CN113094981A - Lithium ion battery reliability evaluation method based on grey neural network model and self-service method - Google Patents

Lithium ion battery reliability evaluation method based on grey neural network model and self-service method Download PDF

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CN113094981A
CN113094981A CN202110329522.6A CN202110329522A CN113094981A CN 113094981 A CN113094981 A CN 113094981A CN 202110329522 A CN202110329522 A CN 202110329522A CN 113094981 A CN113094981 A CN 113094981A
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张子正
胡欲立
李炬晨
郝泽花
宋保维
郑乙
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Abstract

According to the lithium ion battery reliability assessment method based on the metabolism gray neural network model and the self-service method, the prediction accuracy is remarkably improved compared with that of a common metabolism gray model and a BP neural network model, the combined model can fully utilize the characteristics of strong learning capability, good nonlinear mapping capability and simple gray model operation of the BP neural network model, and the characteristic of low sample number requirement of the self-service method, can be used for better fitting a battery performance degradation curve, has a good extrapolation prediction effect, finally obtains the pseudo service life of a battery stored under different stresses, further completes reliability assessment more efficiently and more cheaply, and enables the final assessment result to have strong objectivity and comprehensiveness.

Description

Lithium ion battery reliability evaluation method based on grey neural network model and self-service method
Technical Field
The invention belongs to the technical field of application and research of lithium ion battery reliability evaluation, and particularly relates to a lithium ion battery reliability evaluation method based on a metabolism grey neural network model and a self-service method.
Background
The lithium ion battery is used as a kind of energy supply equipment commonly used by underwater weapons driven by electric power, has the advantages of high specific energy, small volume, long service life, no memory, environmental protection and the like, and is widely applied to the field of national defense. In the peaceful age, these equipment are in storage and service for long periods of time after service. The effects of long-term environmental stresses such as temperature, humidity, etc. can destroy its normal internal structure and operational capabilities. The storage reliability of the equipment will decrease with the increase of the storage time, and the high reliability of the storage period is the basic guarantee for the normal use of the weapon equipment in the service period. With the continuous improvement of the requirements of modern war on the performance of weapon equipment and the increasing complexity of equipment composition, the reliability problem becomes more and more prominent. After the equipment with poor reliability is delivered for use, the guarantee cost is greatly increased, the whole life cycle cost is greatly increased, and irreparable losses such as casualties and the like are caused in serious cases. Therefore, designers are confronted with the contradiction between unnecessary waste caused by too conservative life evaluation of equipment with expensive design and manufacturing cost and the requirement that the relevant equipment cannot complete the battle mission caused by too optimistic life evaluation, so that the storage reliability of the equipment is predicted relatively accurately, and the method has important significance for reasonably arranging equipment battle plans.
The method for evaluating the reliability of the lithium ion battery by domestic and foreign researchers mainly comprises a failure model method taking working current and working temperature as main consideration factors, a method for evaluating the reliability by means of an accelerated life test and a mathematical statistics means, and a method for establishing a fuzzy membership function according to normal battery data to process incomplete data so as to obtain the storage reliability. The method is proved to have certain effectiveness and practicability through practice and inspection.
Aiming at the particularity of storage and use of a lithium ion battery serving for an underwater weapon, a failure model method is difficult to accurately evaluate reliability indexes, and simultaneously, a fuzzy membership function method needs too many samples. The method for accelerating the service life test uses the environmental stress parameters which are harsher than the real working conditions, can meet the requirement on the accuracy degree of the reliability evaluation result of the lithium ion battery, has the advantage of not needing a large number of samples, and is suitable for the reliability evaluation of the lithium ion battery.
Disclosure of Invention
The technical problem solved by the invention is as follows: in order to solve the problem that the sample size is small in the existing lithium ion battery reliability assessment serving for the underwater weapon, the invention provides a method for conducting reliability assessment by processing a small sample stress accelerated life test result based on a metabolism grey neural network model and a self-service method.
The technical scheme of the invention is as follows: the lithium ion battery reliability evaluation method based on the metabolism grey neural network model and the self-service method comprises the following steps:
step 1: randomly sampling lithium ion batteries of the same type and the same batch;
step 2: activating the sample obtained in the step 1;
and step 3: performing an accelerated storage experiment on the samples subjected to the activation treatment in the step 2, and grouping the samples at the same time, wherein the number of batteries in each group is more than or equal to 2;
and 4, step 4: carrying out capacity measurement and internal resistance measurement on the battery stored at each temperature every other period T, and not testing and maintaining the battery in the period to obtain data which is continuously updated along with time, and simultaneously obtaining the change curves of the battery capacity and the internal resistance along with the time under different stress conditions;
and 5: accumulating the data obtained in step 4 to generate a metabolic sequence, comprising the following substeps:
step 5.1: the capacity value sequence defining the metabolism of the kth cell at n time nodes is:
C(0)(k)＝{c(0)(1),c(0)(2),…,c(0)(n)}k
to C(0)(k) The data are accumulated to obtain a metabolic sequence:
C(1)(k)＝{c(1)(1),c(1)(2),…,c(1)(n)}k
step 5.2: to the sequence
Figure BDA0002995890610000031
The operation is performed m times, and the generated sequence is as follows:
Figure BDA0002995890610000032
step 6: predicting the sequence obtained in the step 5 by using a metabolism gray model to obtain a predicted value of the measured value in the step 4, and comprising the following substeps:
step 6.1: according to the formula z(1)(k)＝0.5cm(1)(k)+0.5cm(1)(k-1), k 1,2, …, n yielding Cm(1)Of the sequence of closely adjacent means Z(1)：
Z(1)＝{z(1)(1),z(1)(2),…,z(1)(n)}；
Step 6.2: according to the gray color differential equation in the gray theory as
Figure BDA0002995890610000033
The following relationships are established:
cm(0)(k)+az(1)(k)＝b (6)
where parameter a is the principal variable parameter or system development coefficient and b is the gray effect coefficient or background value of the gray model.
Step 6.3: calculating least squares estimation parameters of a processing method
Figure BDA0002995890610000034
Is a parameter column of the gray model, order
Figure BDA0002995890610000035
The least squares estimation parameter column for the gray model satisfies
Figure BDA0002995890610000036
Step 6.4: calculating the analog value of the original X sequence
Figure BDA0002995890610000037
The time response sequence of the model obtained in equation (6) is:
Figure BDA0002995890610000038
the sequence X generated by the primary accumulation can be solved by the formula (11)(1)Analog value of
Figure BDA0002995890610000039
Figure BDA0002995890610000041
Step 6.5: for those generated after accumulation in step 6.4
Figure BDA0002995890610000042
Reducing the sequence to obtain a predicted sequence:
Figure BDA0002995890610000043
the sequence of the grey prediction model is thus:
Figure BDA0002995890610000044
step 6.6: subtracting the measured value in the step 4 according to the grey model prediction sequence of the capacity obtained in the step 6.4 to obtain a residual sequence;
and 7: establishing a BP neural network for the capacity and the residual sequence obtained by processing in the step 6 and training to obtain a predicted value of the capacity and an error sequence of the predicted value and the ideal value;
step 7.1: the capacity fading sequence C ═ C over time obtained in step 61,c2,…cnNormalizing the ith quantity X in the X sequence obtained in the step 66 and the residual value sequence obtained in the stepiComprises the following steps:
Figure BDA0002995890610000045
wherein, Cmin、CmaxThe minimum value and the maximum value in the original sequence are respectively, wherein a is 0.8, and b is (1-a)/2.
Step 7.2: after normalization, performing inverse normalization operation to make the output data and the original data fall in the same region, according to step 7.1:
Figure BDA0002995890610000046
obtaining a normalized sequence X1＝{x1,x2,…,xnAfter the previous step, let Xk＝{xk,xk+1,…,xk+(n-1)Let T be the kth input samplek＝{xk+(n-1)+1Is the kth output sample.
Step 7.3: assigning values to the capacity sequence and the residual sequence which are input and output by the sequence processed by the steps 7.1 and 7.2;
step 7.4: establishing a neural network related to a capacity sequence and a residual sequence, and setting a learning rate, a maximum learning frequency and a minimum mean square error of training;
step 7.5: training the neural network established in the step 7.4 by taking the capacity sequence measured value in the step 4 and the capacity sequence predicted value and residual sequence predicted value obtained in the step 6 until all training samples are trained;
step 7.6: randomly selecting a group of input samples and output samples from the learning samples again, returning to the step 7.1 until the network global error E is smaller than a preset minimum value, namely the network is converged, and finishing the learning;
and 8: training step 7, establishing a neural network to realize the prediction of the nonlinear change battery capacity and obtain the battery pseudo-life under different stress storage conditions under a given failure threshold;
and step 9: calculating to obtain the reliability index of the whole batch of lithium batteries by taking the pseudo life of the sample obtained in the step 8 as a self-service sample of the whole batch of lithium batteries of the model;
step 9.1: and calculating the statistical parameters and estimation errors of the pseudo life sequence. Note that the pseudo life sequence X of the battery obtained in step 9 is { X ═ X1,x2,…，xnIs sample data, X is the maximum likelihood theoryi～N(μ,σ2)，μ，σ2Are all unknowns, i is 1,2, …, n, n is 12, then the mean of the samples X
Figure BDA0002995890610000051
Comprises the following steps:
Figure BDA0002995890610000052
variance S2Comprises the following steps:
Figure BDA0002995890610000053
μ，σ2is estimated value R1(X, F) and R2(X, F) are each
Figure BDA0002995890610000054
Figure BDA0002995890610000055
Wherein F represents a distribution containing all battery pseudo-life values;
x is to be1,x2,…,xnIn order from small to large, an empirical distribution function of the sample X is obtained:
Figure BDA0002995890610000056
step 9.2: sub-samples are extracted from the pseudo-life sequence and their estimation errors and statistical parameters are calculated. From FnSelf-service subsample X for secondary extraction(k)＝(x1 (k),x2 (k),…,xn (k)) And k is 1,2, … N, then corresponds to R1(X, F) and R2(X, F) self-help statistic R1 (n)(X, F) and R2 (n)(X, F) are respectively:
Figure BDA0002995890610000061
Figure BDA0002995890610000062
Figure BDA0002995890610000063
and σ(n)2Is the mean and variance of the bootstrap sample, which can be represented by R1 (n)(X, F) and R2 (n)(X, F) simulation of R1(X, F) and R2(X, F), N (N1000) samples were taken from R of each group1 (n)j(X, F) and R2 (n)j(X, F) can be solved for μ and σ2Each set of estimates of [ mu ], [ mu ]1,μ2,…,μNAnd S1 2,S2 2,…,SN 2. Then μ and σ can be obtained2The point estimation value of the sample distribution can be obtained as follows:
Figure BDA0002995890610000064
Figure BDA0002995890610000065
then a lifetime distribution can be obtained as:
Figure BDA0002995890610000066
the reliability function is:
Figure BDA0002995890610000067
the confidence lower limit of the reliability is:
Figure BDA0002995890610000068
the obtained service life distribution function, the reliability function and the lower confidence limit of the service life distribution function and the reliability function are the reliability indexes of the lithium ion batteries of the batch of the model
The further technical scheme of the invention is as follows: the product of the learning rate and the negative gradient determines the adjustment amount of the weight and the threshold, the learning rate of the standard BP neural network is always kept unchanged in the learning process, and the value range is in the interval of [0.01,0.8 ].
The further technical scheme of the invention is as follows: the maximum number of learning should be set to 1000 or more; the minimum mean square error of the BP neural network for small samples should be less than 0.01.
The further technical scheme of the invention is as follows: the accelerated storage test in step 3 comprises the following steps:
step 3.1: carrying out initial capacity test on the extracted lithium battery sample;
step 3.2: respectively carrying out constant-current and constant-voltage charging on the samples processed in the step 3.1 to a certain charge state in an 1/3C mode, wherein the specific value is selected from 0-100%, and a plurality of groups are arranged;
step 3.3: and (3) placing the samples processed in the step (3.2) in a constant temperature box for storage, wherein multiple groups of storage temperatures are set, and multiple groups of batteries with different charge states are stored at each temperature.
The further technical scheme of the invention is as follows: in step 6, the gray model is used to predict the lifetime of the non-linear system, i.e. the lithium ion battery, and the method comprises the following steps:
step 6.1: according to the formula z(1)(k)＝0.5cm(1)(k)+0.5cm(1)(k-1), k ═ 1,2, …, n production step 5 yielded Cm(1)Sequence of closely adjacent means of sequence Z(1)：
Z(1)＝{z(1)(1),z(1)(2),…,z(1)(n)}；
Step 6.2: according to the gray color differential equation in the gray theory as
Figure BDA0002995890610000071
The following relationships are established:
cm(0)(k)+az(1)(k)＝b (6)
where parameter a is the principal variable parameter or system development coefficient and b is the gray effect coefficient or background value of the gray model.
Step 6.3: calculating least squares estimation parameters of a processing method
Figure BDA0002995890610000072
Is a parameter column of the gray model, order
Figure BDA0002995890610000073
The least squares estimation parameter column for the gray model satisfies
Figure BDA0002995890610000074
Step 6.4: calculating the original X sequenceAnalog value of (2) will
Figure BDA0002995890610000075
The time response sequence of the model obtained in equation (6) is:
Figure BDA0002995890610000081
the sequence X generated by the primary accumulation can be solved by the formula (11)(1)Analog value of
Figure BDA0002995890610000082
Figure BDA0002995890610000083
Step 6.5: for those generated after accumulation in step 6.4
Figure BDA0002995890610000084
Reducing the sequence to obtain a predicted sequence:
Figure BDA0002995890610000085
the sequence of the grey prediction model is thus:
Figure BDA0002995890610000086
the further technical scheme of the invention is as follows: in the step 8, the trained BP neural network is used for predicting the pseudo life of the lithium ion battery, and the method comprises the following steps:
and 8: training step 7, establishing a neural network to realize the prediction of the nonlinear change battery capacity and obtain the battery pseudo-life under different stress storage conditions under a given failure threshold;
step 8.1: predicting a predicted value sequence of the capacity in the fourth week by using a gray model from the capacity measured value sequences in the previous weeks;
step 8.2: subtracting a residual sequence predicted by taking the neural network as a learning sample in the week from the predicted value sequence of the capacity obtained in step 1 to obtain a battery pseudo-life (pseudo-measured value) sequence predicted by the method in the next week;
the hidden layer nodes are trained from 3, the training is gradually increased to a network with better prediction results, and the learning rate, the maximum allowable error and the training times are set.
The change curve of the capacity of the sample with time under each stress storage state (temperature and charge state) is obtained through learning and prediction.
Effects of the invention
The invention has the technical effects that: according to the lithium ion battery reliability assessment method based on the metabolism grey neural network model and the self-service method, the prediction accuracy is remarkably improved compared with that of a common metabolism grey model and a BP neural network model, the combined model can fully utilize the characteristics of strong learning capability and good nonlinear mapping capability of the BP neural network model, the grey model method is simple in operation and low in sample number requirement, a battery performance degradation curve can be well fitted, a good extrapolation prediction effect is achieved, the pseudo life of a battery during storage under different stresses is finally obtained, and reliability assessment is further completed more efficiently and more cheaply. The specific effects are as follows:
1. the stress conditions selected in the accelerated gravitation storage experiment are the charge state and the temperature, and are matched with main factors influencing the service life of the lithium ion battery in the actual storage.
2.2 batteries are arranged under each storage condition in the accelerated stress storage experiment, so that the accidental property of the measurement result is avoided
3. The gray model is used for predicting the capacity sequence of the battery, the capacity sequence is well mapped with a lithium ion battery, namely a nonlinear system, and the prediction result is relatively accurate.
4. The combined structural algorithm of the metabolic gray model and the BP neural network is simple and has strong learning ability.
5. And the reliability index of the whole is calculated by adopting a self-help method, and the characteristics of the small sample are used for accurately reflecting the characteristics of the whole.
The prediction accuracy of the method is remarkably improved compared with that of a common metabolism gray model and a BP neural network model, the combined model can fully utilize the characteristics of strong learning ability and good nonlinear mapping ability of the BP neural network model, simple operation of a gray model method and low requirement on the number of samples, a battery performance degradation curve can be well fitted, a good extrapolation prediction effect is achieved, the pseudo-life of the battery during storage under different stresses is finally obtained, and then reliability evaluation is completed more efficiently and more cheaply.
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FIG. 1 is a flow chart of the present invention
FIG. 2 is a schematic diagram of a battery testing system for a charge/discharge experiment
FIG. 3 is a flow chart of the 1/3C mode charge-discharge cycle test
Fig. 4 is a comparison graph of the effect of the accumulation sequence generated under the gray model and the original sequence, and it can be seen from fig. 4 that the function image corresponding to the new accumulation sequence is smoother, the more the accumulation times are, the higher the order of the independent variable time derivative is, and the mapping relation of the nonlinear system can be better reflected, so that the better the prediction effect obtained after the BP neural network learning is.
FIG. 5 is a flow chart of a neural network algorithm
Detailed Description
In the description of the present invention, it is to be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", and the like, indicate orientations and positional relationships based on those shown in the drawings, and are used only for convenience of description and simplicity of description, and do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be considered as limiting the present invention.
Referring to fig. 1 to 5, the lithium ion battery reliability evaluation method based on the metabolic gray neural network model and the self-service method provided by the invention comprises the following steps:
step 1: randomly sampling lithium ion batteries of the same type and the same batch;
step 2: performing activation treatment on the sample obtained in the step 1;
step 2.1: an 1/3C mode charge-discharge cycle test was performed on the battery sample obtained in step 1, and the actual charge-discharge capacity of the battery was recorded.
Wherein the value of C is equal to the rated capacity of the lithium ion battery;
step 2.1.1: discharging the sample to a discharge cut-off voltage at a constant current of 1/3C (the lithium ion battery is generally 2.7v-3.0 v);
step 2.1.2: standing for 10 minutes;
step 2.1.3: the sample was charged to the charge cut-off voltage at a constant current of 1/3C (typical for lithium ion batteries is 4.2 v);
step 2.1.4: charging the sample at a constant voltage of 4.2v until the current drops to 0.02C;
step 2.1.5: standing for 10 minutes;
step 2.1.6: discharging the sample to a discharge cutoff voltage at a constant current 1/3C;
step 2.2: repeating the step 2.1 until the error of the battery capacity is within 5 percent after three times of continuous tests;
and step 3: performing an accelerated storage experiment on the sample processed through the step 2;
step 3.1: carrying out initial capacity test on the extracted lithium battery sample;
step 3.2: respectively carrying out constant-current and constant-voltage charging on the samples processed in the step 3.1 to a certain charge state in an 1/3C mode, wherein the specific value is selected from 0-100%, and a plurality of groups are arranged;
step 3.3: placing the sample processed in the step 3.2 in a constant temperature box for storage, wherein multiple groups of batteries with different charge states are stored at each temperature (the number of the groups is determined by the charge state number in the step 2.2), and each group comprises 2 batteries so as to reduce the errors of the battery capacity and the internal resistance measurement value in a certain charge state;
and 4, step 4: testing the capacity and the internal resistance of the battery stored at each temperature in the step 2.3 once every week, and not testing and maintaining the battery in the storage period, so as to finally obtain the change curves of the capacity and the internal resistance of the battery along with time under different stress conditions (storage temperature and charge state) and the storage conditions which are beneficial to relieving the service life attenuation of the battery;
step 4.1: discharging the sample to a discharge cut-off voltage at a constant current of 1/3C (the lithium ion battery is generally 2.7v-3.0 v);
step 4.2: standing for 10 minutes;
step 4.3: the sample was charged to the charge cut-off voltage at a constant current of 1/3C (typical for lithium ion batteries is 4.2 v);
step 4.4: charging the sample at a constant voltage of 4.2v until the current drops to 0.02C;
step 4.5: standing for 10 minutes;
step 4.6: discharging the sample to a discharge cutoff voltage at a constant current 1/3C;
and 5: and accumulating the data which is obtained in the step 4 and can be updated continuously according to the node increase along with the time to generate a metabolic sequence.
Step 5.1: note C as a capacity value of a certain battery sample in the sample, C is a capacity value measured in a single test action, and a real-time capacity value sequence C of the certain battery sample capacity value C at each time node is { C (1), C (2), C (3), …, C (n) }:
taking C ═ { C (1), C (2), C (3), …, C (n) } as an original sequence, and replacing the data on the early time node n ═ 1 with the capacity information value on the new time node n +1, so as to obtain a metabolism data sequence: y ═ c (2), …, c (n), c (n +1) }, the number of times that substitutions are made depends on the number of capacity values available at the new time node.
Step 5.2: if the capacity value sequence of the metabolism of the kth battery on the n time nodes in the sample updated in the step 5.1 is recorded as:
C(0)(k)＝{c(0)(1),c(0)(2),…,c(0)(n)}k (1)
to C(0)(k) Accumulating by the accumulation formula as in (2):
Figure BDA0002995890610000121
and (3) generating a sequence:
C(1)(k)＝{c(1)(1),c(1)(2),…,c(1)(n)}k (3)
step 5.3: the original sequence is operated m times in step 5.2, and the generated sequence is:
Figure BDA0002995890610000122
step 6: and (4) predicting the data obtained in the step (5) by using a metabolism gray model to obtain a predicted value of the measured value in the step (4).
Step 6.1: according to the formula z(1)(k)＝0.5cm(1)(k)+0.5cm(1)(k-1), k 1,2, …, n yielding Cm(1)Of the sequence of closely adjacent means Z(1)：
Z(1)＝{z(1)(1),z(1)(2),…,z(1)(n)} (5)
Step 6.2: according to the gray color differential equation in the gray theory as
Figure BDA0002995890610000131
The following relationships are established:
cm(0)(k)+az(1)(k)＝b (6)
where parameter a is the principal variable parameter or system development coefficient and b is the gray effect coefficient or background value of the gray model.
Step 6.3: calculating least squares estimation parameters of a processing method
Figure BDA0002995890610000132
Is a list of parameters for the gray model,order to
Figure BDA0002995890610000133
Substituting B and Y into S formula (6) to obtain error sequence epsilon represented by
Figure BDA0002995890610000134
Solving the sum of squares of the error sequences epsilon to obtain:
Figure BDA0002995890610000135
the least squares estimation parameter column for the gray model satisfies
Figure BDA0002995890610000136
Step 6.3: calculating the analog value of the original C sequence
Figure BDA0002995890610000137
The time response sequence of the model obtained in equation (6) is:
Figure BDA0002995890610000138
the sequence C generated by the primary accumulation can be solved by the formula (11)(1)Analog value of
Figure BDA0002995890610000139
Figure BDA00029958906100001310
Step 6.4: for those generated after accumulation in step 6.3
Figure BDA00029958906100001311
Reducing the sequence to obtain a predicted sequence:
Figure BDA0002995890610000141
the sequence of the grey prediction model is therefore:
Figure BDA0002995890610000142
the program describing step 6, written using the commercial software MATLAB, is as follows:
Figure BDA0002995890610000143
Figure BDA0002995890610000151
Figure BDA0002995890610000161
and 7: establishing a BP neural network for the capacity and the residual sequence obtained by processing in the step 6 and training to obtain a predicted value of the capacity and an error sequence of the predicted value and the ideal value;
step 7.1: the capacity fading sequence C ═ C over time obtained by processing samples stored under a certain stress state (temperature and state of charge) via step 61,c2,…cnAnd the ith quantity X in the X sequence obtained by carrying out normalization processing on the residue value sequence obtained by subtracting the predicted value sequence obtained in the step 6 and the real value measured in the step 4, and the residue value sequenceiComprises the following steps:
Figure BDA0002995890610000162
wherein, Cmin、CmaxThe minimum value and the maximum value in the original sequence are respectively, wherein a is 0.8, and b is (1-a)/2.
Step 7.2: after normalization, performing inverse normalization operation to make the output data and the original data fall in the same region, according to step 7.1:
Figure BDA0002995890610000163
obtaining a normalized sequence X1＝{x1,x2,…,xnAfter the previous step, let Xk＝{xk,xk+1,…,xk+(n-1)Let T be the kth input samplek＝{xk+(n-1)+1Is the kth output sample.
Step 7.3: assigning values to the capacity sequence and the residual sequence which are input and output by the sequence processed by the steps 7.1 and 7.2;
step 7.4: establishing a neural network about a capacity sequence and a residual sequence;
step 7.5: setting the learning rate to 0.05;
step 7.6: setting the maximum learning times to 2000 times;
step 7.7: setting the minimum mean square error of training to be 0.001;
step 7.8: training the neural network to form a predicted value and an ideal value of the capacity sequence to obtain an ideal error and an expected error;
step 7.9: randomly selecting the next learning sample vector to provide for the network, and returning to the step 6.3 until all the training samples are trained;
step 7.10: randomly selecting a group of input samples and output samples from the learning samples again, returning to the step 7.1 until the network global error E is smaller than a preset minimum value, namely the network is converged, and finishing the learning;
taking the input capacity series of [ 2557.052538.852498.252491.252474.72464.92444.852480.12473.92409.72400.62373.22397 ] and the residual value series of [ -9.61-9.74628.665.16-24.5720.2410.1118.44-24.29 ], the program written using the commercial software MATLAB is as follows:
Figure BDA0002995890610000171
Figure BDA0002995890610000181
Figure BDA0002995890610000191
where p0 sequence is the input sequence for the capacity and t0 is the residual sequence. The BP neural network established by calling newff function in the program is composed of an input layer responsible for receiving external input information, a hidden layer responsible for processing information and an output layer outputting processing results to the outside, and the number of nodes of the hidden layer is determined by the following formula:
Figure BDA0002995890610000192
wherein m is the number of nodes in the hidden layer, ninIs the number of input layer nodes, noutThe number of output layer nodes.
Sigmoid excitation function for the input capacity and residual sequence:
Figure BDA0002995890610000193
the hidden layer output calculation is according to the following formula:
Figure BDA0002995890610000194
wherein, ω isijRepresenting connections between input layer neurons and hidden layer neuronsReceiving the weight value of aj(j＝1,2,…,nout) Representing the threshold of each neuron in the hidden layer.
Output layer output calculation is according to the following equation:
Figure BDA0002995890610000195
wherein, ω isjkRepresenting the connection weights between hidden layer neurons and output layer neurons, bk(k is 1,2, …, m) represents the neuron threshold of the output layer, i is 1,2, …, nin，j＝1,2,…,nout，k＝1,2,…,m。
The neural network calculates the error, if the output vector is represented by Y, according to the following equation:
Figure BDA0002995890610000196
wherein, YkIs the desired output value. Remember Yk-Ok＝ekThen, again can be written as:
Figure BDA0002995890610000197
and (3) updating the weights from the hidden layer to the output layer and from the input layer to the hidden layer by using a gradient descent method through the BP neural network established by the Newff function, so that the error function obtained in the step (22) reaches the minimum value in error back propagation. The results obtained according to formulae (19), (20) and (21) are shown in
Figure BDA0002995890610000201
Updating the weights from the hidden layer to the input layer to obtain a formula for updating the weights from the hidden layer to the input layer:
ωjk＝ωjk+ηHjek (23)
where η represents the learning rate.
According to the formula
Figure BDA0002995890610000202
Updating the weight from the input layer to the hidden layer to obtain a weight updating formula from the input layer to the hidden layer:
Figure BDA0002995890610000203
wherein the content of the first and second substances,
Figure BDA0002995890610000204
Figure BDA0002995890610000205
BP neural network basis
Figure BDA0002995890610000206
Updating the threshold value from the hidden layer to the output layer to obtain an updating formula of the threshold value from the hidden layer to the output layer:
bk＝bk+ηek (27)
according to the formula
Figure BDA0002995890610000207
Updating the threshold value from the input layer to the hidden layer to obtain an updating formula of the threshold value from the input layer to the hidden layer:
Figure BDA0002995890610000208
wherein the content of the first and second substances,
Figure BDA0002995890610000211
Figure BDA0002995890610000212
Figure BDA0002995890610000213
the activation function of a hidden layer of a network transfer function selected by the BP neural network is a logsig function, the output data is mapped to a (0,1) interval, and the calculation formula is as follows:
Figure BDA0002995890610000214
the activation function of the output layer is a purelin function, the input and output values can take any value, and the calculation formula is as follows:
f(x)＝x (32)
and 8: training step 7, establishing a neural network to realize the prediction of the nonlinear change battery capacity and obtain the battery pseudo-life under different stress storage conditions under a given failure threshold;
the method comprises the steps of taking the battery capacity predicted by a metabolism model for a plurality of continuous weeks as an input value of a neural network, taking a predicted residual error value of the next week as an output value of the neural network model, training the network by removing the last two groups of data, training and predicting by using the remaining two groups of data after training is finished, training hidden layer nodes from 3, gradually increasing the hidden layer nodes to be good in network prediction results, and setting learning rate, maximum allowable error and training times.
The change curve of the capacity of the sample with time under each stress storage state (temperature and charge state) is obtained through learning and prediction.
Taking as an example the prediction of the sequence of pseudo-measurements (pseudo-lifetimes) for the fourth week using the sequence of capacity measurements for the first week, the second week and the third week:
step 8.1: predicting a sequence of predicted values of the capacity at the fourth week by using a gray model with the sequence of capacity measurements at the first week, the second week and the third week;
step 8.2: subtracting residual error sequences predicted by taking the neural network as a learning sample in the first week, the second week and the third week from the predicted value sequence of the capacity obtained in the step 1 to obtain a battery pseudo-life (pseudo-measured value) sequence predicted by the method;
and step 9: the pseudo life of the sample obtained in the step 8 is used as a self-service sample of the whole batch of lithium batteries of the model, and the statistical parameters of the sample are calculated so as to simulate the reliability index of the whole batch of lithium batteries;
after the false failure life of the battery under normal stress in the step 8, the distribution hypothesis test is carried out on the battery, and the failure life distribution of the high-reliability long-life product is obtained by testing the statistical parameters of the battery and obeys Weibull distribution. The reliability of the lithium ion battery is high, the lithium ion battery is difficult to lose efficacy in a short time, the obtained sample life test data is less, and the self-service sample information is obtained through sampling to analyze the reliability of the battery.
Step 9.1: and calculating the statistical parameters and estimation errors of the pseudo life sequence. Note that the pseudo life sequence X of the battery obtained in step 9 is { X ═ X1,x2,…，xnIs sample data, X is the maximum likelihood theoryi～N(μ,σ2)，μ，σ2Are all unknowns, i is 1,2, …, n, n is 12, then the mean of the samples X
Figure BDA0002995890610000221
Comprises the following steps:
Figure BDA0002995890610000222
variance S2Comprises the following steps:
Figure BDA0002995890610000223
μ，σ2is estimated value R1(X, F) and R2(X, F) are each
Figure BDA0002995890610000224
Figure BDA0002995890610000225
Where F represents a distribution that contains all of the battery pseudo-life values.
X is to be1,x2,…,xnIn order from small to large, an empirical distribution function of the sample X is obtained:
Figure BDA0002995890610000231
step 9.2: sub-samples are extracted from the pseudo-life sequence and their estimation errors and statistical parameters are calculated. From FnSelf-service subsample X for secondary extraction(k)＝(x1 (k),x2 (k),…,xn (k)) And k is 1,2, … N, then corresponds to R1(X, F) and R2(X, F) self-help statistic R1 (n)(X, F) and R2 (n)(X, F) are respectively:
Figure BDA0002995890610000232
Figure BDA0002995890610000233
Figure BDA0002995890610000234
and σ(n)2Is the mean and variance of the bootstrap sample, which can be represented by R1 (n)(X, F) and R2 (n)(X, F) simulation of R1(X, F) and R2(X, F), N (N1000) samples were taken from R of each group1 (n)j(X, F) and R2 (n)j(X, F) can be solved for μ and σ2Each set of estimates of [ mu ], [ mu ]1,μ2,…,μNAnd S1 2,S2 2,…,SN 2. Then μ and σ can be obtained2The point estimation value of the sample distribution can be obtained as follows:
Figure BDA0002995890610000235
Figure BDA0002995890610000236
then a lifetime distribution can be obtained as:
Figure BDA0002995890610000237
the reliability function is:
Figure BDA0002995890610000238
the confidence lower limit of the reliability is:
Figure BDA0002995890610000239
and (3) the reliability function and the corresponding lower confidence limit of the service life distribution function calculated by the formula (42), the formula (43) and the formula (44) are reliability indexes of the lithium ion battery of the batch of the model.

Claims (6)

1. The lithium ion battery reliability assessment method based on the metabolism grey neural network model and the self-service method is characterized by comprising the following steps of:
step 1: randomly sampling lithium ion batteries of the same type and the same batch;
step 2: activating the sample obtained in the step 1;
and step 3: performing an accelerated storage experiment on the samples subjected to the activation treatment in the step 2, and grouping the samples at the same time, wherein the number of batteries in each group is more than or equal to 2;
and 4, step 4: carrying out capacity measurement and internal resistance measurement on the battery stored at each temperature every other period T, and not testing and maintaining the battery in the period to obtain data which is continuously updated along with time, and simultaneously obtaining the change curves of the battery capacity and the internal resistance along with the time under different stress conditions;
and 5: accumulating the data obtained in step 4 to generate a metabolic sequence, comprising the following substeps:
step 5.1: the capacity value sequence defining the metabolism of the kth cell at n time nodes is:
C(0)(k)＝{c(0)(1),c(0)(2),…,c(0)(n)}k
to C(0)(k) The data are accumulated to obtain a metabolic sequence:
C(1)(k)＝{c(1)(1),c(1)(2),…,c(1)(n)}k
step 5.2: to the sequence
Figure FDA0002995890600000011
The operation is performed m times, and the generated sequence is as follows:
Figure FDA0002995890600000012
step 6: predicting the sequence obtained in the step 5 by using a metabolism gray model to obtain a predicted value of the measured value in the step 4, and comprising the following substeps:
step 6.1: according to the formula z(1)(k)＝0.5cm(1)(k)+0.5cm(1)(k-1), k 1,2, …, n yielding Cm(1)Of the sequence of closely adjacent means Z(1)：
Z(1)＝{z(1)(1),z(1)(2),…,z(1)(n)}；
Step 6.2: according to the gray color differential equation in the gray theory as
Figure FDA0002995890600000021
The following relationships are established:
cm(0)(k)+az(1)(k)＝b
where parameter a is the principal variable parameter or system development coefficient and b is the gray effect coefficient or background value of the gray model.
Step 6.3: calculating least squares estimation parameters of a processing method
Figure FDA0002995890600000022
Is a parameter column of the gray model, order
Figure FDA0002995890600000023
The least squares estimation parameter column for the gray model satisfies
Figure FDA0002995890600000024
Step 6.4: calculating the analog value of the original X sequence
Figure FDA0002995890600000025
The time response sequence of the model obtained in equation (6) is:
Figure FDA0002995890600000026
the sequence X generated by the primary accumulation can be solved by the formula (11)(1)Analog value of
Figure FDA0002995890600000027
Figure FDA0002995890600000028
Step 6.5: for those generated after accumulation in step 6.4
Figure FDA0002995890600000029
Reducing the sequence to obtain a predicted sequence:
Figure FDA00029958906000000210
the sequence of the grey prediction model is thus:
Figure FDA00029958906000000211
step 6.6: subtracting the measured value in the step 4 according to the grey model prediction sequence of the capacity obtained in the step 6.4 to obtain a residual sequence;
and 7: establishing a BP neural network for the capacity and the residual sequence obtained by processing in the step 6 and training to obtain a predicted value of the capacity and an error sequence of the predicted value and the ideal value;
step 7.1: the capacity fading sequence C ═ C over time obtained in step 61,c2,…cnNormalizing the ith quantity X in the X sequence obtained in the step 66 and the residual value sequence obtained in the stepiComprises the following steps:
Figure FDA0002995890600000031
wherein, Cmin、CmaxThe minimum value and the maximum value in the original sequence are respectively, wherein a is 0.8, and b is (1-a)/2.
Step 7.2: after normalization, performing inverse normalization operation to make the output data and the original data fall in the same region, according to step 7.1:
Figure FDA0002995890600000032
obtaining a normalized sequence X1＝{x1,x2,…,xnAfter the previous step, let Xk＝{xk,xk+1,…,xk+(n-1)Let T be the kth input samplek＝{xk+(n-1)+1Is the kth output sample.
Step 7.3: assigning values to the capacity sequence and the residual sequence which are input and output by the sequence processed by the steps 7.1 and 7.2;
step 7.4: establishing a neural network related to a capacity sequence and a residual sequence, and setting a learning rate, a maximum learning frequency and a minimum mean square error of training;
step 7.5: training the neural network established in the step 7.4 by taking the capacity sequence measured value in the step 4 and the capacity sequence predicted value and residual sequence predicted value obtained in the step 6 until all training samples are trained;
step 7.6: randomly selecting a group of input samples and output samples from the learning samples again, returning to the step 7.1 until the network global error E is smaller than a preset minimum value, namely the network is converged, and finishing the learning;
and 8: training step 7, establishing a neural network to realize the prediction of the nonlinear change battery capacity and obtain the battery pseudo-life under different stress storage conditions under a given failure threshold;
and step 9: calculating to obtain the reliability index of the whole batch of lithium batteries by taking the pseudo life of the sample obtained in the step 8 as a self-service sample of the whole batch of lithium batteries of the model;
step 9.1: and calculating the statistical parameters and estimation errors of the pseudo life sequence. Note that the pseudo life sequence X of the battery obtained in step 9 is { X ═ X1,x2,…，xnIs sample data, X is the maximum likelihood theoryi～N(μ,σ2)，μ，σ2Are all unknowns, i is 1,2, …, n, n is 12, then the mean of the samples X
Figure FDA0002995890600000041
Comprises the following steps:
Figure FDA0002995890600000042
variance S2Comprises the following steps:
Figure FDA0002995890600000043
μ，σ2is estimated value R1(X, F) and R2(X, F) are each
Figure FDA0002995890600000044
Figure FDA0002995890600000045
Wherein F represents a distribution containing all battery pseudo-life values;
x is to be1,x2,…,xnIn order from small to large, an empirical distribution function of the sample X is obtained:
Figure FDA0002995890600000046
step 9.2: sub-samples are extracted from the pseudo-life sequence and their estimation errors and statistical parameters are calculated. From FnSelf-service subsample X for secondary extraction(k)＝(x1 (k),x2 (k),…,xn (k)) And k is 1,2, … N, then corresponds to R1(X, F) and R2(X, F) self-help statistic R1 (n)(X, F) and R2 (n)(X, F) are respectively:
Figure FDA0002995890600000047
Figure FDA0002995890600000048
Figure FDA0002995890600000049
and σ(n)2Is the mean and variance of the bootstrap sample, which can be represented by R1 (n)(X, F) and R2 (n)(X, F) simulation of R1(X, F) and R2(X, F), N (N1000) samples were taken from R of each group1 (n)j(X, F) and R2 (n)j(X, F) can be solved for μ and σ2Each set of estimates of [ mu ], [ mu ]1,μ2,…,μNAnd S1 2,S2 2,…,SN 2. Then μ and σ can be obtained2The point estimation value of the sample distribution can be obtained as follows:
Figure FDA00029958906000000410
Figure FDA0002995890600000051
then a lifetime distribution can be obtained as:
Figure FDA0002995890600000052
the reliability function is:
Figure FDA0002995890600000053
the confidence lower limit of the reliability is:
Figure FDA0002995890600000054
and the obtained service life distribution function, the reliability function and the lower confidence limit of the service life distribution function and the reliability function are reliability indexes of the lithium ion batteries of the batch of the model.
2. The lithium ion battery reliability assessment method based on the metabolism gray neural network model and the self-service method as claimed in claim 1, wherein the product of the learning rate and the negative gradient determines the adjustment amount of the weight and the threshold, the learning rate of the standard BP neural network is always kept unchanged in the learning process, and the value range is within the interval of [0.01,0.8 ].
3. The lithium ion battery reliability evaluation method based on the metabolism gray neural network model and the self-service method according to claim 1, wherein the maximum learning number should be set to more than 1000; the minimum mean square error of the BP neural network for small samples should be less than 0.01.
4. The lithium ion battery reliability assessment method based on the metabolism gray neural network model and the self-service method according to claim 1, wherein the accelerated storage experiment in the step 3 comprises the following steps:
step 3.1: carrying out initial capacity test on the extracted lithium battery sample;
step 3.2: respectively carrying out constant-current and constant-voltage charging on the samples processed in the step 3.1 to a certain charge state in an 1/3C mode, wherein the specific value is selected from 0-100%, and a plurality of groups are arranged;
step 3.3: and (3) placing the samples processed in the step (3.2) in a constant temperature box for storage, wherein multiple groups of storage temperatures are set, and multiple groups of batteries with different charge states are stored at each temperature.
5. The lithium ion battery reliability assessment method based on the metabolism gray neural network model and the self-help method as claimed in claim 1, wherein the step 6 of predicting the life of the non-linear system of the lithium ion battery by using the gray model comprises the following steps:
step 6.1: according to the formula z(1)(k)＝0.5cm(1)(k)+0.5cm(1)(k-1), k ═ 1,2, …, n production step 5 yielded Cm (1)Sequence of closely adjacent means of sequence Z(1)：
Z(1)＝{z(1)(1),z(1)(2),…,z(1)(n)}；
Step 6.2: according to the gray color differential equation in the gray theory as
Figure FDA0002995890600000061
The following relationships are established:
cm(0)(k)+az(1)(k)＝b (6)
where parameter a is the principal variable parameter or system development coefficient and b is the gray effect coefficient or background value of the gray model.
Step 6.3: calculating least squares estimation parameters of a processing method
Figure FDA0002995890600000062
Is a parameter column of the gray model, order
Figure FDA0002995890600000063
The least squares estimation parameter column for the gray model satisfies
Figure FDA0002995890600000064
Step 6.4: calculating the analog value of the original X sequence
Figure FDA0002995890600000065
The time response sequence of the model obtained in equation (6) is:
Figure FDA0002995890600000066
the sequence X generated by the primary accumulation can be solved by the formula (11)(1)Analog value of
Figure FDA0002995890600000067
Figure FDA0002995890600000068
Step 6.5: for those generated after accumulation in step 6.4
Figure FDA0002995890600000069
Reducing the sequence to obtain a predicted sequence:
Figure FDA0002995890600000071
the sequence of the grey prediction model is thus:
Figure FDA0002995890600000072
。
6. the lithium ion battery reliability assessment method based on the metabolism gray neural network model and the self-service method as claimed in claim 1, wherein the step 8 of predicting the pseudo-life of the lithium ion battery by using the trained BP neural network comprises the following steps:
and 8: training step 7, establishing a neural network to realize the prediction of the nonlinear change battery capacity and obtain the battery pseudo-life under different stress storage conditions under a given failure threshold;
step 8.1: predicting a predicted value sequence of the capacity in the fourth week by using a gray model from the capacity measured value sequences in the previous weeks;
step 8.2: subtracting a residual sequence predicted by taking the neural network as a learning sample in the week from the predicted value sequence of the capacity obtained in step 1 to obtain a battery pseudo-life (pseudo-measured value) sequence predicted by the method in the next week;
the hidden layer nodes are trained from 3, the training is gradually increased to a network with better prediction results, and the learning rate, the maximum allowable error and the training times are set.
The change curve of the capacity of the sample with time under each stress storage state (temperature and charge state) is obtained through learning and prediction.
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