Adaptive prediction method for remaining life of lithium battery based on error correction

Abstract

This invention discloses an adaptive prediction method for the remaining life (RUL) of lithium batteries based on error correction. It obtains the characteristic quantities of historical lithium batteries at different times by accelerating the life test of historical lithium batteries. Then, it uses maximum likelihood estimation and particle filtering algorithms to obtain the error data of historical lithium batteries and trains the corresponding LSTM neural network using this error data. Next, based on the Euclidean distance between the characteristic quantities of the target lithium battery and historical lithium batteries, it selects the corresponding LSTM neural network as the error correction function for the target lithium battery and uses this error correction function to improve the fitting ability of the Wiener process model to the degradation trend of the target lithium battery. Finally, it calculates the probability density function of the RUL of the target lithium battery at the current time using an inverse Gaussian distribution. This method features high prediction accuracy, good real-time performance, and fast prediction speed.

Description

Technical Field

[0001] This invention belongs to the field of reliability analysis technology, and more specifically, relates to an adaptive prediction method for the remaining life of lithium batteries based on error correction. Background Technology

[0002] Due to the high energy density and long service life of lithium batteries, they have been widely used in power modules of various electronic systems. In recent years, with the increasing integration of electronic systems, the frequency of power module failures in these systems has also increased. For the power supplies of various functional modules in complex electronic systems, their reliability affects the operational stability of the entire system. Therefore, research on the remaining usable life (RUL) prediction technology of each power module has become essential. It has the following important significances: (1) It is an important way to obtain reliability information of complex electronic systems, which can further provide a basis for realizing online monitoring and health management of the system; (2) It is conducive to better designing accelerated aging tests of lithium batteries to obtain more accurate aging data; (3) It enables condition-based maintenance, allowing end users to obtain more life information of complex electronic systems to reduce investment in system maintenance.

[0003] In recent years, data-driven RUL prediction methods have gradually become a research hotspot in the field of lithium battery reliability analysis. Existing data-driven methods are mainly divided into two categories: artificial intelligence-based methods and probabilistic statistical methods. While artificial intelligence-based prediction techniques have good prediction accuracy, these methods require a large amount of historical lithium battery degradation data to train the AI ​​model, and the resulting RUL predictions often lack relevant uncertainty descriptions, making it difficult to provide sufficient information for subsequent device reliability analysis. Probabilistic statistical methods, on the other hand, use probabilistic statistical models to describe the degradation trend of lithium batteries, effectively characterizing the uncertainties in the degradation process. Among probabilistic statistical methods, Wiener process-based probabilistic statistical models are widely used for RUL prediction of various types of lithium batteries. However, when dealing with lithium batteries with complex degradation trends, the prediction accuracy of the Wiener process model is greatly affected by the choice of its degradation trend function type. This significantly limits the application scope of the Wiener process model in RUL prediction. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide an adaptive prediction method for the remaining life of lithium batteries based on error correction. The method uses a long short-term memory neural network (LSTM) as an error function to correct the Wiener process, thereby enhancing the Wiener process's ability to fit the degradation trend of lithium batteries and improving the accuracy of remaining life prediction.

[0005] To achieve the above-mentioned objectives, the present invention provides an adaptive prediction method for the remaining life of lithium batteries based on error correction, characterized by comprising the following steps:

[0006] (1) Data preprocessing;

[0007] By accelerating the lifespan experiments of N historical lithium batteries, the capacity of each historical lithium battery was sampled at different times. Then, the Savitzky-Golay filter was used to smooth these N sets of capacity data to obtain N sets of smoothed data. Where i = 1, 2, ..., N, Let represent the initial capacity of the i-th historical lithium battery. This represents the smoothed value of the capacity of the i-th historical lithium battery at time t, where t = 1, 2, ..., m. i m i This represents the sampling time number of the i-th historical lithium battery;

[0008] (2) Construct Wiener process models of historical lithium batteries at each sampling time;

[0009] X(t) = x0 + at b +σ B B(t)

[0010] Where x0 represents the initial capacity of the historical lithium battery; a represents the drift coefficient of the Wiener process; t b The function representing the historical degradation trend of lithium battery capacity, where b is a parameter of the degradation trend function; σ B is the diffusion coefficient of the Wiener process; B(t) represents the standard Brownian motion.

[0011] (3) Construct the error function of each historical lithium battery Wiener process model;

[0012] (3.1) Construct the likelihood function for each historical lithium battery:

[0013]

[0014] in, Represents the parameters of the i-th historical lithium-ion battery Wiener process model; This represents the first-order difference of the capacity of the i-th historical lithium battery. Let represent the first-order difference of the i-th historical lithium battery trend function at different sampling times; Represents ΔX i The covariance matrix, For m i -1 order identity matrix;

[0015] (3.2) Solve for the parameters of each likelihood function;

[0016] Let the above likelihood function with respect to a i and The first-order partial derivative is 0, so we get:

[0017]

[0018]

[0019] Then, the above a i and Substituting the expression into the Wiener process model, and using the particle filter algorithm, the parameter estimates of N historical lithium batteries are obtained, namely [a1, a2, ... a N ],[b1,b2,...b N ]and

[0020] (3.3) Solving for the error function

[0021] Based on the parameters obtained in (3.2) and the Wiener process model in (2), N sets of simulation capacity data are generated.

[0022] Then use actual data Subtract simulation data Obtain error data in,

[0023] Then, using these N sets of error data, N long short-term memory neural networks (LSTM) are trained respectively. These N LSTM neural networks represent the error functions of N historical lithium battery Wiener process models.

[0024] (4) Real-time prediction of the remaining lifespan of the target lithium battery.

[0025] (4.1) Obtain the current capacity of the target lithium battery;

[0026] Using the method in step (1), obtain the current time t. c Next target lithium battery capacity data judge If the failure threshold w has been exceeded, proceed to step (5) and the algorithm ends; if not, proceed to step (4.2).

[0027] (4.2) Estimate the Wiener process model parameters of the target lithium battery;

[0028] Calculate the target lithium battery capacity data X and the historical lithium battery capacity data X. i Euclidean distance between them ED i :

[0029]

[0030] Let E be the error data corresponding to the historical lithium battery with the smallest Euclidean distance. min The corresponding error function is f(t) = LSTM min ;

[0031] Based on the Wiener process model, a particle filter algorithm is used to estimate the model parameters of the target lithium battery, making the error data of the target lithium battery approximate E. min Let the estimated parameters be .

[0032] (4.3) Construct a Wiener process model based on error function correction for the target lithium battery;

[0033]

[0034] Where x0 represents the initial capacity of the target lithium battery; a min t represents the drift coefficient of the target lithium battery; b b represents the degradation trend function of the target lithium battery capacity. min The parameters of the degradation trend function are f(t) = LSTM. min σ represents the error function of the target lithium battery. B，min is the diffusion coefficient of the Wiener process; B(t) represents the standard Brownian motion.

[0035] (4.4) Calculate the target lithium battery at the current time t c The remaining lifespan;

[0036] Based on the Wiener process model with error function correction, the remaining lifetime probability density function F(l) of the target lithium battery is calculated:

[0037]

[0038] Where l represents the time variable, q(l)=f(l+t c )-f(t c f′(t) represents the first derivative of the error function f(t) at time t;

[0039] (4.5) Select the time corresponding to the maximum value in F(l) as the current time t. c The remaining life prediction value of the lithium battery under test is given, and then t is set. c =t c +1, jump back to step (4.1);

[0040] (5) When the degradation of the target lithium battery capacity reaches the failure threshold w, the prediction terminates and the algorithm ends.

[0041] The objective of this invention is achieved as follows:

[0042] This invention discloses an adaptive prediction method for the remaining life (RUL) of lithium batteries based on error correction. It obtains the characteristic quantities of historical lithium batteries at different times by accelerating life tests of historical lithium batteries. Then, it uses maximum likelihood estimation and particle filtering algorithms to obtain the error data of historical lithium batteries and trains a corresponding LSTM neural network using this error data. Next, based on the Euclidean distance between the characteristic quantities of the target lithium battery and historical lithium batteries, it selects the corresponding LSTM neural network as the error correction function for the target lithium battery and uses this error correction function to improve the fitting ability of the Wiener process model to the degradation trend of the target lithium battery. Finally, it calculates the probability density function of the RUL of the target lithium battery at the current time using an inverse Gaussian distribution. This method features high prediction accuracy, good real-time performance, and fast prediction speed. Attached Figure Description

[0043] Figure 1 This is a flowchart of an adaptive prediction method for the remaining life of lithium batteries based on error correction according to the present invention.

[0044] Figure 2 These are data on the degradation of lithium battery capacity obtained from accelerated life testing.

[0045] Figure 3 This is a comparison chart of the simulated degradation trend and the actual capacity degradation trajectory of lithium batteries obtained based on the traditional Wiener process model;

[0046] Figure 4 This is a comparison chart of the simulated degradation trend and the actual capacity degradation trajectory of lithium batteries obtained from the Wiener process based on error function correction.

[0047] Figure 5 This is a graph showing the remaining life prediction results of an adaptive prediction method for lithium battery remaining life based on error correction proposed in this invention:

[0048] Figure 6 The results of three prediction models for the remaining life of lithium batteries are as follows: (1) a remaining life prediction model based on LSTM neural network; (2) a remaining life prediction model based on traditional Wiener process; and (3) an adaptive prediction method model for the remaining life of lithium batteries based on error correction. Detailed Implementation

[0049] The specific embodiments of the present invention will now be described with reference to the accompanying drawings to enable those skilled in the art to better understand the invention. It should be particularly noted that in the following description, detailed descriptions of known functions and designs that might obscure the main content of the invention will be omitted here.

[0050] Example

[0051] Figure 1 This is a flowchart of an adaptive prediction method for the remaining life of lithium batteries based on error correction, according to the present invention.

[0052] In this embodiment, a lithium battery is selected as the test device, such as... Figure 1 As shown, the present invention provides an adaptive prediction method for the remaining life of lithium batteries based on error correction, comprising the following steps:

[0053] (1) Data preprocessing;

[0054] Obtain the degradation amount of the lithium battery under test at different times;

[0055] By accelerating the lifespan experiment of N lithium-ion batteries under test, the characteristic values ​​of each battery were sampled at different times. Then, the Savitzky-Golay filter was used to smooth these N sets of characteristic values, resulting in N sets of smoothed data. Let the i-th set of smoothed data be denoted as . Where i = 1, 2, ..., N, Let represent the initial characteristic quantity of the i-th lithium battery to be tested. This represents the smoothed value of the characteristic quantity of the i-th lithium battery under test at time t, where t = 1, 2, ..., m i m i This represents the sampling time number of the i-th lithium battery under test;

[0056] (2) Construct Wiener process model of the lithium battery under test at each sampling time;

[0057] X(t) = x0 + at b +σ B B(t)

[0058] Where x0 represents the initial characteristic quantity of the lithium battery under test; a represents the drift coefficient of the Wiener process; t b The degradation trend function represents the characteristic quantity of the lithium battery under test, where b is the parameter of the degradation trend function; σ B is the diffusion coefficient of the Wiener process; B(t) represents the standard Brownian motion.

[0059] (3) Calculate the error function of the Wiener process model for each lithium battery under test;

[0060] (3.1) Construct the likelihood function for each lithium battery under test:

[0061]

[0062] in, Represents the parameters of the Wiener process model for the i-th lithium-ion battery under test; Let represent the first-order difference of the i-th lithium battery feature quantity to be tested; Let represent the first-order difference of the trend function of the i-th lithium battery under test at different sampling times; Represents ΔX i The covariance matrix, For m i -1 order identity matrix;

[0063] (3.2) Solve for the parameters of the likelihood function;

[0064] Let the above likelihood function with respect to a i and The first-order partial derivative is 0, so we get:

[0065]

[0066]

[0067] Then, the above a i and Substituting the expression into the Wiener process model, and using the particle filter algorithm, the parameter estimates of N historical lithium batteries under test are obtained, namely [a1, a2, ..., a...]. N ],[b1,b2,...,b N ]and

[0068] (3.3) Solving for the error function

[0069] Based on the parameters obtained in (3.2) and the Wiener process model in (2), N sets of simulation feature data are generated.

[0070] Then use actual data Subtract simulation data Obtain error data in,

[0071] Then, using these N sets of error data, N Long Short-Term Memory (LSTM) neural networks are trained respectively. These N LSTM neural networks represent the error functions of the N historical Wiener process models.

[0072] (4) Real-time prediction of the remaining lifespan of the target lithium battery.

[0073] (4.1) Obtain the feature data of the target device at the current time.

[0074] Obtain the feature values ​​of the target lithium battery at the current moment;

[0075] Using the method in step (1), obtain the current time t. cCharacteristic quantities of the target lithium battery judge If the failure threshold w has been exceeded, proceed to step (5) and the algorithm ends; if not, proceed to step (4.2).

[0076] (4.2) Estimate the Wiener process model parameters of the target lithium battery;

[0077] Calculate the target lithium battery characteristic X and the characteristic X of each historical lithium battery under test. i Euclidean distance between them ED i :

[0078]

[0079] Let E be the error data corresponding to the historical lithium battery under test with the smallest Euclidean distance. min The corresponding error function is f(t) = LSTM min ;

[0080] Based on the Wiener process model, a particle filter algorithm is used to estimate the model parameters of the target lithium battery, making the error data of the target lithium battery approximate E. min Let the estimated parameters be .

[0081] (4.3) Construct a Wiener process model based on error function correction for the target lithium battery;

[0082]

[0083] Where x0 represents the initial characteristic quantity of the target lithium battery; a min t represents the drift coefficient of the target lithium battery; b b represents the degradation trend function of the target lithium battery characteristic quantity. min The parameters of the degradation trend function are f(t) = LSTM. min σ represents the error function of the target lithium battery. B，min is the diffusion coefficient of the Wiener process; B(t) represents the standard Brownian motion.

[0084] (4.4) Calculate the target lithium battery at the current time t c The remaining lifespan;

[0085] Based on the Wiener process model with error function correction, the remaining lifetime probability density function F(l) of the target lithium battery is calculated:

[0086]

[0087] in, q(l)=f(l+t c )-f(tc f′(t) represents the first derivative of the error function f(t) at time t.

[0088] (4.5) Select the time corresponding to the maximum value in F(l) as the current time t. c The remaining life prediction value of the lithium battery under test is given; then let t c =t c +1, jump back to step (4.1);

[0089] (5) When the degradation of the lithium battery characteristic quantity to be tested reaches the failure threshold w, the prediction terminates and the algorithm ends.

[0090] To illustrate the technical effects of this invention, lithium battery B1 was selected as the subject of this patent, and the remaining lifespan of the lithium battery was predicted under simulated real-time working conditions by selecting the other three sets of lithium battery degradation data as historical degradation data. Figure 2 These are data on the capacity degradation of four groups of lithium batteries obtained from the experiment.

[0091] The parameters of the four lithium batteries estimated using the method in step (3) are shown in Table 1:

[0092]

[0093] Table 1

[0094] Based on the above parameters, the degradation trends of these four lithium batteries were simulated using the traditional Wiener process, and compared with the actual degradation trajectories of lithium batteries. The results are as follows: Figure 3 As shown. Figure 3 The results shown indicate that, due to the degradation trend function t b Due to limitations, the traditional Wiener process is difficult to accurately fit the degradation trend of this type of lithium battery.

[0095] To simulate the remaining life prediction process in actual engineering, we set lithium battery B1 as the target battery, and lithium batteries B2, B3, and B4 as historical batteries. The prediction started at cycle 402, and life prediction was performed every 10 cycles. The prediction terminated when the battery capacity dropped to 88% of its initial capacity. Figure 4 This paper presents a comparison between simulated degradation trend data of lithium battery B1 obtained by the novel method for predicting remaining lifetime using a combination of error function correction and Wiener process, as proposed in this invention, and actual degradation data of B1. It can be clearly seen that after correction using the error function, the obtained simulated degradation data is very close to the actual lithium battery degradation data, demonstrating the effectiveness of the method proposed in this invention.

[0096] The remaining life curves of lithium battery B1 predicted at different times using this invention are as follows: Figure 5As shown, the remaining lifetime prediction curve obtained using this invention can clearly provide the probability density function curve of the remaining lifetime at different times, which can provide more information for device maintenance and support, thereby facilitating device maintenance.

[0097] In order to quantitatively compare and measure prediction performance, Figure 6 This paper demonstrates the prediction results of the present invention, the conventional Wiener process, and the Long Short-Term Memory Neural Network (LSTM) for the remaining lifetime of lithium battery B1. Through... Figure 6 The prediction results of different types of models for the RUL of lithium batteries show that, because the present invention uses an error function based on an LSTM neural network to correct the traditional Wiener process, the present invention fits the degradation trend of lithium batteries better than the traditional Wiener process. Furthermore, because the present invention includes the Wiener process, compared to directly using an LSTM network for prediction, the present invention can provide the uncertainty of the prediction result at each time step. Table 2 shows the average RUL prediction error of each model for lithium battery B1.

[0098] LSTM Wiener process This invention average error 9.9 cycles 28.8 cycles 5.7 cycles

[0099] Table 2

[0100] As can be seen from the prediction results shown in Table 2, the accuracy of the remaining lifetime prediction results of this model is much higher than that of other models. This directly illustrates the advantages of the new remaining lifetime prediction method proposed in this invention, which combines error function correction and Wiener process. Therefore, this invention is more suitable for the needs of remaining lifetime prediction in practical engineering.

[0101] Although the illustrative specific embodiments of the present invention have been described above to enable those skilled in the art to understand the invention, it should be understood that the invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of the present invention are protected.

Claims

1. A method for adaptive prediction of the remaining life of a lithium battery based on error correction, characterized in that, Includes the following steps: (1) Data preprocessing; By accelerating the life experiment of N historical lithium batteries, sampling the capacity of each historical lithium battery at different time, and then smoothing the N groups of capacity respectively by using filter to obtain N groups of smoothed data wherein, , represents the initial capacity of the th historical lithium battery, represents the smoothed value of the capacity of the th historical lithium battery at the th time, , represents the number of sampling time of the th historical lithium battery; (2) Construct Wiener process models of historical lithium batteries at each sampling time; ； wherein, represents the initial capacity of the historical lithium battery; a represents the drift coefficient of the Wiener process; represents the degradation trend function of the historical lithium battery capacity, b is the parameter of the degradation trend function; is the diffusion coefficient of the Wiener process; is a standard Brownian motion; (3) Construct the error function of each historical lithium battery Wiener process model; (3.1) Construct the likelihood function for each historical lithium battery: ； in, Represents the parameters of the i-th historical lithium-ion battery Wiener process model; This represents the first-order difference of the capacity of the i-th historical lithium battery. Let represent the first-order difference of the i-th historical lithium battery trend function at different sampling times; express The covariance matrix, for An identity matrix of order 1; (3.2) Solve for the parameters of each likelihood function; Let the above likelihood function be about and The first-order partial derivative is 0, so we get: ； ； Then the above and Substituting the expression into the Wiener process model, and using the particle filter algorithm, the parameter estimates of N historical lithium batteries are obtained, respectively. , and ; (3.3) Solve for the error function; Based on the parameters obtained in (3.2) and the Wiener process model in (2), N sets of simulation capacity data are generated. ; Then use actual data Subtract simulation data To obtain error data ,in, ; Then, using these N sets of error data, N long short-term memory neural networks (LSTM) are trained respectively. These N LSTM neural networks represent the error functions of N historical lithium battery Wiener process models. (4) Real-time prediction of the remaining lifespan of the target lithium battery; (4.1) Obtain the current capacity of the target lithium battery; Use the method in step (1) to obtain the current time. Next target lithium battery capacity data ,judge Has the failure threshold been exceeded? If the value exceeds the limit, proceed to step (5) and the algorithm ends; if the value does not exceed the limit, proceed to step (4.2). (4.2) Estimate the Wiener process model parameters of the target lithium battery; Calculate the target lithium battery capacity data X and the historical lithium battery capacity data. Euclidean distance between : ； Let the error data corresponding to the historical lithium battery with the smallest Euclidean distance be denoted as Its corresponding error function is ; Based on the Wiener process model, a particle filter algorithm is used to estimate the model parameters of the target lithium battery, thereby approximating the error data of the target lithium battery. Let the estimated parameters be . ; (4.3) Construct a Wiener process model based on error function correction for the target lithium battery; ； in, Indicates the initial capacity of the target lithium battery; This represents the drift coefficient of the target lithium battery; The function representing the degradation trend of the target lithium battery capacity. These are the parameters of the degradation trend function; The error function representing the target lithium battery is... It is the diffusion coefficient of the Wiener process; it is Standard Brownian motion; (4.4) Calculate the target lithium battery at the current time. The remaining lifespan; Based on the Wiener process model with error function correction, the remaining lifetime probability density function of the target lithium battery is calculated. : ； in, Represents a time variable. ; ; ; Representing the error function The first derivative at time t; (4.5) Selection The time corresponding to the maximum value is taken as the current time. The remaining life prediction value of the lithium battery under test is given, and then let... Then jump back to step (4.1). (5) The degradation of the target lithium battery capacity reaches the failure threshold. The prediction terminates, and the algorithm ends.

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