A lithium battery residual life prediction method based on adaptive wiener process

Abstract

The application discloses a lithium battery residual life prediction method based on an adaptive Wiener process, obtains the degradation amount of a sample lithium battery at different moments by accelerating the life experiment of multiple sample lithium batteries; then acquires the model prior parameters of a target lithium battery by using a maximum likelihood estimation algorithm; and then the model parameters are updated by using a Kalman filtering algorithm and a transfer learning algorithm, and the updated parameters are used to calculate the residual life probability density function of the target lithium battery at the current moment, so that the lithium battery residual life prediction method has the characteristics of high prediction accuracy, good real-time performance and strong self-adaptive capability.

Description

Technical Field

[0001] This invention belongs to the field of reliability analysis technology, and more specifically, relates to a method for predicting the remaining lifetime of an improved adaptive Wiener process based on a long short-term memory neural network. Background Technology

[0002] In recent years, with the increasing integration of electronic systems, the frequency of system failures has also increased. For each functional module in a complex electronic system, their reliability affects the operational stability of the entire system equipment. Therefore, research on the remaining useful life (RUL) prediction technology of each module has become very necessary. 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 helps manufacturers to improve the process of various system modules (introducing new materials and improving packaging technology); (3) It is conducive to better designing accelerated aging tests to obtain more accurate aging data; (4) It enables condition-based maintenance, allowing end users to obtain more life information of complex electronic systems to reduce investment in system maintenance.

[0003] Existing research on Residual Lifetime (RUL) prediction techniques mainly falls into two categories: physical model-driven prediction techniques and data-driven prediction techniques. While physical model-driven prediction techniques can describe the RUL information of each system module from a materials perspective, they require a deep understanding of the inherent properties of the materials used in device manufacturing and the manufacturing process. Furthermore, the acquired physical models often lack sufficient accuracy, and the modeling process can easily lose the nonlinear relationships between object parameters, leading to increased errors. Data-driven prediction techniques, on the other hand, learn the mapping relationship between inputs and outputs from historical aging data of the output features of system modules. These are mainly divided into probabilistic statistical methods and machine learning methods. Machine learning methods can effectively learn the degradation trend of lithium batteries using powerful computing capabilities, achieving high accuracy in RUL prediction. However, their accuracy heavily relies on a large amount of training data and cannot describe the uncertainty of the prediction results. Probabilistic statistical methods use probabilistic statistical models to describe the degradation trend of lithium batteries, effectively characterizing the uncertainty in the degradation process. However, the probability density function of the remaining lifetime is difficult to solve. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a lithium battery remaining life prediction method based on the adaptive Wiener process. It combines the advantages of deep learning and the adaptive Wiener process, and uses an adaptive drift coefficient and deep learning method to replace the nonlinear function in the traditional Wiener process, thereby enhancing the Wiener process's ability to fit complex dynamic nonlinear degradation trends and improving the accuracy of lithium battery remaining life prediction.

[0005] To achieve the above-mentioned objectives, this invention provides a method for predicting the remaining life of lithium batteries based on an adaptive Wiener process, characterized by the following main steps:

[0006] (1) Obtain the degradation amount of the sample lithium battery at different times;

[0007] (2) Construct an adaptive Wiener process model of the target lithium battery at each sampling time;

[0008] (3) Estimate the model prior parameters of the target lithium battery using sample lithium batteries;

[0009] (4) Real-time prediction of the remaining lifetime of the target sample;

[0010] The objective of this invention is achieved as follows:

[0011] This invention presents a lithium battery remaining lifetime prediction method based on the adaptive Wiener process. It accelerates lifetime experiments on multiple sample lithium batteries to obtain the degradation amount of the sample lithium batteries at different times. Then, it uses a maximum likelihood estimation algorithm to obtain the model prior parameters of the target lithium battery. Next, it updates the model parameters using a Kalman filter algorithm and a transfer learning algorithm, and uses the updated parameters to calculate the remaining lifetime probability density function of the target lithium battery at the current time. This method features high prediction accuracy, good real-time performance, and strong adaptability. Attached Figure Description

[0012] Figure 1 This is a flowchart of the lithium battery remaining life prediction method based on the adaptive Wiener process of this invention;

[0013] Figure 2 These are data on the degradation of lithium battery capacity obtained from accelerated life testing.

[0014] Figure 3 It is the probability density function of the remaining lifetime at a certain moment;

[0015] Figure 4 This is a graph showing the predicted remaining lifespan of the lithium battery according to the present invention:

[0016] Figure 5The 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) a new method model for remaining life prediction based on improved adaptive Wiener process based on long short-term memory neural network. Detailed Implementation

[0017] 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.

[0018] Example

[0019] Figure 1 This is a flowchart of a novel method for predicting remaining lifetime based on an improved adaptive Wiener process using a long short-term memory neural network, according to the present invention.

[0020] In this embodiment, as Figure 1 As shown, the present invention provides a lithium battery remaining life prediction method based on the adaptive Wiener process, comprising the following steps:

[0021] (1) Obtain the degradation amount of the sample lithium battery at different times;

[0022] By accelerating the lifespan experiment of M sample lithium batteries, the degradation data of each sample lithium battery at different times were obtained, where the degradation data of the i-th sample lithium battery at different times is denoted as . Where i = 1, 2, 3...M, This represents the initial feature degradation amount of the i-th sample lithium battery. This represents the degradation of a feature value of the i-th sample lithium battery at time t. This represents the sampling time of the i-th lithium battery sample;

[0023] (2) Construct an adaptive Wiener process model of the target lithium battery at each sampling time;

[0024] X(t) = X(0) + ∫0 t v(τ)df(τ)+σ B B(t)

[0025] v(t) = v0 + kW(t)

[0026] Where X(0) represents the initial characteristic degradation of the target lithium battery, f(τ) represents the degradation trend function fitted by a long short-term memory neural network, v(t) represents the adaptive drift coefficient of the Wiener process, v0 is the initial value of v(t), k is a constant coefficient, W(t) and B(t) are independent standard Brownian motions, and σ B It is the diffusion coefficient of the Wiener process;

[0027] (3) Estimate the model prior parameters of the target lithium battery using sample lithium batteries;

[0028] (3.1) Obtain the characteristic degradation data of the target lithium battery at the current moment;

[0029] Obtain the current time t according to step (1). n Degradation data 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 (3.2).

[0030] (3.2) Using the Savitzky-Golay filter, the degradation data of the M groups of sample lithium batteries and the degradation data of the target lithium battery are smoothed to obtain the smoothed degradation data of the M groups of sample lithium batteries. And the degradation data of the target lithium battery after smoothing. in, This indicates that the degradation data of the i-th historical sample is in the i-th... The smoothed value at each moment;

[0031] (3.3) Using the smoothed data of the sample lithium batteries obtained in step (3.2). Train a Long Short-Term Memory (LSTM) neural network with q input nodes and 1 output node. all , where t n >q>0;

[0032] Extracting the smoothed degradation data of the target lithium battery Then input into LSTM all Perform multi-step prediction. The output of the p-th prediction is denoted as the function value of f(t) at the t = q + p, where p is the number of training steps and p > 0.

[0033] (3.4) Based on the Wiener process in step (2), the corresponding likelihood function is constructed as follows:

[0034]

[0035] Where θ=[v0,k,σ BThe symbol indicates that the Wiener process model in step (2) contains a set of parameters. Let f(t) be the vector representing the function values ​​of f(t) at different times; (·) T Represents the transpose of a matrix; express The covariance matrix, where D i and Q i All are m i ×m i m-order matrix i D represents the number of feature degradation data for the i-th sample lithium battery. i and Q i The expression is as follows:

[0036]

[0037]

[0038] The above likelihood function For v0 and σ respectively B By taking the partial derivative and setting it to zero, we can obtain the model parameters v0 and σ of the target lithium battery. B Prior estimate and

[0039]

[0040]

[0041] in,

[0042] Finally, and Substituting back into the likelihood function, we get Then, the "fmincon" function in MATLAB software is used to search the above likelihood function to obtain the optimal value of r, thereby obtaining the prior estimate of the target lithium battery model parameters.

[0043] (4) Real-time prediction of the remaining lifetime of the target sample;

[0044] (4.1) Updating the LSTM neural network using transfer learning all And the degradation trend function f(t);

[0045] Based on the smoothed degradation data of the sample lithium battery and the target lithium battery obtained in step (3.2) and Calculate X respectively s and Euclidean distance E i :

[0046]

[0047] LSTM neural network all The learning rate for parameters between all layers except the fully connected layer is set to 0, and the learning rate for parameters between the fully connected layer and other layers is set to 1. The minimum E is selected. i Corresponding smoothed data To LSTM all The neural network LSTM is then trained again to obtain a fine-tuned version. all，fine-tune ;

[0048] (4.2) Take X from step (4.1) s The last q data As a neural network LSTM all，fine-tune The input is used to obtain the predicted output. Then the predicted data As a neural network LSTM all，fine-tune Input, to obtain predicted data Repeat the above steps until the predicted data is obtained. When the prediction stops, the data... That is, the updated value of the function f(t) from time t1 to T;

[0049] (4.3) Update the model parameters of the target lithium battery;

[0050] Based on the mathematical expression of the Wiener process in step (2), the state transition equations for the target lithium battery model parameters are obtained as follows:

[0051] v(t j )=v(t j-1 )+kΔW j

[0052]

[0053] Among them, t j ∈(t1, t2, ..., t n );ΔW j =W(t) j )-W(t j-1 );Δf j =f(t) j )-f(t j-1 );ΔB j =B(t) j )-B(t j-1 ).

[0054] The above equation can be expressed as:

[0055]

[0056] The observation equations for reconstructing the model parameters are as follows:

[0057]

[0058] Where, ξ j ~N(0,0) represents a Gaussian distribution with a mean and variance of 0;

[0059] When the field degradation data of the target lithium battery is obtained Then, assume adaptive drift coefficients If it follows a normal distribution, then when the target lithium battery is obtained at time t... j After the degraded data at time step, the distribution parameters of the drift coefficients are updated using the Kalman filter algorithm:

[0060]

[0061]

[0062] in, X(t) represents j ) and v(t) j The covariance matrix of ) is:

[0063] П j (1, 1) = k 2 Δt j

[0064]

[0065]

[0066] Where, Δt j =t j -t j-1 ;

[0067] In the above parameter update equation, the initial value of v(t) is:

[0068]

[0069] (4.4) Calculate the current time t n The probability density function of the remaining lifetime of the target lithium battery;

[0070] The distribution parameters of the adaptive drift coefficients updated based on steps (4.2) and (4.3) And the degradation trend function f(t) can be used to calculate the degradation trend at time t. n At time t, the probability density function g of the remaining lifetime of the target lithium battery RUL (ln ):

[0071]

[0072] Where w represents the failure threshold of the target lithium battery; express For l n The first derivative; Represents ψ(l) n For l n The first derivative;

[0073] (4.5) Select g RUL (l n The time l corresponding to the maximum value in ) n，max As the current t n The predicted remaining lifespan of the target lithium battery at time t; then let t n =t n+1 Then, jump back to step (4.1);

[0074] (5) When the degraded data of the target sample reaches the failure threshold w, the prediction terminates and the algorithm ends.

[0075] To illustrate the technical effects of this invention, lithium battery B5 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 5 sets of lithium battery degradation data as historical degradation data. Figure 2 These are data on the capacity degradation of six groups of lithium batteries obtained from the experiment.

[0076] In the prior parameter estimation based on historical sample degradation data, the model parameters of the B5 lithium battery estimated using the remaining 5 sets of lithium battery degradation data are shown in the table below:

[0077] Table 1. Model parameters of historical lithium batteries

[0078]

[0079] Then, the transfer learning algorithm in step (4.2) and the Kalman filtering algorithm in step (4.3) are used to update the posterior parameters of the target lithium battery model, so that the model parameters can adaptively fit the degradation characteristics of the target lithium battery as the amount of field data increases. Based on the updated posterior parameters, the probability density curve of the target lithium battery at the current time is obtained using the remaining lifetime probability density function in step (4.4). Figure 3 The probability density curve of the remaining lifetime of the target lithium battery obtained by this invention at a certain point in the remaining lifetime prediction is shown. The remaining lifetime curves of lithium battery B5 predicted using this invention at different times are shown below. Figure 4As shown, the remaining life prediction curve obtained using this invention can clearly provide the probability density function curve of the remaining life at different times, which can provide more information for the maintenance and support of lithium batteries, thereby helping to carry out the maintenance and support work of related power supply systems.

[0080] In order to quantitatively compare and measure prediction performance, Figure 5 This paper presents the prediction results of the remaining lifespan of lithium battery B5 using the present invention, a traditional nonlinear Wiener process (the nonlinear function is a exp(bt), where a and b are parameters), and a long short-term memory neural network model. Figure 5 The prediction results of different types of models for the remaining life of lithium batteries show that, because this invention uses adaptive drift coefficients and a long short-term memory neural network model based on transfer learning to adaptively fit the degradation trend of the target lithium battery on the basis of the Wiener process, it performs better than the traditional method of fitting with a fixed nonlinear function (a exp(bt) in this example). Furthermore, because this invention includes the Wiener process, it can provide the uncertainty of the prediction result at each time step compared to directly using the long short-term memory neural network model. In addition, the long short-term memory neural network model heavily relies on a large amount of training data, while this invention can obtain more accurate prediction results with less training data. Table 2 shows the average prediction error of each model for the remaining life of lithium battery B5.

[0081] Table 2. Average error of different models in predicting the remaining lifespan of B5

[0082] Long Short-Term Memory Neural Network Traditional Wiener process This invention average error 57.4 cycles 23.0 cycle 15.8 cycles

[0083] 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 demonstrates the advantages of the new remaining lifetime prediction method based on the improved adaptive Wiener process using a long short-term memory neural network proposed in this invention.

[0084] 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 predicting the remaining life of a lithium battery based on an adaptive Wiener process, characterized in that, Includes the following steps: (1) Obtain the degradation amount of the sample lithium battery at different times; By accelerating the lifespan experiment of M sample lithium batteries, the degradation data of each sample lithium battery at different times were obtained, where the degradation data of the i-th sample lithium battery at different times is denoted as . Where i = 1, 2, 3...M, This represents the initial feature degradation amount of the i-th sample lithium battery. This represents the degradation of a feature value of the i-th sample lithium battery at time t. This represents the sampling time of the i-th lithium battery sample; (2) Construct an adaptive Wiener process model of the target lithium battery at each sampling time; v(t) = v0 + kW(t) Where X(0) represents the initial characteristic degradation of the target lithium battery, f(τ) represents the degradation trend function fitted by a long short-term memory neural network, v(t) represents the adaptive drift coefficient of the Wiener process, v0 is the initial value of v(t), k is a constant coefficient, W(t) and B(t) are independent standard Brownian motions, and σ B It is the diffusion coefficient of the Wiener process; (3) Estimate the model prior parameters of the target lithium battery using sample lithium batteries; (3.1) Obtain the characteristic degradation data of the target lithium battery at the current moment; Obtain the current time t according to step (1). n Degradation data 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 (3.2). (3.2) Using the Savitzky-Golay filter, the degradation data of the M groups of sample lithium batteries and the degradation data of the target lithium battery are smoothed to obtain the smoothed degradation data of the M groups of sample lithium batteries. And the degradation data of the target lithium battery after smoothing. in, This indicates that the degradation data of the i-th historical sample is in the i-th... The smoothed value at each moment; (3.3) Using the smoothed data of the sample lithium batteries obtained in step (3.2). Train a KSTM long short-term memory neural network with q input nodes and 1 output node. all , where t n >q>0; Extracting the smoothed degradation data of the target lithium battery Then input into LSTM all Perform multi-step prediction. The output of the p-th prediction is denoted as the function value of f(t) at the t = q + p, where p is the number of training steps and p > 0. (3.4) Based on the Wiener process in step (2), the corresponding likelihood function is constructed as follows: Where θ=[v0,k,σ B The symbol indicates that the Wiener process model in step (2) contains a set of parameters. Let f(t) be the vector representing the function values ​​of f(t) at different times; (·) T Represents the transpose of a matrix; express The covariance matrix, where D i and Q i All are m i ×m i m-order matrix i D represents the number of feature degradation data for the i-th sample lithium battery. i and Q i The expression is as follows: The above likelihood function For v0 and σ respectively B By taking the partial derivative and setting it to zero, we can obtain the model parameters v0 and σ of the target lithium battery. B Prior estimate and in, Finally, and Substituting back into the likelihood function, we get Then, the "fmincon" function in MATLAB software is used to search the above likelihood function to obtain the optimal value of r, thereby obtaining the prior estimate of the target lithium battery model parameters. (4) Real-time prediction of the remaining lifetime of the target sample; (4.1) Updating the LSTM neural network using transfer learning all And the degradation trend function f(t); Based on the smoothed degradation data of the sample lithium battery and the target lithium battery obtained in step (3.2) and Calculate X respectively s and Euclidean distance E i : LSTM neural network all The learning rate for parameters between all layers except the fully connected layer is set to 0, and the learning rate for parameters between the fully connected layer and other layers is set to 1. The minimum E is selected. i Corresponding smoothed data To LSTM all The neural network LSTM is then trained again to obtain a fine-tuned version. all，fine-tune ; (4.2) Take X from step (4.1) S The last q data As a neural network LSTM all，fine-tune The input is used to obtain the predicted output. Then the predicted data As a neural network LSTM all，fine-tune Input, to obtain predicted data Repeat the above steps until the predicted data is obtained. When the prediction stops, the data... That is, the updated value of the function f(t) from time t1 to T; (4.3) Update the model parameters of the target lithium battery; Based on the mathematical expression of the Wiener process in step (2), the state transition equations for the target lithium battery model parameters are obtained as follows: v(t j )=v(t j-1 )+kΔW j where, t j ∈(t1, t2,..., t n ); ΔW j = W(t j ) - W(t j-1 ); Δf j = f(t j ) - f(t j-1 ); ΔB j = B(t j ) - B(t j-1 ); The above equation can be expressed as: The observation equations for reconstructing the model parameters are as follows: Where, ξ j ~N(0,0) represents a Gaussian distribution with a mean and variance of 0; When the field degradation data of the target lithium battery is obtained Then, assume adaptive drift coefficients If it follows a normal distribution, then when the target lithium battery is obtained at time t... j After the degraded data at time step, the Kalman filter algorithm is used to update the distribution parameters of the drift coefficients: Where, ΔX j =X(t) j )-X(t j-1 ); X(t) represents j ) and v(t) j The covariance matrix of ) is: P j (1,1)=k 2 Δt j Where, Δt j =t j -t j-1 ; In the above parameter update equation, the initial value of v(t) is: (4.4) Calculate the current time t n The probability density function of the remaining lifetime of the target lithium battery; The distribution parameters of the adaptive drift coefficients updated based on steps (4.2) and (4.3) And the degradation trend function f(t) can be used to calculate the degradation trend at time t. n At time t, the probability density function g of the remaining lifetime of the target lithium battery RUL (l n ): Where w represents the failure threshold of the target lithium battery; express For l n The first derivative; Represents ψ(l) n For l n The first derivative; (4.5) Select g RUL (l n The time l corresponding to the maximum value in ) n，max As the current t n The predicted remaining lifespan of the target lithium battery at time t; then let t n =t n+1 Then, jump back to step (4.1); (5) When the degraded data of the target sample reaches the failure threshold w, the prediction terminates and the algorithm ends.

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