Lithium battery remaining service life prediction method based on Stacking fusion

Abstract

The invention discloses a lithium battery remaining service life prediction method based on Stacking fusion, which comprises the following steps: firstly decomposing lithium battery capacity data through robust local mean decomposition, and then reducing the number of sequences through fuzzy entropy aggregation; carrying out secondary decomposition by utilizing a modal component with the highest entropy value of time-varying filtering empirical mode decomposition, inputting the processed data into a lightweight time sequence analysis model and a non-inverse extreme learning machine for prediction, and carrying out parameter optimization on an FITS model and an IFELM model by adopting an improved wave search algorithm; the prediction values of the two models are fused by using a Stacking algorithm, then error correction is carried out, finally, the fused prediction result and the error prediction result are superposed to obtain a final lithium battery capacity prediction result, and the prediction result is obtained according to the relationship between the capacity data and the residual life. According to the method, the prediction model precision of the residual life of the lithium battery can be effectively improved, and a reliable basis is provided for safety judgment of the lithium battery.

Description

Technical Field

[0001] The present invention belongs to the technical field of lithium batteries, and in particular relates to a method for predicting the remaining service life of a lithium battery based on Stacking fusion. Background Art

[0002] At present, the global energy structure mainly relies on fossil fuels, but with the gradual depletion of these resources and the intensification of environmental problems, the development of new energy has become particularly urgent. In order to reduce energy consumption and alleviate the energy crisis, the development and application of new energy are rapidly expanding. As one of the key technologies in the field of new energy, the extension and maintenance of the service life of lithium batteries are crucial. However, the performance of lithium batteries will gradually degrade over time, which requires us to accurately predict the life of the battery. Battery life prediction has become a research field with great practical significance. Existing prediction methods often face challenges in data screening and feature extraction when processing lithium battery data, which may affect the accuracy of model prediction. In addition, the capacitance data of lithium batteries is highly diverse, which may interfere with the prediction model. In order to improve the reliability of the prediction, adopting a fusion strategy of multiple models and introducing an error correction mechanism is an effective solution. Summary of the invention

[0003] Purpose of the invention: In view of the problems existing in the prior art, the present invention provides a method for predicting the remaining service life of a lithium battery based on Stacking fusion, which can improve the accuracy of the lithium battery life prediction model and more accurately predict the remaining service life of a lithium battery.

[0004] Technical solution: The present invention discloses a method for predicting the remaining service life of a lithium battery based on stacking fusion, comprising the following steps:

[0005] (1) Obtain historical capacitance data of lithium batteries in advance, decompose the historical capacitance data using robust local mean decomposition, and introduce fuzzy entropy to aggregate the component data to reduce the number of sequences;

[0006] (2) Using time-varying filtered empirical mode decomposition (TVFEMD) to perform secondary decomposition on the modal component with the highest entropy value, a subsequence with higher resolution is obtained; the original capacitance data is then divided into a sequence with higher resolution after TVFEMD decomposition and a sequence without TVFEMD decomposition;

[0007] (3) The reverse learning strategy is used to improve the initialization population of the wave search algorithm WSA, and the IWSA algorithm is obtained to improve the global search capability and avoid falling into the local optimum;

[0008] (4) The lightweight time series analysis model FITS is used to process the higher resolution series after TVFEMD decomposition, and the inverse extreme learning machine model IFELM is used to process the series without TVFEMD decomposition. The IWSA algorithm is used to optimize the interpolation rate of the FITS model and the regularization parameter of the IFELM model to obtain preliminary lithium battery capacitance prediction results;

[0009] (5) The prediction values ​​of the FITS and IFELM models are fused using the Stacking algorithm, and XGBoost is selected as the second-layer meta-learner of the Stacking framework to obtain the fused capacitance prediction results;

[0010] (6) There is an error between the predicted result obtained in step (5) and the observed value. The error sequence is re-input into the FITS model to perform error prediction and obtain the capacitance error prediction result;

[0011] (7) The prediction results in step (5) and step (6) are superimposed to obtain the final capacitance prediction result, and finally converted according to the capacitance-life formula to obtain the remaining life prediction result of the lithium battery.

[0012] Furthermore, the implementation process of step (1) is as follows:

[0013] First, the mirror expansion algorithm is used to select capacitance data symmetrically at the left and right ends, and then the data is mirrored and expanded, and then the boundary conditions are calculated;

[0014] Next, perform envelope calculation and define the step center as:

[0015]

[0016]

[0017] In the formula, B zhong is the step center, B chang is the step size, P(g) is the probability of capacitance data in each step, P * (g) is the probability value of the capacitance data within the step and at the step boundary; P ** (g) refers to the probability that each capacitance data is at the edge of the step;

[0018] Define the step size standard deviation τ r for:

[0019]

[0020] The definition expression of envelope data in RLMD is as follows:

[0021]

[0022] In the formula, represents the root mean square value, Represents the value of kurtosis, which are defined as follows:

[0023]

[0024]

[0025] In the formula, β j (i) represents the instantaneous amplitude of the jth component, represents the average value of capacitance data;

[0026] The fuzzy entropy of the time series is calculated as follows:

[0027]

[0028] In the formula, Q RWD is the embedding dimension, S JCD is the data length, F W is the similarity tolerance in the range of (0.1-0.25SD), SD is the standard deviation of the raw capacitance data.

[0029] Furthermore, the implementation process of step (2) is as follows:

[0030] (21) For the capacitor data with the highest input entropy value, TFV shuru Perform Hilbert transform to obtain the transformed TFV * shuru , and calculate its instantaneous amplitude SF and instantaneous phase XF, the formula is as follows:

[0031]

[0032] XF = arctan[TFV shuru / TFV * shuru ]

[0033] Corresponding analytical capacitance data JIE xi for:

[0034] JIE xi =TFV shuru +TFV * shuru =SFe XF

[0035] (22) Interpolate according to the local upper and lower limits of SF to obtain the curve QU xian1 and QU xian2 , the corresponding amplitude is expressed as Zheng F1He Zheng F2 :

[0036]

[0037]

[0038] About SF 2 Interpolate the upper and lower limits to get SF cz1 , SF cz2 , calculate the instantaneous frequency component SP * 1 and SP * 2:

[0039]

[0040]

[0041] Local cutoff frequency JIE * zhi calculate:

[0042]

[0043] by The local extreme points are used as nodes, and the B-spline approximate filter is used to filter QU xian Further interpolation is performed to obtain the filtering result Lv * :

[0044] If θ=S K / SP avg ≤ζ=0.1, then TFV shuru As an IMF component, otherwise TFV shuru -Lu * As the new capacitance input data, and repeat steps (21) to (23); where ζ is the bandwidth threshold, SP avg is the weighted mean instantaneous frequency, S K is the instantaneous bandwidth;

[0045] (24) Capacitor data with the highest entropy value TFV shuru After TVFEMD decomposition, we get S subsequences {Lu i |i=1,2,…,S},Lu i is the ith subsequence, and satisfies:

[0046]

[0047] By applying the time-varying filtering empirical mode decomposition technology, the sequence with the highest entropy value is decomposed to obtain a subsequence with higher resolution, which is used for the prediction of the FITS model; other sequences that have not undergone time-varying filtering empirical mode decomposition are used for the prediction of the IFELM model.

[0048] Furthermore, the implementation process of step (3) is as follows:

[0049] (31) In the initialization stage, the number of particles is set to n, and the matrix is ​​used to simulate the position of the electromagnetic wave particle Elc:

[0050]

[0051] Where d represents the dimension of the problem; the fitness value of the population can be represented by a vector:

[0052] FIT=[fit([Elc 11 ,Elc 12 ,…Elc 1d ]); fit([Elc 21 ,Elc 22 ,…Elc 2d ])…fit([Elc n1 ,Elc n2 ,…Elc nd ])]

[0053] In the formula, fit([Elc n1 ,Elc n2 ,…Elc nd ]) represents the fitness value of the individual; prepare u random numbers q1, q2..., q u Initialize the particle position from 0 to 1:

[0054]

[0055] Elc=Loc * (ub-lb)+lb

[0056] In the formula, Loc i is the uniform q i ,Loc * is a random value in x, lb and ub represent the upper and lower boundaries of the search space;

[0057] (32) In the global exploration phase, let the vector Elc min Contains the minimum value of the variable Elc in each dimension, the vector Elc max Contains the maximum value of Elc in each dimension; fit mean is the average value of the sum of all particle fitness values, and rand1 represents a random variable between 0 and 1:

[0058]

[0059]

[0060] (33) The local survey phase is divided into three stages: transmitting electromagnetic waves, reflecting electromagnetic waves, and receiving electromagnetic waves;

[0061] (34) Deterministic optimization technology is introduced, and the mathematical formula is:

[0062]

[0063] Elc i =Elc i -Ssf·Dot i

[0064] Where Ssf represents the step size coefficient;

[0065] (35) Determine the particles that exceed the boundary and randomly set them within the search range. The formula is as follows:

[0066] Elc i =lb+rand·(ub-lb)if Elc i >ub or Elc i <lb

[0067] In the formula, rand represents a d-dimensional randomized column vector between (0, 1);

[0068] (36) The initialization of the population is crucial to finding the optimal solution. Therefore, a reverse learning strategy is introduced to generate a reverse learning population to enhance the diversity of the population and reduce the probability of falling into the local optimal value, thereby enhancing the performance of the WSA algorithm. The reverse learning model is defined as follows:

[0069] RL * I =ub+lb-RL I

[0070] In the formula, RL I ∈[lb,ub], I∈[1,d].

[0071] Furthermore, the implementation process of using the lightweight time series analysis model FITS to process the higher resolution sequence decomposed by TVFEMD in step (4) is as follows:

[0072] The discrete Fourier transform DFT of the complex sequence is calculated by fast Fourier transform FFT to map the discrete time signal from the time domain to the complex frequency domain; the complex formula of the frequency component is:

[0073] Fr(f)=|Fr(f)|e jθ(f)

[0074] Where Fr(f) is the complex number of the frequency component at frequency f, |Fr(f)| is the amplitude of the component, and θ(f) is the phase of the component;

[0075] The time shift of a signal corresponds to a phase shift in the frequency domain, especially in the complex frequency domain, which is represented by multiplying a unit complex exponential element with the corresponding phase.

[0076] If the signal Xi(t) is shifted forward in time by a constant τ, the signal Xi(t-τ) is obtained, and the Fourier transform is given as follows:

[0077] Fr τ (f) = e -j2πfτ Fr(f)=|Fr(f)|e j(θ(f)-2πfτ) =[cos(-2πfτ)+jsin(-2πfτ)]Fr(f)The amplitude of the shifted signal is still |Fr(f)|, but the phase θ τ The displacement of (f) = θ(f)-2πfτ is linearly related to the time shift; in the complex frequency domain, each frequency component is represented by a complex number, which contains amplitude and phase information;

[0078] A low-pass filter LPF is introduced to produce a simpler frequency domain by discarding frequency components higher than the specified cutoff frequency COF;

[0079] The complex-valued linear layer is responsible for performing interpolation operations in the complex frequency domain. It realizes the prediction or anomaly detection of time series by learning the amplitude adjustment and phase shift of frequency components. In order to control the output length of the model, the interpolation rate is introduced and applied to the frequency domain. The formula is as follows:

[0080]

[0081] In the formula, η is the difference rate, which represents the output length L of the model o Corresponding to the input length L i The ratio of

[0082] The interpolated complex frequency domain data is converted back to the time domain through inverse rFFT to form a time series segment for supervised learning. The formula is as follows:

[0083] Xi -1 (t) = FFT -1 Fr(f)

[0084] In the formula, Xi -1 (t) is the capacitance time series data after interpolation processing, FFT -1 is the inverse Fourier transform.

[0085] Furthermore, the implementation process of using the inverse-free extreme learning machine model IFELM to process the sequence that has not been decomposed by TVFEMD in step (4) is as follows:

[0086] Assume that in an ELM with l hidden layer nodes, an additional hidden layer node is added, and the output weight is:

[0087]

[0088] The input bias is At this time, the hidden layer output is expressed as:

[0089]

[0090] In the formula, Yc i (i=l,l+1) represents the ELM output with i hidden layer nodes;

[0091] Use the no-inverse algorithm to update the regularized pseudo-inverse to avoid the inverse operation in the weight update process. The operation method is:

[0092]

[0093] Iterative Calculation The calculation method is:

[0094]

[0095] The calculation method is:

[0096]

[0097] make but Substituting in:

[0098]

[0099] Furthermore, in step (4), the interpolation rate of the FITS model and the regularization coefficient of the IFELM model are optimized by using the IWSA algorithm, and the steps are as follows:

[0100] Initialize the relevant parameters of the IWSA algorithm, including the initial particle position, the upper and lower limits of the search space, the maximum number of iterations, and the current number of iterations;

[0101] The training set of lithium battery capacitance data is input into the FITS and IFELM models, and the interpolation rate and regularization coefficient of the models are optimized respectively;

[0102] After the three steps of transmitting electromagnetic waves, reflecting electromagnetic waves and receiving electromagnetic waves in the local survey phase of the IWSA algorithm, the new particle position is obtained, and the fitness value of each particle is calculated. When the preset termination condition of the model is met, the optimal particle position is determined, which is the optimal value of the interpolation rate of the FITS model and the regularization coefficient of the IFELM model.

[0103] The optimized FITS model predicts the component with the highest entropy value after TVFEMD decomposition, and the optimized IFELM model predicts the remaining components to obtain preliminary lithium battery capacitance prediction data.

[0104] Furthermore, the implementation process of step (5) is as follows:

[0105] (51) FITS and IFELM are used as the basic models of the first layer, and the preliminary lithium battery capacitance prediction results obtained in step (4) are used as the input of the second layer metamodel;

[0106] (52) XGBoost is selected as the second-layer meta-learner. The mathematical expression of XGBoost is:

[0107]

[0108] in, is the final x j The corresponding model prediction value; x j is the jth sample; Num tree is the number of decision trees; Num test is the number of training samples; ALL tree is the set of all trees;

[0109] In each iteration, a newly generated regression tree is added based on the previous step to fit the residual of the previous prediction. The iterative process is as follows:

[0110]

[0111] The XGBoost objective function is:

[0112]

[0113] In the formula, y j is the true value; is the loss function;

[0114] XGBoost is iterated for t rounds using incremental training, and the objective function is updated to:

[0115]

[0116] The final output of XGBoost is:

[0117]

[0118] (53) After training and testing the second-layer meta-learner, the output results are the lithium battery capacitance prediction results after stacking fusion of the FITS model and the IFELM model.

[0119] Furthermore, the implementation process of step (6) is as follows:

[0120] The initial prediction after stacking fusion will produce a prediction error with the original data. The actual capacitance data is subtracted from the initial prediction result to obtain the error time series of the capacitance data:

[0121] Error cap =Ovalue cap -Ivalue cap

[0122] In the formula, Error cap Indicates the error value of capacitance data, Ovalue cap Represents the actual observed value of the capacitance data, Ivalue cap represents the preliminary predicted value of capacitance data;

[0123] The error time series of lithium battery capacitance data is reconstructed into input, and the Error is analyzed using the FITS model. cap Make a prediction and get the error prediction result IError of the capacitance data cap .

[0124] Furthermore, the implementation process of step (7) is as follows:

[0125] Add the initial prediction result and the error prediction result to get the final prediction result:

[0126] Fvalue=Ivalue+IError

[0127] In the formula, Fvalue cap Indicates the final predicted value of lithium battery capacitance, Error cap Indicates the error value of capacitance data, IError cap is the error prediction result of capacitance data;

[0128] Define appropriate failure thresholds based on different lithium battery capacitance data. When the capacitance prediction value reaches the set failure threshold, calculate the remaining life of the lithium battery:

[0129]

[0130] Sbc now =Sbc Max safe -Sbc current =RUL

[0131] In the formula, Sbc Max safe Represents the maximum safe cycle number of lithium batteries, Sbc current Represents the current number of lithium battery cycles, Sbc now It is the current remaining number of safe cycles, that is, the remaining life of the lithium battery.

[0132] Beneficial effects: Compared with the prior art, the present invention has the following beneficial effects:

[0133] In view of the fact that lithium battery capacitance data has the characteristics of correlation and large data volume, the prediction accuracy of the prediction model will be disturbed. Therefore, the robust local mean decomposition (RLMD) is firstly used to decompose the collected historical lithium battery capacitance data, and then fuzzy entropy (FE) is introduced to aggregate the decomposed sequences to further reduce the number of sequences and improve the model prediction efficiency. Then, time-varying filtered empirical mode decomposition (TVFEMD) is used to decompose the sequence with the highest entropy value after aggregation, so as to improve the resolution of the subsequence and enhance the prediction accuracy of the model for capacitance data.

[0134] Aiming at the limitations of the traditional WSA algorithm, the reverse learning strategy is used to improve the initialization population of WSA to obtain the IWSA algorithm, which improves the global search ability and obtains better convergence effect; the complex sequence is input into the frequency interpolation time series model (FITS) and the simple sequence is input into the inverse extreme learning machine (IFELM) for prediction, and the IWSA algorithm is used to optimize the interpolation rate of the FITS model and the regularization parameter of the IFELM model to improve the performance of the model, so that the model can better fit the lithium battery capacitance data, improve the generalization ability of the model, and improve the accuracy and reliability of the prediction;

[0135] The Stacking algorithm is used to fuse the predicted values ​​of the FITS model and the IFELM model, and XGBoost with strong generalization ability is selected as the meta-learner of the second layer to correct the prediction error of the first layer model. Then, the error correction technology is introduced to further correct the errors of the fused prediction results to improve the accuracy of the final capacitance prediction results. BRIEF DESCRIPTION OF THE DRAWINGS

[0136] Figure 1 is a flow chart of the present invention;

[0137] Figure 2 A schematic diagram of the flow of the improved WSA algorithm provided by the present invention;

[0138] Figure 3 A flowchart for implementing the Stacking fusion algorithm provided by the present invention;

[0139] Figure 4 The error correction flow chart provided by the present invention. DETAILED DESCRIPTION

[0140] The present invention will be further described in detail below in conjunction with the accompanying drawings.

[0141] like Figure 1 As shown, the present invention provides a method for predicting the remaining service life of a lithium battery based on Stacking fusion, and uses a robust local decomposition method (RLMD) to perform a preliminary decomposition on the original data of the lithium battery capacitor; then, fuzzy entropy (FE) is introduced to aggregate the data after the preliminary decomposition to reduce the number of sequences; then, the sequence with the highest entropy value is secondary decomposed using time-varying filter empirical mode decomposition (TVFEMD) to improve the resolution of the sequence; in view of the influence of the interpolation rate of the frequency interpolation time series model (FITS) and the regularization parameter of the inverse-free extreme learning machine (IFELM) on the prediction performance of the model, a wave search algorithm (WSA) is used to optimize the key parameters, and at the same time, in order to solve the defects of the WSA algorithm, a T reverse learning strategy is introduced to improve the algorithm to obtain IWSA; using the Stacking framework, XGBoost is selected as the meta-learner, and the prediction results of the FITS model and the IFELM model are input into XGBoost for fusion to obtain a new prediction result; considering the existence of errors, the errors between the prediction results and the original data are composed of error sequences, which are input into the FITS model for error correction to improve the prediction accuracy, and finally the fused prediction value and the error correction value are superimposed to obtain the final prediction result. The specific steps are as follows:

[0142] Step 1: Collect historical lithium battery capacitance data in advance as input data.

[0143] Robust Local Mean Decomposition (RLMD) first uses a mirror extension algorithm to select capacitance data symmetrically on the left and right ends, then performs data mirroring extension, and then calculates boundary conditions.

[0144] Next, perform envelope calculation. Define the step center as:

[0145]

[0146] In the formula, B zhong is the step center, B chang is the step length, P(g) is recorded as the probability of capacitance data at each step length, P * (g) is recorded as the probability value of the capacitance data within the step and at the step boundary.

[0147] The probability value P of the capacitance data within the step size and the step size boundary * (g) is calculated as follows:

[0148]

[0149] Where P ** (g) refers to the probability that each capacitance data is at the edge of the step.

[0150] Define the step size standard deviation as:

[0151]

[0152] In the formula, τ r is the step size standard deviation.

[0153] The definition expression of the envelope capacitance data in RLMD is as follows:

[0154]

[0155] In the formula, represents the root mean square value, Represents the value of kurtosis, which are defined as follows:

[0156]

[0157]

[0158] In the formula, β j (i) represents the instantaneous amplitude of the jth component, Represents the average value of the capacitance data.

[0159] The lithium battery capacitance data after RLMD decomposition is used to decompose the complex original capacitance sequence of the lithium battery into simpler subsequences, and then the decomposed capacitance sequence is aggregated using fuzzy entropy (FE) to further reduce the number of components obtained by decomposition. Fuzzy entropy (FE) is a measurement method based on approximate entropy (AE) that aims to measure the orderliness and prediction difficulty of time series and further detect the emergence of new information in time series. The fuzzy entropy of time series is calculated as follows:

[0160]

[0161] In the formula, Q RWD is the embedding dimension, S JCD is the data length, F W is the similarity tolerance in the range of (0.1-0.25SD) (SD is the standard deviation of the original data).

[0162] Using fuzzy entropy to aggregate the capacitance data after RLMD decomposition can reduce the amount of capacitance data and reduce the repeatability of the experiment, which will greatly improve the prediction efficiency of the model.

[0163] Step 2: The modal component with the highest entropy value in step 1 is further decomposed by time-varying filter empirical mode decomposition (TVFEMD) to obtain a subsequence with higher resolution. The specific decomposition steps are as follows:

[0164] Step 2.1: Input capacitance data TFV shuru Perform Hilbert transform to obtain the transformed TFV * shuru , and calculate its instantaneous amplitude SF and instantaneous phase XF, the formula is as follows:

[0165]

[0166] XF = arctan[TFV shuru / TFV * shuru ]

[0167] Corresponding analytical capacitance data JIE xi for:

[0168] JIE xi =TFV shuru +TFV * shuru =SFe XF

[0169] Step 2.2: Interpolate according to the local upper and lower limits of SF to obtain the curve QU xian1 and QU xian2 , the corresponding amplitude is expressed as Zheng F1 He Zheng F2 :

[0170]

[0171]

[0172] About SF 2 Interpolate the upper and lower limits of SF cz1 , SF cz2 , calculate the instantaneous frequency component SP * 1 and SP * 2:

[0173]

[0174]

[0175] Local cutoff frequency JIE * zhi calculate:

[0176]

[0177] Step 2.3: Signal by The local extreme points are used as nodes, and the B-spline approximate filter is used to filter QU xian Further interpolation is performed to obtain the filtering result Lv * .

[0178] If θ=S K / SP avg ≤ζ=0.1, then TFV shuru As an IMF component, otherwise TFV shuru -Lu * As a new input signal, repeat the above steps. Where ζ is the bandwidth threshold, SP avg is the weighted mean instantaneous frequency, S K is the instantaneous bandwidth.

[0179] Step 2.4: Capacitor data TFV with the highest final entropy value shuru After TVFEMD decomposition, we get S subsequences {Lu i |i=1,2,…,S},Lu i is the ith subsequence, and satisfies:

[0180]

[0181] By applying the time-varying filtering empirical mode decomposition technology, we successfully decomposed the sequence with the highest entropy value and improved the model's ability to recognize the sequence; this innovative method significantly reduced the interference of data noise on the prediction model, enabling the model to more accurately capture the intrinsic characteristics of the data and improve the model's prediction accuracy.

[0182] Step 3: If Figure 2 As shown in the figure, the reverse learning strategy is used to improve the wave search algorithm (WSA) to obtain the IWSA algorithm. The process is as follows:

[0183] Step 3.1: Initialization stage, set the number of particles to n, and use the matrix to simulate the position of the electromagnetic wave particle Elc:

[0184]

[0185] Where d represents the dimension of the problem. The fitness value of the population can be represented by a vector:

[0186] FIT=[fit([Elc 11,Elc 12 ,…Elc 1d ]); fit([Elc 21 ,Elc 22 ,…Elc 2d ])…fit([Elc n1 ,Elc n2 ,…Elc nd ])]

[0187] In the formula, fit([Elc n1 ,Elc n2 ,…Elc nd ]) represents the fitness value of the individual.

[0188] Prepare u random numbers q1, q2, ..., q u Initialize the particle position from 0 to 1:

[0189]

[0190] Elc=Loc * (ub-lb)+lb

[0191] In the formula, Loc i is the uniform q i ,Loc * is a random value in x, and lb and ub represent the upper and lower bounds of the search space.

[0192] Step 3.2: Global exploration phase, let the vector Elc min Contains the minimum value of the variable Elc in each dimension, the vector Elc max Contains the maximum value of Elc in each dimension; fit mean is the average value of the sum of all particle fitness values, and rand1 represents a random variable between 0 and 1:

[0193] Elc i new =Elc min +rand1·(Elc max -Elc min )

[0194]

[0195] Step 3.3: The local survey phase is divided into three main phases: transmitting electromagnetic waves, reflecting electromagnetic waves, and receiving electromagnetic waves. The specific steps are as follows:

[0196] In the electromagnetic wave emission stage, let BF be used to adjust the amplitude of the waveform, CV represents a column vector whose elements come from a normal distribution and are arranged in a certain order, Elcbest is the best position vector found in the current iteration, Elc i is a position matrix whose elements are located according to their relationship with Elc best Rearrange the proximity of max Represents the maximum fitness in the population, the formula is as follows:

[0197]

[0198]

[0199]

[0200] This stage simulates the outward diffusion of electromagnetic waves, reducing the possibility of falling into local optimality and improving search efficiency.

[0201] In the electromagnetic wave reflection stage, it simulates the particles with lower fitness value encountering obstacles and moving towards Elc best Reflection, while particles with higher fitness values ​​stay away from Elc best Continue to spread outward, the formula is as follows:

[0202]

[0203]

[0204]

[0205] Where Ref is the reflection intensity coefficient, rand2 represents a random value between (0, 1), and n Elc2 Represents the number of particles simulating reflected electromagnetic waves, the matrix Elc ju Indicates the position of Elc after rearrangement in the order of fitness value from small to large.

[0206] In the electromagnetic wave receiving stage, the radar is simulated to receive electromagnetic waves normally, but sometimes it is interfered and needs to be corrected and processed. The formula is as follows:

[0207]

[0208]

[0209]

[0210] In the formula, Rec represents the receiving coefficient, Rn represents a random number that obeys the normal distribution, and n Elc3 is the number of particles simulating the reception of electromagnetic waves; is the historical optimal position, rand3, rand4, rand5, rand6 are random numbers between (0, 1); Cor is the correction factor.

[0211] Step 3.4: Introduce deterministic optimization technology, the mathematical formula is:

[0212]

[0213] Elc i =Elc i -Ssf·Dot i

[0214] In the formula, Ssf represents the step size coefficient, and its initial value is set to 0.3. Deterministic optimization technology is introduced to search for the optimal solution to improve the search efficiency and accuracy.

[0215] Step 3.5: Determine the particles that are beyond the boundary and randomly set them within the search range. The formula is as follows:

[0216] Elc i =lb+rand·(ub-lb)if Elc i >ub or Elc i <lb

[0217] Where rand represents a d-dimensional randomized column vector between (0, 1).

[0218] Step 3.6: The initialization of the population is crucial to finding the optimal solution, so the reverse learning strategy is introduced to generate a reverse learning population to enhance the diversity of the population and reduce the probability of falling into the local optimal value, thereby enhancing the performance of the WSA algorithm. The reverse learning model is defined as follows:

[0219] RL * I =ub+lb-RL I

[0220] Where: RL I ∈[lb,ub], I∈[1,d].

[0221] The improved wave search algorithm (IWSA) can help the model find better parameters more accurately and quickly, enhance the generalization ability of the model, and improve the accuracy of the model's prediction of lithium battery capacitance data.

[0222] Step 4: Select the FITS model to process the subsequence with higher resolution obtained after TVFEMD decomposition in step 2, and the IFELM model to process the sequence that has not been decomposed by TVFEMD in step 2, and use the IWSA algorithm to optimize the interpolation rate of the frequency interpolation time series model (FITS) and the regularization parameter of the inverse extreme learning machine (IFELM).

[0223] The FITS model is an advanced time series analysis model that demonstrates excellent performance in time series forecasting tasks with its lightweight and efficient data processing capabilities. The implementation process is as follows:

[0224] The discrete Fourier transform (DFT) of a complex sequence is calculated by the fast Fourier transform (FFT) to map the discrete time signal from the time domain to the complex frequency domain. In time series analysis, the real fast Fourier transform is often used to process real input signals. It compresses the input of N real numbers into a sequence of N / 2+1 complex numbers, representing the signal in the complex frequency domain.

[0225] In Fourier analysis, the complex frequency domain is a representation of the signal, in which each frequency component is represented by a complex number; this complex number captures the amplitude and phase of the component. The amplitude of the frequency component represents the amplitude of the component in the original time domain signal, and the phase of the frequency component represents the time displacement introduced by the component in the original time domain signal. The complex number formula of the frequency component is:

[0226] Fr(f)=|Fr(f)|e jθ(f)

[0227] Where Fr(f) is the complex number of the frequency component at frequency f, |Fr(f)| is the amplitude of the component, and θ(f) is the phase of the component.

[0228] The time shift of a signal corresponds to a phase shift in the frequency domain, especially in the complex frequency domain. We can represent this phase shift by multiplying a unit complex exponential element with the corresponding phase.

[0229] If the signal Xi(t) is shifted forward in time by a constant τ, the signal Xi(t-τ) is obtained, and the Fourier transform is given as follows:

[0230] Fr τ (f) = e -j2πfτ Fr(f)=|Fr(f)|e j(θ(f)-2πfτ) =[cos(-2πfτ)+jsin(-2πfτ)]Fr(f)

[0231] The amplitude of the shifted signal is still |Fr(f)|, but the phase θ τ The displacement of (f) = θ(f)-2πfτ is linearly related to the time shift. In the complex frequency domain, each frequency component is represented by a complex number that contains amplitude and phase information.

[0232] A low-pass filter (LPF) is introduced to produce a simpler frequency domain by discarding frequency components above the specified cutoff frequency (COF). Finally, the complex-valued linear layer is responsible for performing interpolation operations in the complex frequency domain. This layer achieves prediction or anomaly detection of time series by learning the amplitude adjustment and phase shift of frequency components. In order to control the output length of the model, the interpolation rate is introduced and applied to the frequency domain. The formula is as follows:

[0233]

[0234] In the formula, η is the difference rate, which represents the output length L of the model o Corresponding to the input length L i ratio.

[0235] The interpolated complex frequency domain data is converted back to the time domain through inverse rFFT to form a time series segment for supervised learning. The formula is as follows:

[0236] Xi -1 (t) = FFT -1 Fr(f)

[0237] In the formula, Xi -1 (t) is the capacitance time series data after interpolation processing, FFT -1 is the inverse Fourier transform.

[0238] The Inverse-Free Extreme Learning Machine (IFELM) is a machine learning method that gradually increases the number of hidden layer nodes and gradually and optimally updates the connection weights based on the traditional extreme learning machine (ELM). The implementation is as follows:

[0239] Assume that in an ELM with l hidden layer nodes, an additional hidden layer node is added, and the output weight is:

[0240]

[0241] The input bias is At this time, the hidden layer output is expressed as:

[0242]

[0243] In the formula, Yc i (i=l,l+1) represents the ELM output with i hidden layer nodes.

[0244] Use the no-inverse algorithm to update the regularized pseudo-inverse to avoid the inverse operation in the weight update process. The operation method is:

[0245]

[0246] Iterative Calculation The calculation method is:

[0247]

[0248] The calculation method is:

[0249]

[0250] make but Substituting in:

[0251]

[0252] The IWSA algorithm is used to optimize the interpolation rate of the FITS model and the regularization coefficient of the IFELM model: the relevant parameters of the IWSA algorithm are initialized, including the initial particle position, the upper and lower limits of the search space, the maximum number of iterations, and the current number of iterations; the training set of lithium battery capacitance data is input into the FITS and IFELM models, and the interpolation rate and regularization coefficient of the model are optimized respectively; the new particle position is obtained through the three steps of transmitting electromagnetic waves, reflecting electromagnetic waves, and receiving electromagnetic waves in the local survey phase of the IWSA algorithm, and the fitness value of each particle is calculated. When the preset termination conditions of the model are met, the optimal particle position is determined, which is the optimal value of the interpolation rate of the FITS model and the regularization coefficient of the IFELM model. Finally, the optimized FITS model predicts the component with the highest entropy value after TVFEMD decomposition, and the optimized IFELM model predicts the other remaining components, and the preliminary lithium battery capacitance prediction data is obtained.

[0253] Step 5: Figure 3 As shown, the prediction values ​​of the two models are fused using the Stacking algorithm, and XGBoost is selected as the second-layer meta-learner of the Stacking framework. The process is as follows:

[0254] Step 5.1: According to step 4, select FITS and IFELM as the basic models of the first layer, and the lithium battery capacitance prediction results obtained in step 4 are used as the input of the second layer metamodel;

[0255] Step 5.2: When selecting the second-layer meta-learner, we fully consider that a model with strong generalization ability can better correct the prediction error of the first layer and make the final prediction result more accurate. Therefore, XGBoost is selected as the second-layer meta-learner as follows:

[0256] The mathematical expression of XGBoost is:

[0257]

[0258] in, is the final x j The corresponding model prediction value; x j is the jth sample; Num tree is the number of decision trees; Num test is the number of training samples; ALL tree is the set of all trees.

[0259] In each iteration, a newly generated regression tree is added based on the previous step to fit the residual of the previous prediction. The iterative process is as follows:

[0260]

[0261] The XGBoost objective function is:

[0262]

[0263] In the formula, y j is the true value; is the loss function.

[0264] XGBoost is iterated for t rounds using incremental training, and the objective function is updated to:

[0265]

[0266] The final output of XGBoost is:

[0267]

[0268] Step 5.3: After the second-layer meta-learner is trained and tested, the output result is the lithium battery capacitance prediction result after stacking fusion of the FITS model and the IFELM model.

[0269] Stacking fusion not only reduces the possible deviation of a single model and improves the accuracy of the overall prediction, but also utilizes the diversity of models to improve the overall performance and enhance the model's ability to generalize data.

[0270] Step 6: Figure 4 As shown in the figure, in view of the error between the predicted result and the observed value, the error sequence is re-entered into the FITS model to perform error prediction and obtain the capacitance error prediction result. The specific process is as follows:

[0271] The initial prediction after stacking fusion will produce a prediction error with the original data. The actual capacitance data is subtracted from the initial prediction result to obtain the error time series of the capacitance data. The mathematical expression of this process is as follows:

[0272] Errorcap =Ovalue cap -Ivalue cap

[0273] In the formula, Error cap Indicates the error value of capacitance data, Ovalue cap Represents the actual observed value of the capacitance data, Ivalue cap Represents the preliminary predicted value of capacitance data.

[0274] The error time series of the lithium battery capacitance data is reconstructed into input, and the Error is analyzed using the FITS model. cap Make a prediction and get the error prediction result IError of the capacitance data cap .

[0275] Step 7: Superimpose the prediction results in step 5 and step 6 to obtain the final capacitance prediction result, convert it according to the capacitance-life formula, and obtain the remaining life prediction result of the lithium battery.

[0276] The final prediction result is obtained by adding the initial prediction result and the error prediction result. The formula is as follows:

[0277] Fvalue cap =Ivalue cap +IError cap

[0278] In the formula, Fvalue cap Represents the final predicted value of lithium battery capacitance.

[0279] Define appropriate failure thresholds based on different lithium battery capacitance data. When the capacitance prediction value reaches the set failure threshold, calculate the remaining life of the lithium battery. The formula is as follows:

[0280]

[0281] Sbc now =Sbc Max safe -Sbc current =RUL

[0282] In the formula, Sbc Max safe Represents the maximum safe cycle number of lithium batteries, Sbc current Represents the current number of lithium battery cycles, Sbc now It is the current remaining number of safe cycles, that is, the remaining life of the lithium battery.

[0283] This application only needs to obtain a large amount of historical lithium battery capacitance data and decompose and process these data to evaluate the performance of the battery. It has a faster response speed and higher prediction accuracy, can effectively predict the capacitance data of the lithium battery, and judge the remaining life of the lithium battery.

[0284] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable people familiar with the technology to understand the content of the present invention and implement it accordingly, and they cannot be used to limit the protection scope of the present invention. Any equivalent transformation or modification made according to the spirit of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for predicting the remaining service life of a lithium battery based on Stacking fusion, characterized in that: The following steps are involved: (1) Obtain historical capacitance data of lithium batteries in advance, decompose the historical capacitance data using robust local mean decomposition, and introduce fuzzy entropy to aggregate the component data to reduce the number of sequences; (2) Using time-varying filtered empirical mode decomposition (TVFEMD) to perform secondary decomposition on the modal component with the highest entropy value, a subsequence with higher resolution is obtained; the original capacitance data is then divided into a sequence with higher resolution after TVFEMD decomposition and a sequence without TVFEMD decomposition; (3) The reverse learning strategy is used to improve the initialization population of the wave search algorithm WSA, and the IWSA algorithm is obtained to improve the global search capability and avoid falling into the local optimum; (4) The lightweight time series analysis model FITS is used to process the higher resolution series after TVFEMD decomposition, and the inverse extreme learning machine model IFELM is used to process the series without TVFEMD decomposition. The IWSA algorithm is used to optimize the interpolation rate of the FITS model and the regularization parameter of the IFELM model to obtain preliminary lithium battery capacitance prediction results; (5) The prediction values ​​of the FITS and IFELM models are fused using the Stacking algorithm, and XGBoost is selected as the second-layer meta-learner of the Stacking framework to obtain the fused capacitance prediction results; (6) There is an error between the predicted result obtained in step (5) and the observed value. The error sequence is re-input into the FITS model to perform error prediction and obtain the capacitance error prediction result; (7) The prediction results in step (5) and step (6) are superimposed to obtain the final capacitance prediction result, and finally converted according to the capacitance-life formula to obtain the remaining life prediction result of the lithium battery.

2. According to claim 1, a method for predicting the remaining service life of a lithium battery based on stacking fusion, characterized in that: The implementation process of step (1) is as follows: First, the mirror expansion algorithm is used to select capacitance data symmetrically at the left and right ends, and then the data is mirrored and expanded, and then the boundary conditions are calculated; Next, perform envelope calculation and define the step center as: In the formula, B zhong is the step center, B chang is the step size, P(g) is the probability of capacitance data in each step, P * (g) is the probability value of the capacitance data within the step and at the step boundary; P ** (g) refers to the probability that each capacitance data is at the edge of the step; Define the step size standard deviation τ r for: The definition expression of envelope data in RLMD is as follows: In the formula, represents the root mean square value, Represents the value of kurtosis, which are defined as follows: In the formula, β j (i) represents the instantaneous amplitude of the jth component, represents the average value of capacitance data; The fuzzy entropy of the time series is calculated as follows: In the formula, Q RWD is the embedding dimension, S JCD is the data length, F W is the similarity tolerance in the range of (0.1-0.25SD), SD is the standard deviation of the raw capacitance data.

3. The method for predicting the remaining service life of a lithium battery based on stacking fusion according to claim 1, characterized in that: The implementation process of step (2) is as follows: (21) For the capacitor data with the highest input entropy value, TFV shuru Perform Hilbert transform to obtain the transformed TFV * shuru , and calculate its instantaneous amplitude SF and instantaneous phase XF, the formula is as follows: XF=arctan[TFV shuru / TFV * shuru ] Corresponding analytical capacitance data JIE xi for: JIE xi =TFV shuru +TFV * shuru =SFe XF (22) Interpolate according to the local upper and lower limits of SF to obtain the curve QU xian1 and QU xian2 , the corresponding amplitude is expressed as Zheng F1 He Zheng F2 : About SF 2 Interpolate the upper and lower limits to get SF cz1 , SF cz2 , calculate the instantaneous frequency component SP * 1 and SP * 2: Local cutoff frequency JIE * zhi calculate: (twenty three) by The local extreme points are used as nodes, and the B-spline approximate filter is used to filter QU xian Further interpolation is performed to obtain the filtering result Lv * : If θ=S K / SP avg ≤ζ=0.1, then TFV shuru As an IMF component, otherwise TFV shuru -Lu * As the new capacitance input data, and repeat steps (21) to (23); where ζ is the bandwidth threshold, SP avg is the weighted mean instantaneous frequency, S K is the instantaneous bandwidth; (24) Capacitor data with the highest entropy value TFV shuru After TVFEMD decomposition, we get S subsequences {Lu i |i=1,2,…,S},Lu i is the ith subsequence, and satisfies: By applying the time-varying filtering empirical mode decomposition technology, the sequence with the highest entropy value is decomposed to obtain a subsequence with higher resolution, which is used for the prediction of the FITS model; other sequences that have not undergone time-varying filtering empirical mode decomposition are used for the prediction of the IFELM model.

4. The method for predicting the remaining service life of a lithium battery based on stacking fusion according to claim 1, characterized in that: The implementation process of step (3) is as follows: (31) In the initialization stage, the number of particles is set to n, and the matrix is ​​used to simulate the position of the electromagnetic wave particle Elc: Where d represents the dimension of the problem; the fitness value of the population can be represented by a vector: FIT=[fit([Elc 11 ,Elc 12 ,…Elc 1d ]);fit([Elc 21 ,Elc 22 ,…Elc 2d ])…fit([Elc n1 ,Elc n2 ,…Elc nd ])] In the formula, fit([Elc n1 ,Elc n2 ,…Elc nd ]) represents the fitness value of the individual; Prepare u random numbers q1, q2, ..., q u Initialize the particle position from 0 to 1: Elc=Loc * (ub-lb)+lb In the formula, Loc i is the uniform q i ,Loc * is a random value in x, lb and ub represent the upper and lower boundaries of the search space; (32) In the global exploration phase, let the vector Elc min Contains the minimum value of the variable Elc in each dimension, the vector Elc max Contains the maximum value of Elc in each dimension; fit mean is the average value of the sum of all particle fitness values, and rand1 represents a random variable between 0 and 1: (33) The local survey phase is divided into three stages: transmitting electromagnetic waves, reflecting electromagnetic waves, and receiving electromagnetic waves; (34) Deterministic optimization technology is introduced, and the mathematical formula is: Elc i =Elc i -Ssf·Dot i Where Ssf represents the step size coefficient; (35) Determine the particles that exceed the boundary and randomly set them within the search range. The formula is as follows: Elc i =lb+rand·(ub-lb)if Elc i >ub or Elc i <lb In the formula, rand represents a d-dimensional randomized column vector between (0, 1); (36) The initialization of the population is crucial to finding the optimal solution. Therefore, a reverse learning strategy is introduced to generate a reverse learning population to enhance the diversity of the population and reduce the probability of falling into the local optimal value, thereby enhancing the performance of the WSA algorithm. The reverse learning model is defined as follows: RL * I =ub+lb-RL I Where RL I ∈[lb,ub], I∈[1,d].

5. The method for predicting the remaining service life of a lithium battery based on stacking fusion according to claim 1, characterized in that: The implementation process of using the lightweight time series analysis model FITS to process the higher resolution sequence decomposed by TVFEMD in step (4) is as follows: The discrete Fourier transform DFT of the complex sequence is calculated by fast Fourier transform FFT to map the discrete time signal from the time domain to the complex frequency domain; the complex formula of the frequency component is: Fri(f)=|Fri(f)|e jθ(f) Where Fr(f) is the complex number of the frequency component at frequency f, |Fr(f)| is the amplitude of the component, and θ(f) is the phase of the component; The time shift of a signal corresponds to a phase shift in the frequency domain, especially in the complex frequency domain, which is represented by multiplying a unit complex exponential element with the corresponding phase. If the signal Xi(t) is shifted forward in time by a constant τ, the signal Xi(t-τ) is obtained, and the Fourier transform is given as follows: Fr τ (f)=e -j2πfτ Fr(f)=|Fr(f)|e j(θ(f)-2πfτ) =[cos(-2πfτ)+jsin(-2πfτ)]Fr(f) The amplitude of the shifted signal is still |Fr(f)|, but the phase θ τ The displacement of (f) = θ(f)-2πfτ is linearly related to the time shift; in the complex frequency domain, each frequency component is represented by a complex number, which contains amplitude and phase information; A low-pass filter LPF is introduced to produce a simpler frequency domain by discarding frequency components higher than the specified cutoff frequency COF; The complex-valued linear layer is responsible for performing interpolation operations in the complex frequency domain. It realizes the prediction or anomaly detection of time series by learning the amplitude adjustment and phase shift of frequency components. In order to control the output length of the model, the interpolation rate is introduced and applied to the frequency domain. The formula is as follows: In the formula, η is the difference rate, which represents the output length L of the model o Corresponding to the input length L i The ratio of The interpolated complex frequency domain data is converted back to the time domain through inverse rFFT to form a time series segment for supervised learning. The formula is as follows: Xi -1 (t)=FFT -1 Fr(f) In the formula, Xi -1 (t) is the capacitance time series data after interpolation processing, FFT -1 is the inverse Fourier transform.

6. The method for predicting the remaining service life of a lithium battery based on stacking fusion according to claim 1, characterized in that: The implementation process of using the inverse extreme learning machine model IFELM to process the sequence that has not been decomposed by TVFEMD in step (4) is as follows: Assume that in an ELM with l hidden layer nodes, an additional hidden layer node is added, and the output weight is: The input bias is At this time, the hidden layer output is expressed as: In the formula, Yc i (i=l,l+1) represents the ELM output with i hidden layer nodes; Use the no-inverse algorithm to update the regularized pseudo-inverse to avoid the inverse operation in the weight update process. The operation method is: Iterative Calculation The calculation method is: The calculation method is: make but Substituting in:

7. The method for predicting the remaining service life of a lithium battery based on stacking fusion according to claim 1, characterized in that: In step (4), the IWSA algorithm is used to optimize the interpolation rate of the FITS model and the regularization coefficient of the IFELM model, and the steps are as follows: Initialize the relevant parameters of the IWSA algorithm, including the initial particle position, the upper and lower limits of the search space, the maximum number of iterations, and the current number of iterations; The training set of lithium battery capacitance data is input into the FITS and IFELM models, and the interpolation rate and regularization coefficient of the models are optimized respectively; After the three steps of transmitting electromagnetic waves, reflecting electromagnetic waves and receiving electromagnetic waves in the local survey phase of the IWSA algorithm, the new particle position is obtained, and the fitness value of each particle is calculated. When the preset termination condition of the model is met, the optimal particle position is determined, which is the optimal value of the interpolation rate of the FITS model and the regularization coefficient of the IFELM model. The optimized FITS model predicts the component with the highest entropy value after TVFEMD decomposition, and the optimized IFELM model predicts the remaining components to obtain preliminary lithium battery capacitance prediction data.

8. The method for predicting the remaining service life of a lithium battery based on stacking fusion according to claim 1, characterized in that: The implementation process of step (5) is as follows: (51) FITS and IFELM are used as the basic models of the first layer, and the preliminary lithium battery capacitance prediction results obtained in step (4) are used as the input of the second layer metamodel; (52) XGBoost is selected as the second-layer meta-learner. The mathematical expression of XGBoost is: in, is the final x j The corresponding model prediction value; x j is the jth sample; Num tree is the number of decision trees; Num test is the number of training samples; ALL tree is the set of all trees; In each iteration, a newly generated regression tree is added based on the previous step to fit the residual of the previous prediction. The iterative process is as follows: The XGBoost objective function is: In the formula, y j is the true value; is the loss function; XGBoost is iterated for t rounds using incremental training, and the objective function is updated to: The final output of XGBoost is: (53) After training and testing the second-layer meta-learner, the output results are the lithium battery capacitance prediction results after stacking fusion of the FITS model and the IFELM model.

9. The method for predicting the remaining service life of a lithium battery based on stacking fusion according to claim 1, characterized in that: The implementation process of step (6) is as follows: The initial prediction after stacking fusion will produce a prediction error with the original data. The actual capacitance data is subtracted from the initial prediction result to obtain the error time series of the capacitance data: Error cap =Ovalue cap -Ivalue cap In the formula, Error cap Indicates the error value of capacitance data, Ovalue cap Represents the actual observed value of the capacitance data, Ivalue cap represents the preliminary predicted value of capacitance data; The error time series of lithium battery capacitance data is reconstructed into input, and the Error is analyzed using the FITS model. cap Make a prediction and get the error prediction result IError of the capacitance data cap .

10. The method for predicting the remaining service life of a lithium battery based on stacking fusion according to claim 1, characterized in that: The implementation process of step (7) is as follows: Add the initial prediction result and the error prediction result to get the final prediction result: Fvalue cap =Ivalue cap +IError cap In the formula, Fvalue cap Indicates the final predicted value of lithium battery capacitance, Error cap Indicates the error value of capacitance data, IError cap is the error prediction result of capacitance data; Define appropriate failure thresholds based on different lithium battery capacitance data. When the capacitance prediction value reaches the set failure threshold, calculate the remaining life of the lithium battery: Sbc now =Sbc Maxsafe -Sbc current =RUL In the formula, Sbc Maxsafe Represents the maximum safe cycle number of lithium batteries, Sbc current Represents the current number of lithium battery cycles, Sbc now It is the current remaining number of safe cycles, that is, the remaining life of the lithium battery.

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