probability model based on the Weibull probability model;
determining a mathematical expression of the secondary characteristic parameters related to the Weibull characteristic parameters based on the three Weibull characteristic parameters of the Weibull probability model;
estimating the secondary characteristic parameters based on statistical characteristics of the battery capacity observation value distribution;
estimating three Weibull characteristic parameters of the Weibull probability model based on a secondary characteristic parameter expression;
and obtaining the statistical characteristics and abnormal values of the consistency distribution of the battery capacity based on the three Weibull characteristic parameters.
3. The method according to claim 2, wherein the establishing a consistency statistical model based on the Weibull probability model comprises:
determining three Weibull characteristic parameters of a Weibull probability model, wherein the three Weibull characteristic parameters comprise a size parameter, a shape parameter and a position parameter;
constructing a cumulative probability function, a probability density function and a derivative function of the probability density function of the Weibull distribution based on the size parameter, the shape parameter and the position parameter;
wherein the size parameter is used for reflecting the discrete characteristic of the distribution, the shape parameter is used for reflecting the symmetrical characteristic of the distribution, and the position parameter is used for reflecting the minimum numerical range of the distribution.
4. The method according to claim 2, wherein the determining a mathematical expression about the Weibull characteristic parameters of the secondary characteristic parameters based on the three Weibull characteristic parameters of the Weibull probability model comprises:
the Weibull secondary characteristic parameters comprise Weibull probability density peak values, Weibull probability density peak value position values and distribution cumulative probability ratio values;
acquiring a mathematical expression of the Weibull probability density peak position value relative to Weibull characteristic parameters according to the derivative function of the Weibull probability density function;
obtaining the cumulative probability on the left side of the Weibull probability density peak value and the cumulative probability on the right side of the Weibull probability density peak value based on the Weibull probability density peak value and the Weibull cumulative probability function;
and obtaining a mathematical expression of the distribution cumulative probability ratio function on the Weibull characteristic parameter according to the ratio of the left cumulative probability of the Weibull probability density peak position value and the right part cumulative probability of the Weibull probability density peak position value.
5. The battery capacity consistency estimation method according to claim 2, wherein estimating the secondary characteristic parameter based on the statistical characteristic of the battery capacity observation value distribution includes:
obtaining a plurality of equidistant subintervals in the distribution interval and corresponding subinterval distribution probabilities based on the distribution interval and the distribution probability of the battery capacity observation value, replacing the equidistant subintervals by a median value of each subinterval, and dividing the subinterval distribution probabilities by the subinterval spacing values to obtain distribution probability densities corresponding to the median values of the subintervals;
respectively obtaining the maximum value of the probability density of the preset number from the probability density of the battery capacity distribution subintervals, and obtaining the position value of the maximum value of the probability density of the preset number of battery capacity distribution on the basis of the maximum value of the probability density of the preset number of battery capacity distribution and the median of the preset number distribution subintervals;
obtaining the cumulative probability at the maximum value of the distribution probability density of the preset number of the battery capacities based on the position value of the maximum value of the distribution probability density of the preset number of the battery capacities;
calculating a weighted mean value of the position of the peak value of the probability density according to the position values of the maximum values of the distribution probability densities of the preset number of the battery capacities, and taking the distribution probability at the position of the peak value of the distribution probability density as a weighting coefficient to obtain an estimated mean value of the position of the peak value of the distribution probability density of the battery capacities;
establishing a linear equation set between the position value of the maximum value of the distribution probability density of the battery capacity of the preset number and the cumulative probability at the maximum value of the distribution probability density of the battery capacity of the preset number based on the characteristic that the Weibull cumulative probability function is approximately linear near the position value of the peak value of the probability density, and establishing a linear function expression of the Weibull cumulative probability density function of the battery capacity distribution at the peak value of the distribution probability density through the slope average value and the intercept average value of the linear function obtained by solving two equations in the equation set;
substituting the estimated mean value of the battery capacity distribution probability peak value position value into a linear function expression of the Weibull cumulative probability density function of the battery capacity at the distribution probability density peak value to obtain an estimated value of the cumulative probability at the battery capacity distribution probability density peak value;
obtaining an estimated value of a battery capacity distribution probability density peak value at the position value of the distribution probability density peak value according to the average value of the maximum values of the probability densities of the preset number;
and obtaining the ratio of the cumulative probabilities of the battery capacity distribution on the left and right sides of the probability density peak according to the cumulative probabilities on the left and right sides of the battery capacity distribution probability density peak.
6. The method according to claim 2, wherein estimating three Weibull characteristic parameters of the battery capacity distribution based on a secondary characteristic parameter expression and a secondary characteristic parameter estimated based on statistical characteristics of the battery capacity observation distribution comprises:
establishing an equation based on a mathematical expression of the battery capacity distribution cumulative probability ratio function about Weibull characteristic parameters and the ratio of the cumulative probabilities of the battery capacity distribution on the left side and the right side of the probability density peak value to obtain shape parameters of the battery capacity Weibull distribution;
substituting the shape parameters of the battery capacity Weibull distribution into a mathematical expression of the probability density peak value about Weibull characteristic parameters, and establishing an equation with the estimation peak value at the battery capacity distribution probability peak value to obtain the size parameters of the battery capacity Weibull distribution;
substituting the shape parameter of the battery capacity Weibull distribution and the size parameter of the battery capacity Weibull distribution into a mathematical expression of the distribution probability density peak position value and the Weibull characteristic parameter, and establishing an equation with an estimated value of the battery capacity distribution probability peak position value to obtain the position parameter of the battery capacity Weibull distribution.
7. The method for estimating consistency of battery capacity according to claim 1, wherein verifying the estimation results of the three characteristic parameters of the Weibull model, and determining whether the statistical distribution statistical characteristics of the battery capacity described by the estimation results of the three characteristic parameters of the Weibull model are consistent with the statistical distribution statistical characteristics of the actual battery capacity based on the verification results comprises:
and judging based on a preset hypothesis test method, if the capacity distribution described by the three characteristic parameter estimation results of the Weibull model of the battery capacity distribution and the actual observation value distribution accord with the difference range under a preset confidence coefficient, determining that the parameter estimation results are the actual distribution statistical characteristics capable of reflecting the battery capacity, otherwise, determining that the parameter estimation results cannot reflect the actual distribution statistical characteristics of the battery capacity.
8. The method according to claim 1, wherein the using three characteristic parameters of the Weibull model for battery capacity consistency evaluation and abnormal value identification of battery capacity distribution comprises:
evaluating the statistical characteristics of the consistency of the battery capacity distribution based on the three characteristic parameters of the Weibull model obtained by estimation, evaluating the discreteness of the battery capacity distribution based on the size parameters, and evaluating the symmetry of the battery distribution based on the shape parameters; determining a minimum value range of the battery capacity distribution based on the position parameter;
comparing the Weibull position parameter obtained by estimation with the distribution range of the actual battery capacity observed value, determining the capacity value of the Weibull position parameter obtained by estimation, which is smaller than the actual battery capacity observed value, as the abnormal value of the battery capacity distribution, determining the capacity observed value of the Weibull position parameter obtained by estimation as the abnormal value of the battery capacity, and determining the battery with the capacity value smaller than the Weibull position parameter as the abnormal value of the battery capacity.
9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the steps of the battery capacity consistency estimation method according to any one of claims 1 to 8 when executing the program.
10. A non-transitory computer-readable storage medium having stored thereon a computer program, which when executed by a processor implements the steps of the battery capacity consistency estimation method according to any one of claims 1 to 8.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117930064A (en) * 2024-03-21 2024-04-26 四川新能源汽车创新中心有限公司 Method, system, computing equipment and medium for nondestructive testing lithium precipitation

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