Lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism

Abstract

The invention discloses a lithium battery RUL prediction method based on phase space reconstruction and a multi-space attention mechanism. The lithium battery RUL prediction method comprises the following steps: 1) acquiring a charging current and a voltage sequence in each charging and discharging cycle of a lithium battery; 2) constructing a capacity phase space reconstruction model, and inputting the obtained data to obtain a capacity phase space reconstruction matrix; 3) dividing the capacity phase space reconstruction matrix into different subspaces; 4) calculating attention scores of different subspaces, and combining the attention scores into a multi-space attention matrix; 5) constructing an off-line RUL prediction model; and 6) collecting a charging current sequence and a charging voltage sequence of the lithium battery to be predicted, and sequentially inputting the collected data into the capacity phase space reconstruction model and the offline RUL prediction model to obtain a predicted RUL. According to the method, the C-C algorithm is used for carrying out space-time embedding on the degradation capacity of the lithium battery, the degradation mode and trend in a multi-dimensional subspace are reconstructed, and the weights of different degradation rate stages are dynamically and selectively adjusted in combination with a multi-space attention mechanism, so that the prediction precision is improved.

Description

Technical Field

[0001] The present invention relates to the field of battery technology, and in particular to a lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism. Background Art

[0002] As an important supporting technology for promoting the optimization of modern energy structure, energy storage system has become an indispensable core component of modern energy system. As an environmentally friendly, high-energy and recyclable energy storage solution, lithium-ion battery has become one of the mainstream choices of current energy storage technology. However, during the degradation process of lithium batteries, the performance of the battery gradually decreases, and the degradation rates at different stages usually show significant differences. For example, the degradation rate is relatively slow in the initial stage, but it may show accelerated or even nonlinear drastic changes in the middle and late stages. This multi-stage and multi-rate degradation behavior makes it difficult for the analysis based on one-dimensional capacity data to fully capture the complex dynamic characteristics and degradation laws of each stage, which has an adverse impact on the accuracy and reliability of the remaining useful life (RUL) prediction.

[0003] Therefore, a nonlinear dynamic analysis technology is urgently needed to reveal the dynamic characteristics of battery capacity degradation and a characterization mechanism of different degradation stages with dynamic weight allocation, so as to improve the adaptability of RUL prediction model in complex nonlinear degradation environment. This is of great significance for the life optimization management of energy storage system. Summary of the invention

[0004] The object of the present invention is to provide a lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism, comprising the following steps:

[0005] 1) Obtain the charging current sequence and charging voltage sequence in each charge and discharge cycle of the lithium battery.

[0006] 2) Construct a capacity phase space reconstruction model, and input the acquired charging current sequence and charging voltage sequence into the capacity phase space reconstruction model to obtain a capacity phase space reconstruction matrix.

[0007] 3) According to the capacity degradation rate characteristics of the capacity phase space reconstruction matrix, the capacity phase space reconstruction matrix is ​​divided into different subspaces.

[0008] 4) A multi-head attention mechanism is applied to calculate the attention scores of different subspaces, and the attention scores of different subspaces are combined into a multi-space attention matrix through a fully connected layer.

[0009] 5) The multi-spatial attention matrix is ​​passed to the recurrent neural network GRU to construct an offline RUL prediction model with the capacity phase space reconstruction matrix as input and the remaining service life RUL of the lithium battery as output.

[0010] 6) Collect the charging current sequence and charging voltage sequence of the lithium battery to be predicted, and input them into the capacity phase space reconstruction model to obtain the capacity phase space reconstruction matrix of the lithium battery to be predicted.

[0011] 7) The capacity phase space reconstruction matrix of the lithium battery to be predicted is input into the offline RUL prediction model to predict the remaining service life RUL of the lithium battery to be predicted.

[0012] Further, in step 2), the steps of obtaining the capacity phase space reconstruction matrix are as follows:

[0013] 2.1) Smoothing the data input into the capacity phase space reconstruction model to obtain processed data.

[0014] 2.2) Based on the processed data, calculate the battery capacity.

[0015] 2.3) Based on the battery capacity, the CC algorithm is used to determine the optimal embedding dimension and time delay, and the capacity phase space reconstruction matrix is ​​constructed.

[0016] Furthermore, the smoothing process uses sliding mean filtering, as shown below:

[0017]

[0018] Where i is the charge-discharge cycle index. t represents the time. p is the data collection number. L is the sliding window size. Respectively represent the current and voltage data at time t in the i-th cycle after smoothing. i,t 、V i,t They respectively represent the collected values ​​of current and voltage at time t in the i-th cycle.

[0019] Further, the battery capacity is as follows:

[0020]

[0021] Where i is the charge-discharge cycle index, n is the total number of cycles, t represents the time, p is the data collection number, and e is the end time. Respectively represent the current and voltage data at time t in the i-th cycle after smoothing. nom is the nominal voltage. Q i represents the charging capacity of the i-th cycle.

[0022] Furthermore, the battery capacity is normalized by normalization processing, and the calculation formula of the normalization processing is as follows:

[0023]

[0024] Where, X * is the data after normalization, X is the data to be normalized, X max , X min are the maximum and minimum values ​​in the sequence X respectively.

[0025] Further, in step 2.3), the steps of determining the optimal embedding dimension and time delay using the CC algorithm are as follows:

[0026] 2.3.1) Based on the battery capacity, calculate the cross-correlation integral as follows:

[0027]

[0028] Where C(m,n,r,τ) is the cross-correlation integral. i and j are the charge and discharge cycle indexes, and n is the total number of cycles. i , Q j denote the charge capacity of the i-th and j-th cycles, respectively. m denotes the embedding dimension, M is the number of embedding points in the m-dimensional space, and M = n-(m-1)τ, τ denotes the time delay, and r denotes the spatial distance.

[0029] The piecewise function F is as follows:

[0030]

[0031] 2.3.2) According to the cross-correlation integral and time delay average strategy, the nonlinear characteristic function is calculated as follows:

[0032]

[0033] Where S(m,n,r,τ) is the nonlinear characteristic function, S represents the time delay index, and Both represent cross-correlation integrals.

[0034] 2.3.3) The nonlinear characteristic function S(m,n,r,τ) is converted into the position with the minimum rate of change of any spatial distance r, and the optimal time delay τ is derived.

[0035] The position with the minimum rate of change of the arbitrary spatial distance r is as follows:

[0036] ΔS(m,τ)=max{S(m,r j ,τ)}-min{S(m,r j ,τ)} (7)

[0037] In the formula, ΔS(m,τ) represents the position with the minimum rate of change of any spatial distance r, S(m,r j ,τ) represents the nonlinear characteristic function of any spatial distance r when n is infinite.

[0038] 2.3.4) The optimal embedding dimension is obtained based on the delay window solution, as shown below:

[0039] τ window =(m-1)τ (8)

[0040]

[0041] In the formula, τ window is the delay window. It is the average value of the position with the minimum rate of change of any spatial distance r. is the average value of the nonlinear characteristic function at any spatial distance r.

[0042] Furthermore, the capacity phase space reconstruction matrix is ​​as follows:

[0043]

[0044] Where i is the charge-discharge cycle index, n is the total number of cycles, and m represents the embedding dimension. i represents the charging capacity of the i-th cycle. R , Q No They represent the incremental capacity with regeneration and the incremental capacity without regeneration respectively.

[0045] Furthermore, the regenerative incremental capacity Q R and non-regenerative incremental capacity Q No As shown below:

[0046]

[0047] Where q is the upper limit of the regenerative incremental capacity.

[0048] Furthermore, the multi-spatial attention matrix is ​​as follows:

[0049]

[0050] HAM=σ(MH*W space +b space ) (14)

[0051] Where Attention is the single-head attention score, A is the query vector matrix, K is the key vector matrix, V is the key vector matrix, T is the matrix transpose, and d k is the scaling factor, Concat represents matrix concatenation, i r is the single-head attention index, Represents single-head attention i r The hidden state of h is the number of single-head attention, For single-head attention i r The query vector matrix, For single-head attention i r The key vector matrix of For single-head attention i r The key vector matrix, σ is the activation function, W, W space are the subspace weight matrix and the multi-space weight matrix, respectively, space is the multi-space bias. HAM is the multi-space attention matrix. MH is the concatenated single-head attention matrix.

[0052] Furthermore, the offline RUL prediction model is as follows:

[0053] z t =σ1(w z *[h t-1 ,HAM t ]+b z ) (15)

[0054] r t =σ1(w r *[h t-1 ,HAM t ]+b r ) (16)

[0055]

[0056] In the formula, HAM t is the multi-spatial attention matrix input at time t. t 、r t , h t They represent the update gate, reset gate, candidate hidden state, and hidden state output at time t respectively. t-1 is the output of the hidden state at time t-1. σ1 and σ2 are the sigmoid function and the hyperbolic tangent activation function respectively, and ⊙ is the dot product of the matrix elements. z 、w r 、w h are the weight matrices of the update gate, reset gate, and hidden state, respectively. z 、b r 、b h They are the update gate, reset gate, and hidden state bias respectively.

[0057] The technical effect of the present invention is unquestionable. The present invention proposes a lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism. The method uses the CC algorithm to perform spatiotemporal embedding of lithium battery degradation capacity, reconstructs degradation patterns and trends in multi-dimensional subspaces, and combines the multi-space attention mechanism to dynamically and selectively adjust the weights of different degradation rate stages to improve prediction accuracy.

[0058] The present invention adopts CC algorithm to reconstruct the phase space of one-dimensional sequence data, which can more comprehensively characterize the dynamic behavior patterns and degradation rate differences of lithium batteries in different degradation stages, thereby providing a rich data basis for subsequent feature extraction and analysis.

[0059] In the reconstructed high-dimensional space, the present invention further applies the multi-space attention mechanism to identify the key stages that have a significant impact on the degradation characteristics, give them higher weights first, and effectively balance the feature expression strength of different degradation stages. It is crucial to enhance the robustness and reliability of RUL prediction in short-term and long-term applications.

[0060] The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism proposed in the present invention can effectively capture the dynamic characteristics of the battery at different degradation stages, showing strong robustness and high prediction accuracy, and providing strong support for lithium battery health management and life prediction in practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is a flow chart of a lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism provided by an embodiment of the present invention;

[0062] Figure 2 is the capacity aging curve of batteries B0005 and B0006 of the NASA battery data set provided by an embodiment of the present invention;

[0063] Figure 3 is a smooth curve for calculating the capacity of a B0006 battery provided in an embodiment of the present invention;

[0064] Figure 4 This is a RUL prediction comparison experiment result diagram using the first 30 cycle capacity data of B0006 battery provided by an embodiment of the present invention;

[0065] Figure 5 This is a RUL prediction comparison experiment result diagram using the first 50 cycle capacity data of B0006 battery provided by an embodiment of the present invention;

[0066] Figure 6 This is a graph of RUL prediction comparison experiment results using the first 70 cycle capacity data of B0006 battery provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0067] The present invention is further described below in conjunction with the embodiments, but it should not be understood that the above subject matter of the present invention is limited to the following embodiments. Without departing from the above technical ideas of the present invention, various substitutions and changes are made according to the common technical knowledge and customary means in the art, which should all be included in the protection scope of the present invention.

[0068] Embodiment 1:

[0069] See also Figures 1 to 6 , a lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism includes the following steps:

[0070] 1) Obtain the charging current sequence and charging voltage sequence in each charge and discharge cycle of the lithium battery.

[0071] 2) Construct a capacity phase space reconstruction model, and input the acquired charging current sequence and charging voltage sequence into the capacity phase space reconstruction model to obtain a capacity phase space reconstruction matrix.

[0072] 3) According to the capacity degradation rate characteristics of the capacity phase space reconstruction matrix, the capacity phase space reconstruction matrix is ​​divided into different subspaces.

[0073] 4) A multi-head attention mechanism is applied to calculate the attention scores of different subspaces, and the attention scores of different subspaces are combined into a multi-space attention matrix through a fully connected layer.

[0074] 5) The multi-spatial attention matrix is ​​passed to the recurrent neural network GRU to construct an offline RUL prediction model with the capacity phase space reconstruction matrix as input and the remaining service life RUL of the lithium battery as output.

[0075] 6) Collect the charging current sequence and charging voltage sequence of the lithium battery to be predicted, and input them into the capacity phase space reconstruction model to obtain the capacity phase space reconstruction matrix of the lithium battery to be predicted.

[0076] 7) The capacity phase space reconstruction matrix of the lithium battery to be predicted is input into the offline RUL prediction model to predict the remaining service life RUL of the lithium battery to be predicted.

[0077] Embodiment 2:

[0078] The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism, the main technical content is shown in Example 1, further, in step 2), the steps of obtaining the capacity phase space reconstruction matrix are as follows:

[0079] 2.1) Smoothing the data input into the capacity phase space reconstruction model to obtain processed data.

[0080] 2.2) Based on the processed data, calculate the battery capacity.

[0081] 2.3) Based on the battery capacity, the CC algorithm is used to determine the optimal embedding dimension and time delay, and the capacity phase space reconstruction matrix is ​​constructed.

[0082] Embodiment 3:

[0083] The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism, the main technical content is shown in any one of embodiments 1 to 2, further, the smoothing process adopts sliding mean filtering, as shown below:

[0084]

[0085] Where i is the charge-discharge cycle index. t represents the time. p is the data collection number. L is the sliding window size. Respectively represent the current and voltage data at time t in the i-th cycle after smoothing. i,t 、V i,t They respectively represent the collected values ​​of current and voltage at time t in the i-th cycle.

[0086] Embodiment 4:

[0087] The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism, the main technical content is shown in any one of embodiments 1 to 3, and further, the battery capacity is as follows:

[0088]

[0089] Where i is the charge-discharge cycle index, n is the total number of cycles, t represents the time, p is the data collection number, and e is the end time. Respectively represent the current and voltage data at time t in the i-th cycle after smoothing. nom is the nominal voltage. Q i represents the charging capacity of the i-th cycle.

[0090] Embodiment 5:

[0091] The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism, the main technical content is shown in any one of embodiments 1 to 4, further, the battery capacity is also normalized by normalization processing to standardize the data, and the calculation formula of the normalization processing is as follows:

[0092]

[0093] In the formula, X *is the data after normalization, X is the data to be normalized, X max , X min are the maximum and minimum values ​​in the sequence X respectively.

[0094] Embodiment 6:

[0095] The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism, the main technical content is shown in any one of embodiments 1 to 5, further, in step 2.3), the steps of using the CC algorithm to determine the optimal embedding dimension and time delay are as follows:

[0096] 2.3.1) Based on the battery capacity, calculate the cross-correlation integral as follows:

[0097]

[0098] Where C(m,n,r,τ) is the cross-correlation integral. i and j are the charge and discharge cycle indexes, and n is the total number of cycles. i , Q j denote the charge capacity of the i-th and j-th cycles, respectively. m denotes the embedding dimension, M is the number of embedding points in the m-dimensional space, and M = n-(m-1)τ, τ denotes the time delay, and r denotes the spatial distance.

[0099] The piecewise function F is as follows:

[0100]

[0101] 2.3.2) According to the cross-correlation integral and time delay average strategy, the nonlinear characteristic function is calculated as follows:

[0102]

[0103] Where S(m,n,r,τ) is the nonlinear characteristic function, S represents the time delay index, and Both represent cross-correlation integrals.

[0104] 2.3.3) The nonlinear characteristic function S(m,n,r,τ) is converted into the position with the minimum rate of change of any spatial distance r, and the optimal time delay τ is derived.

[0105] The position with the minimum rate of change of the arbitrary spatial distance r is as follows:

[0106] ΔS(m,τ)=max{S(m,r j ,τ)}-min{S(m,r j ,τ)} (7)

[0107] In the formula, ΔS(m,τ) represents the position with the minimum rate of change of any spatial distance r, S(m,r j ,τ) represents the nonlinear characteristic function of any spatial distance r when n is infinite.

[0108] 2.3.4) The optimal embedding dimension is obtained based on the delay window solution, as shown below:

[0109] τ window =(m-1)τ (8)

[0110]

[0111] In the formula, τ window is the delay window. It is the average value of the position with the minimum rate of change of any spatial distance r. is the average value of the nonlinear characteristic function at any spatial distance r.

[0112] Embodiment 7:

[0113] The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism, the main technical content is shown in any one of embodiments 1 to 6, further, the capacity phase space reconstruction matrix is ​​as follows:

[0114]

[0115] Where i is the charge-discharge cycle index, n is the total number of cycles, m represents the embedding dimension, and Q i represents the charging capacity of the i-th cycle. R , Q No They represent the incremental capacity with regeneration and the incremental capacity without regeneration respectively.

[0116] Embodiment 8:

[0117] A lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism, the main technical content of which is shown in any one of embodiments 1 to 7, further, the regenerative incremental capacity Q R and non-regenerative incremental capacity Q No As shown below:

[0118]

[0119] Where q is the upper limit of the regenerative incremental capacity.

[0120] Embodiment 9:

[0121] The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism, the main technical content is shown in any one of embodiments 1 to 8, and further, the multi-space attention matrix is ​​as follows:

[0122]

[0123] HAM=σ(MH*W space +b space ) (14)

[0124] Where Attention is the single-head attention score, A is the query vector matrix, K is the key vector matrix, V is the key vector matrix, T is the matrix transpose, and d k is the scaling factor, Concat represents matrix concatenation, i r is the single-head attention index, Represents single-head attention i r The hidden state of h is the number of single-head attention, For single-head attention i r The query vector matrix, For single-head attention i r The key vector matrix of For single-head attention i r The key vector matrix, σ is the activation function, W, W space are the subspace weight matrix and the multi-space weight matrix, respectively, space is the multi-space bias. HAM is the multi-space attention matrix. MH is the concatenated single-head attention matrix.

[0125] Embodiment 10:

[0126] The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism, the main technical content is shown in any one of embodiments 1 to 9, further, the offline RUL prediction model is as follows:

[0127] z t =σ1(w z *[h t-1 ,HAM t ]+b z ) (15)

[0128] r t =σ1(w r *[h t-1 ,HAM t ]+b r ) (16)

[0129]

[0130] In the formula, HAM t is the multi-spatial attention matrix input at time t. t 、r t , ht They represent the update gate, reset gate, candidate hidden state, and hidden state output at time t respectively. t-1 is the output of the hidden state at time t-1. σ1 and σ2 are the sigmoid function and the hyperbolic tangent activation function respectively, and ⊙ is the dot product of the matrix elements. z 、w r 、w h are the weight matrices of the update gate, reset gate, and hidden state, respectively. z 、b r 、b h They are the update gate, reset gate, and hidden state bias respectively.

[0131] Embodiment 11:

[0132] See also Figures 1 to 6 , a lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism includes the following steps:

[0133] 1) Obtain the charging current sequence and charging voltage sequence in each charge and discharge cycle of the lithium battery.

[0134] 2) Construct a capacity phase space reconstruction model, and input the acquired charging current sequence and charging voltage sequence into the capacity phase space reconstruction model to obtain a capacity phase space reconstruction matrix.

[0135] 3) According to the capacity degradation rate characteristics of the capacity phase space reconstruction matrix, the capacity phase space reconstruction matrix is ​​divided into different subspaces.

[0136] 4) A multi-head attention mechanism is applied to calculate the attention scores of different subspaces, and the attention scores of different subspaces are combined into a multi-space attention matrix through a fully connected layer.

[0137] The multi-space attention mechanism adjusts the dynamic relationship between different subspaces and prioritizes focusing on key time periods and degradation patterns that have a significant impact on capacity degradation, thereby effectively improving the accuracy and robustness of the model in short-term and long-term prediction tasks.

[0138] 5) The multi-spatial attention matrix is ​​passed to the recurrent neural network GRU to construct an offline RUL prediction model with the capacity phase space reconstruction matrix as input and the remaining service life RUL of the lithium battery as output.

[0139] 6) Collect the charging current sequence and charging voltage sequence of the lithium battery to be predicted, and input them into the capacity phase space reconstruction model to obtain the capacity phase space reconstruction matrix of the lithium battery to be predicted.

[0140] 7) The capacity phase space reconstruction matrix of the lithium battery to be predicted is input into the offline RUL prediction model to predict the remaining service life RUL of the lithium battery to be predicted.

[0141] Embodiment 12:

[0142] The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism, the main technical content is shown in Example 11, further, in step 2), the steps of obtaining the capacity phase space reconstruction matrix are as follows:

[0143] 2.1) Smoothing the data input into the capacity phase space reconstruction model to obtain processed data.

[0144] 2.2) Based on the processed data, calculate the battery capacity.

[0145] 2.3) Based on the battery capacity, the CC algorithm is used to determine the optimal embedding dimension and time delay, and the capacity phase space reconstruction matrix is ​​constructed.

[0146] Embodiment 13:

[0147] A lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism, the main technical content of which is shown in any one of Embodiments 11 to 12. Further, the smoothing process adopts sliding mean filtering, as shown below:

[0148]

[0149] Where i is the charge-discharge cycle index. t represents the time. p is the data collection number. L is the sliding window size. Respectively represent the current and voltage data at time t in the i-th cycle after smoothing. i,t 、V i,t They respectively represent the collected values ​​of current and voltage at time t in the i-th cycle.

[0150] Embodiment 14:

[0151] A lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism, the main technical content of which is shown in any one of Embodiments 11 to 13. Further, the battery capacity is as follows:

[0152]

[0153] Where i is the charge-discharge cycle index, n is the total number of cycles, t represents the time, p is the data collection number, and e is the end time. Respectively represent the current and voltage data at time t in the i-th cycle after smoothing. nom is the nominal voltage. Q irepresents the charging capacity of the i-th cycle.

[0154] Embodiment 15:

[0155] The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism, the main technical content is shown in any one of Examples 11 to 14. Further, the battery capacity also uses normalization processing to standardize the data, and maps the data to the [-1,1] interval to ensure the uniform distribution of the data in the interval. The calculation formula of the normalization processing is as follows:

[0156]

[0157] Where, X * is the data after normalization, X is the data to be normalized, X max , X min are the maximum and minimum values ​​in the sequence X respectively.

[0158] Embodiment 16:

[0159] The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism, the main technical content is shown in any one of Examples 11 to 15, further, in step 2.3), the steps of determining the optimal embedding dimension and time delay using the CC algorithm are as follows:

[0160] 2.3.1) Based on the battery capacity, calculate the cross-correlation integral as follows:

[0161]

[0162] Where C(m,n,r,τ) is the cross-correlation integral. i and j are the charge and discharge cycle indexes, and n is the total number of cycles. i , Q j denote the charge capacity of the i-th and j-th cycles, respectively. m denotes the embedding dimension, M is the number of embedding points in the m-dimensional space, and M = n-(m-1)τ, τ denotes the time delay, and r denotes the spatial distance.

[0163] The piecewise function F is as follows:

[0164]

[0165] 2.3.2) According to the cross-correlation integral and time delay average strategy, the nonlinear characteristic function is calculated as follows:

[0166]

[0167] Where S(m,n,r,τ) is the nonlinear characteristic function, S represents the time delay index, and Both represent cross-correlation integrals.

[0168] 2.3.3) The nonlinear characteristic function S(m,n,r,τ) is converted into the position with the minimum rate of change of any spatial distance r, and the optimal time delay τ is derived.

[0169] Assuming that m and τ are fixed, when n approaches infinity, at all spatial distances r, S(m,n,r,τ) can be derived from the cross-correlation integral C(m,n,r,τ) to be always equal to 0. Therefore, the optimal delay τ can be the position with the minimum rate of change of S(m,n,r,τ) to any relative spatial distance r.

[0170] The position with the minimum rate of change of the arbitrary spatial distance r is as follows:

[0171] ΔS(m,τ)=max{S(m,r j ,τ)}-min{S(m,r j ,τ)} (7)

[0172] In the formula, ΔS(m,τ) represents the position with the minimum rate of change of any spatial distance r, S(m,r j ,τ) represents the nonlinear characteristic function of any spatial distance r when n is infinite.

[0173] 2.3.4) According to the delay window At the minimum value, Equivalent to the time delay τ, the embedding dimension m can be obtained by τ window =(m-1)τ. The optimal embedding dimension is obtained based on the delay window solution, as shown below:

[0174] τ window =(m-1)τ (8)

[0175]

[0176] In the formula, τ wi nd ow is the delay window. It is the average value of the position with the minimum rate of change of any spatial distance r. is the average value of the nonlinear characteristic function at any spatial distance r.

[0177] Embodiment 17:

[0178] The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism, the main technical content is shown in any one of embodiments 11 to 16, further, the capacity phase space reconstruction matrix is ​​as follows:

[0179]

[0180] Where i is the charge-discharge cycle index, n is the total number of cycles, m represents the embedding dimension, and Q i represents the charging capacity of the i-th cycle. R , Q No They represent the incremental capacity with regeneration and the incremental capacity without regeneration respectively.

[0181] Embodiment 18:

[0182] A lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism, the main technical content of which is shown in any one of embodiments 11 to 17, further, the regenerative incremental capacity Q R and non-regenerative incremental capacity Q No As shown below:

[0183]

[0184] Where q is the upper limit of the regenerative incremental capacity.

[0185] Embodiment 19:

[0186] The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism, the main technical content is shown in any one of embodiments 11 to 18, and further, the multi-space attention matrix is ​​as follows:

[0187]

[0188] HAM=σ(MH*W space +b space ) (14)

[0189] Where Attention is the single-head attention score, A is the query vector matrix, K is the key vector matrix, V is the key vector matrix, T is the matrix transpose, and d k is the scaling factor, Concat represents matrix concatenation, i r is the single-head attention index, Represents single-head attention i r The hidden state of h is the number of single-head attention, For single-head attention i r The query vector matrix, For single-head attention i r The key vector matrix of For single-head attention i r The key vector matrix, σ is the activation function, W, W space are the subspace weight matrix and the multi-space weight matrix, respectively, spaceis the multi-space bias. HAM is the multi-space attention matrix. MH is the concatenated single-head attention matrix.

[0190] Embodiment 20:

[0191] The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism, the main technical content is shown in any one of embodiments 11 to 19, further, the offline RUL prediction model is as follows:

[0192] z t =σ1(w z *[h t-1 ,HAM t ]+b z ) (15)

[0193] r t =σ1(w r *[h t-1 ,HAM t ]+b r ) (16)

[0194]

[0195] In the formula, HAM t is the multi-spatial attention matrix input at time t. t 、r t , h t They represent the update gate, reset gate, candidate hidden state, and hidden state output at time t respectively. t-1 is the output of the hidden state at time t-1. σ1 and σ2 are the sigmoid function and the hyperbolic tangent activation function respectively, and ⊙ is the dot product of the matrix elements. z 、w r 、w h are the weight matrices of the update gate, reset gate, and hidden state, respectively. z 、b r 、b h They are the update gate, reset gate, and hidden state bias respectively.

[0196] Embodiment 21:

[0197] See also Figures 1 to 6 , a lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism includes the following steps:

[0198] S1. Collect the charging current and voltage sequence of each charge and discharge cycle of the lithium battery, and use sliding mean filtering to smooth the data.

[0199] S2. Calculate the battery capacity based on the processed current and voltage series and normalize the data.

[0200] S3. Use CC algorithm to determine the optimal embedding dimension and time delay mapping to high-dimensional phase space to obtain the capacity phase space reconstruction matrix.

[0201] S4. Divide the capacity phase space reconstruction matrix into different subspaces according to its capacity degradation rate characteristics.

[0202] S5. Apply the multi-head attention mechanism independently in different subspaces to calculate the attention scores, and combine them into a multi-space attention matrix through the fully connected layer, and pass it to GRU to establish an offline RUL prediction model.

[0203] S6. Execute steps S1-S3 on the lithium battery current and voltage sequence data of the unknown RUL, and input them into step S6 for online lithium battery RUL prediction.

[0204] The specific contents of step S1 are as follows:

[0205] The charging current and voltage sequence in each charge and discharge cycle are [I i,1 ,I i,2 ,…,I i,t …,I i,e ] and [V i,1 ,V i,2 ,…,V i,t …,V i,e ], where I i,t The current value collected at time t in the i-th cycle, e is the end time. V i,t The collected value of the voltage at time t in the i-th cycle, e is the end time. Then the sliding mean filter is used to smooth the current and voltage sequence data to obtain in, and are the smoothed values ​​of current and voltage at time t in the i-th cycle, L is the sliding window size, and p is the data acquisition number.

[0206] The specific contents of step S2 are as follows:

[0207] The battery capacity can be calculated based on the smoothed current and voltage sequence: Among them, Q i is the charging capacity of cycle i, n is the total number of cycles, V nom is the nominal voltage. The data is further normalized by using the maximum and minimum value normalization to map the data to the [-1,1] interval to ensure that the data is evenly distributed within the interval. The normalization formula is: X is the preprocessed data sequence, Xmax and Xmin are the maximum and minimum values ​​in the sequence X respectively.

[0208] The specific content of step S3 is as follows:

[0209] Assume a one-dimensional capacity sequence Q n =[Q1,Q2,…Q i ,…,Q n ], n is the total number of cycles. The optimal embedding dimension and time delay calculated using the CC algorithm.

[0210] First calculate the cross-correlation integral Where M = n-(m-1)τ is the number of embedded points in the m-dimensional space, r represents the spatial distance, τ represents the reconstruction time delay, and the piecewise function

[0211] Then, the nonlinear characteristic function is obtained based on the cross-correlation integral C(m,n,r,τ) and the time delay averaging strategy. Assuming that m and τ are fixed, when n approaches infinity, S(m,n,r,τ) can be derived from the cross-correlation integral C(m,n,r,τ) to be equal to 0 at all spatial distances r. Therefore, the optimal delay τ can be the position where the rate of change of S(m,n,r,τ) to any relative spatial distance r is the minimum, that is, ΔS(m,τ) = max{S(m,r j ,τ)}-min{S(m,r j ,τ)}.

[0212] Finally, according to the delay window At the minimum value, Equivalent to the time delay τ, the embedding dimension m can be obtained by τ window =(m-1)τ and solve.

[0213] The specific content of step S4 is as follows:

[0214] According to the optimal embedding dimension and time delay calculated in step 3, for a one-dimensional capacity sequence Q of length n n =[Q1,Q2,…Q i ,…,Q n ] is reconstructed into a capacity matrix of m×τ dimensions and divided into: capacity degradation with regeneration and without regeneration according to the incremental capacity value. The reconstructed capacity matrix is ​​as follows:

[0215]

[0216] in, The capacity regeneration phenomenon is that the battery capacity will experience a short recovery and increase compared to the previous cycle, with the amplitude usually between 0% and 5%.

[0217] The specific content of step S5 is as follows:

[0218] According to the subspaces with different degradation rates divided in step S4, the multi-head attention mechanism is independently applied to calculate the attention score matrix of each subspace, and they are combined into a multi-space attention matrix HAM through a fully connected layer.

[0219] The multi-space attention mechanism adjusts the dynamic relationship between different subspaces and prioritizes the key periods and degradation patterns that have a significant impact on capacity degradation, thereby effectively improving the accuracy and robustness of the model in short-term and long-term prediction tasks. The calculation process is as follows:

[0220]

[0221] MH=Concat(head1,...,head i ,…,head h )W

[0222] HAM=σ(MH*W space +b space )

[0223] Among them, A is the query vector matrix, K is the key vector matrix, V is the key vector matrix, T is the matrix transpose, dk is the scaling factor, Concat means matrix concatenation, head i =Attention(Q i ,K i ,V i ), i∈{1,2,…,h} is the hidden state of the single-head attention, h is the number of single-head attention, σ is the activation function, W and Wspace are the subspace weight matrix and multi-space weight matrix respectively, and bspace is the multi-space bias.

[0224] Its multi-spatial attention matrix HAM is passed to GRU to establish an offline RUL prediction model as follows:

[0225] z t =σ1(w z *[h t-1 ,HAM t ]+b z )

[0226] r t =σ1(w r *[h t-1 ,HAM t ]+b r )

[0227]

[0228] Among them, HAM tis the multi-spatial attention matrix input at time t. t 、r t , and h t Represent the output of the update gate, reset gate, candidate hidden state and hidden state at time t respectively. σ1 and σ2 are the sigmoid and hyperbolic tangent activation functions respectively, and ⊙ is the dot product of matrix elements. wz, wr and wh are the weight matrices of the update gate, reset gate and hidden layer respectively. bz, br and bh are the biases of the update gate, reset gate and hidden state respectively.

[0229] The specific content of step S6 is as follows:

[0230] Obtaining the phase space reconstruction matrix using lithium battery current and voltage sequence data with unknown RUL It is used as input to the offline RUL prediction model to predict the RUL of unknown lithium batteries.

[0231] Embodiment 22:

[0232] See also Figures 1 to 6 , a lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism includes the following steps:

[0233] S1, collect the charging current and voltage sequence of each charge and discharge cycle of the lithium battery, and use sliding mean filtering to smooth the data;

[0234] In this embodiment, in step S1, the charging current and voltage sequence in each charge and discharge cycle are respectively [I i,1 ,I i,2 ,…,I i,t …,I i,e ] and [V i,1 ,V i,2 ,…,V i,t …,V i,e ], where I i,t The current collected at time t in the i-th cycle, e is the end time; V i,t The collected value of the voltage at time t in the i-th cycle, e is the end time. Then the sliding mean filter is used to smooth the current and voltage sequence data to obtain in, and are the smoothed values ​​of current and voltage at time t in the i-th cycle, L is the sliding window size, and p is the data acquisition number.

[0235] S2, calculating the battery capacity based on the processed current and voltage series and normalizing the data;

[0236] In this embodiment, in step S2, the battery capacity can be calculated based on the smoothed current and voltage sequence: Among them, Q i is the charging capacity of cycle i, n is the total number of cycles, V nom is the nominal voltage. The data is further normalized by using the maximum and minimum value normalization to map the data to the [-1,1] interval to ensure that the data is evenly distributed within the interval; the normalization formula is: X is the preprocessed data sequence, Xmax and Xmin are the maximum and minimum values ​​in the sequence X respectively.

[0237] S3, using CC algorithm to determine the optimal embedding dimension and time delay mapping to high-dimensional phase space, and obtain the capacity phase space reconstruction matrix;

[0238] In this embodiment, in step S3, it is assumed that the one-dimensional capacity sequence Q n =[Q1,Q2,…Q i ,…,Q n ], n is the total number of cycles. The optimal embedding dimension and time delay calculated using the CC algorithm.

[0239] First calculate the cross-correlation integral Where M = n-(m-1)τ is the number of embedded points in the m-dimensional space, r represents the spatial distance, τ represents the reconstruction time delay, and the piecewise function

[0240] Then, the nonlinear characteristic function is obtained based on the cross-correlation integral C(m,n,r,τ) and the time delay averaging strategy. Assuming that m and τ are fixed, when n approaches infinity, S(m,n,r,τ) can be derived from the cross-correlation integral C(m,n,r,τ) to be equal to 0 at all spatial distances r. Therefore, the optimal delay τ can be the position where the rate of change of S(m,n,r,τ) to any relative spatial distance r is the minimum, that is, ΔS(m,τ) = max{S(m,r j ,τ)}-min{S(m,r j ,τ)}.

[0241] Finally, according to the delay window At the minimum value, Equivalent to the time delay τ, the embedding dimension m can be obtained by τ window =(m-1)τ and solve.

[0242] S4, dividing the capacity phase space reconstruction matrix into different subspaces according to the capacity degradation rate characteristics;

[0243] In this embodiment, in step S4, according to the optimal embedding dimension and time delay calculated in step 3, the one-dimensional capacity sequence Q of length n is n =[Q1,Q2,…Q i ,…,Q n ] is reconstructed into a capacity matrix of m×τ dimensions and divided into: capacity degradation with regeneration and without regeneration according to the incremental capacity value. The reconstructed capacity matrix is ​​as follows:

[0244]

[0245] in, The capacity regeneration phenomenon is that the battery capacity will experience a short recovery and increase compared to the previous cycle, usually with an amplitude between 0% and 5%.

[0246] S5. Apply the multi-head attention mechanism independently in different subspaces to calculate the attention scores, combine them into a multi-space attention matrix through the fully connected layer, and pass it to GRU to establish an offline RUL prediction model;

[0247] In this embodiment, in step S5, according to the subspaces with different degradation rates divided in step S4, the multi-head attention mechanism is independently applied to calculate the attention score matrix of each subspace, and they are combined into a multi-space attention matrix HAM through a fully connected layer.

[0248] The multi-space attention mechanism adjusts the dynamic relationship between different subspaces and prioritizes the key periods and degradation patterns that have a significant impact on capacity degradation, thereby effectively improving the accuracy and robustness of the model in short-term and long-term prediction tasks. The calculation process is as follows:

[0249]

[0250] MH=Concat(head1,...,head i ,...,head h )W

[0251] HAM=σ(MH*W space +b space )

[0252] Among them, A is the query vector matrix, K is the key vector matrix, V is the key vector matrix, T is the matrix transpose, dk is the scaling factor, Concat means matrix concatenation, head i =Attention(Q i ,K i ,V i), i∈{1,2,...,h} is the hidden state of the single-head attention, h is the number of single-head attention, σ is the activation function, W and Wspace are the subspace weight matrix and multi-space weight matrix respectively, and bspace is the multi-space bias.

[0253] Its multi-spatial attention matrix HAM is passed to GRU to establish an offline RUL prediction model as follows:

[0254] z t =σ1(w z *[h t-1 ,HAM t ]+b z )

[0255] r t =σ1(w r *[h t-1 ,HAM t ]+b r )

[0256]

[0257] Among them, HAM t is the multi-spatial attention matrix input at time t; z t 、r t , and h t They represent the output of the update gate, reset gate, candidate hidden state and hidden state at time t respectively; σ1 and σ2 are the sigmoid and hyperbolic tangent activation functions respectively, ⊙ is the dot product of the matrix elements; wz, wr and wh are the weight matrices of the update gate, reset gate and hidden layer respectively; bz, br and bh are the biases of the update gate, reset gate and hidden state respectively.

[0258] S6. Execute steps S1-S3 on the lithium battery current and voltage sequence data of the unknown RUL, and input them into step S6 for online lithium battery RUL prediction.

[0259] In this embodiment, in step S6, the phase space reconstruction matrix is ​​obtained using the lithium battery current and voltage sequence data of the unknown RUL It is used as input to the offline RUL prediction model to predict the RUL of unknown lithium batteries.

[0260] Embodiment 23:

[0261] The RUL prediction method of lithium batteries based on phase space reconstruction and multi-space attention mechanism, the main technical content is shown in Example 22, and further, the RUL prediction method of this embodiment is demonstrated with B0005 and B0006 lithium batteries provided by NASA. The charging process uses a constant current of 1.5A to charge to 4.2V, and switches to constant voltage mode after the voltage reaches 4.2V, and continues to charge until the current drops to 20mA; the discharge process is discharged at a constant current of 2A until the battery voltage drops to a set cutoff voltage of 2.7V. The capacity degradation rate of the data shows obvious differences at different stages, which provides an important basis for studying the degradation mode of the battery and its dynamic characteristics, and helps to improve the accuracy and reliability of the battery management system in practical applications. Figure 2 The capacity degradation curves of B0005 and B0006 lithium batteries are shown in Figure 2.

[0262] In this example, the B0005 battery data is used as the training set and the B0006 battery data is used as the test set to carry out the prediction experiment for the RUL of unknown lithium batteries. The hyperparameter settings of the gated recurrent unit network-multi-spatial attention mechanism (GRU-HAM) in this example are shown in Table 1:

[0263] Table 1 Hyperparameters of GRU-HAM

[0264]

[0265] In order to verify the generalization ability of the method in this embodiment, the current and voltage data of B0006 battery in the first 30, 50 and 70 cycles were selected, and the capacity data obtained by smoothing calculation was input into the model for RUL prediction, and then the performance of the model under different cycle data was examined. In addition, four different methods including convolutional neural network (CNN), support vector machine (SVM), long short-term memory neural network (LSTM), gated recurrent unit network and attention mechanism (GRU-AM) were compared. This embodiment uses the absolute error (AE), root mean square error (RMSE), mean absolute error (MAE) and determination coefficient (R 2 ) are used to measure the effectiveness of the method. The RUL prediction results of 30, 50 and 70 cycle data are shown as follows: Figure 3 , Figure 4 , Figure 5 The evaluation index results are shown in Table 2:

[0266] Table 2 Evaluation index results

[0267]

[0268] from Figure 3-5We can clearly see that compared with the results of the other four models, the capacity prediction trajectory of the RUL prediction method proposed in this embodiment is closer to the actual capacity degradation trajectory at the same prediction starting point. It can also be intuitively seen from Table 2 that the prediction error, MAE and RMSE indicators of the method in this embodiment are lower than those of the other four RUL prediction methods. The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism proposed in this embodiment can effectively capture the dynamic characteristics of the battery at different degradation stages, showing strong robustness and high prediction accuracy, and providing strong support for lithium battery health management and life prediction in practical applications.

Claims

1. A lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism, characterized in that: The following steps are involved: 1) Obtain the charging current sequence and charging voltage sequence in each charge and discharge cycle of the lithium battery; 2) constructing a capacity phase space reconstruction model, and inputting the acquired charging current sequence and charging voltage sequence into the capacity phase space reconstruction model to obtain a capacity phase space reconstruction matrix; 3) According to the capacity degradation rate characteristics of the capacity phase space reconstruction matrix, the capacity phase space reconstruction matrix is ​​divided into different subspaces. 4) A multi-head attention mechanism is applied to calculate the attention scores of different subspaces, and the attention scores of different subspaces are combined into a multi-space attention matrix through a fully connected layer. 5) The multi-spatial attention matrix is ​​passed to the recurrent neural network GRU to construct an offline RUL prediction model with the capacity phase space reconstruction matrix as input and the remaining service life RUL of the lithium battery as output; 6) Collecting the charging current sequence and charging voltage sequence of the lithium battery to be predicted, and inputting them into the capacity phase space reconstruction model to obtain the capacity phase space reconstruction matrix of the lithium battery to be predicted; 7) The capacity phase space reconstruction matrix of the lithium battery to be predicted is input into the offline RUL prediction model to predict the remaining service life RUL of the lithium battery to be predicted.

2. The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism according to claim 1 is characterized in that: In step 2), the steps to obtain the capacity phase space reconstruction matrix are as follows: 2.1) Smoothing the data input into the capacity phase space reconstruction model to obtain processed data; 2.2) Calculate the battery capacity based on the processed data; 2.3) Based on the battery capacity, the CC algorithm is used to determine the optimal embedding dimension and time delay, and the capacity phase space reconstruction matrix is ​​constructed.

3. The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism according to claim 2 is characterized in that: The smoothing process uses sliding mean filtering, as shown below: In the formula, i is the charge-discharge cycle index; t represents the time; p is the data collection number; L is the sliding window size; Respectively represent the current and voltage data at time t in the i-th cycle after smoothing; I i,t 、V i,t They respectively represent the collected values ​​of current and voltage at time t in the i-th cycle.

4. The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism according to claim 2 is characterized in that: The battery capacities are as follows: In the formula, i is the charge and discharge cycle index, n is the total number of cycles; t represents the time; p is the data collection number, and e is the end time; Respectively represent the current and voltage data at time t in the i-th cycle after smoothing; V nom is the nominal voltage; Q i represents the charging capacity of the i-th cycle.

5. The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism according to claim 2 is characterized in that: The battery capacity is also normalized by normalization processing, and the calculation formula of the normalization processing is as follows: Where, X * is the data after normalization, X is the data to be normalized, X max , X min are the maximum and minimum values ​​in the sequence X respectively.

6. The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism according to claim 2 is characterized in that: In step 2.3), the steps of determining the optimal embedding dimension and time delay using the CC algorithm are as follows: 2.3.1) Based on the battery capacity, calculate the cross-correlation integral as follows: Where C(m,n,r,τ) is the cross-correlation integral; i and j are charge and discharge cycle indexes, n is the total number of cycles; Q i , Q j denote the charge capacity of the i-th and j-th cycles respectively; m denotes the embedding dimension, M is the number of embedding points in the m-dimensional space, and M = n-(m-1)τ, τ denotes the time delay, and r denotes the spatial distance; The piecewise function F is as follows: 2.3.2) According to the cross-correlation integral and time delay average strategy, the nonlinear characteristic function is calculated as follows: Where S(m,n,r,τ) is the nonlinear characteristic function, S represents the time delay index, and All represent cross-correlation integrals; 2.3.3) The nonlinear characteristic function S(m,n,r,τ) is converted into the position with the minimum rate of change of any spatial distance r, and the optimal time delay τ is derived; The position with the minimum rate of change of the arbitrary spatial distance r is as follows: ΔS(m,τ)=max{S(m,r j ,τ)}-min{S(m,r j ,t)} (7) In the formula, ΔS(m,τ) represents the position with the minimum rate of change of any spatial distance r, S(m,r j ,τ) represents the nonlinear characteristic function of any spatial distance r when n is infinite; 2.3.4) The optimal embedding dimension is obtained based on the delay window solution, as shown below: t window =(m-1)τ (8) In the formula, τ window is the delay window; is the average value of the position with the minimum rate of change of any spatial distance r; is the average value of the nonlinear characteristic function at any spatial distance r.

7. The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism according to claim 2 is characterized in that: The capacity phase space reconstruction matrix is ​​as follows: Where i is the charge-discharge cycle index, n is the total number of cycles, m represents the embedding dimension, and Q i represents the charging capacity of the i-th cycle; Q R , Q No They represent the incremental capacity with regeneration and the incremental capacity without regeneration respectively.

8. The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism according to claim 7 is characterized in that: The regenerative incremental capacity Q R and non-regenerative incremental capacity Q No As shown below: Where q is the upper limit of the regenerative incremental capacity.

9. The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism according to claim 1, characterized in that: The multi-spatial attention matrix is ​​as follows: HAM=σ(MH*W space +b space ) (14) Where Attention is the single-head attention score, A is the query vector matrix, K is the key vector matrix, V is the key vector matrix, T is the matrix transpose, and d k is the scaling factor, Concat represents matrix concatenation, i r is the single-head attention index, Represents single-head attention i r The hidden state of h is the number of single-head attention, For single-head attention i r The query vector matrix, For single-head attention i r The key vector matrix of For single-head attention i r The key vector matrix, σ is the activation function, W, W space are the subspace weight matrix and the multi-space weight matrix, respectively, space is the multi-space bias; HAM is the multi-space attention matrix; MH is the concatenated single-head attention matrix.

10. The lithium battery RUL prediction method based on phase space reconstruction and multi-space attention mechanism according to claim 1, characterized in that: The offline RUL prediction model is as follows: z t =σ1(w z *[h t-1 ,HAM t ]+b z ) (15) r t =σ1(w r *[h t-1 ,HAM t ]+b r ) (16) In the formula, HAM t is the multi-spatial attention matrix input at time t; z t 、r t , h t They represent the update gate, reset gate, candidate hidden state, and hidden state output at time t respectively; h t-1 is the output of the hidden state at time t-1; σ1 and σ2 are the sigmoid function and the hyperbolic tangent activation function respectively, ⊙ is the dot product of the matrix elements; w z 、w r 、w h are the weight matrices of the update gate, reset gate, and hidden state respectively; b z 、b r 、b h They are the update gate, reset gate, and hidden state bias respectively.

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