A multivariate time series long-term prediction method based on deep FCM

Abstract

The present invention proposes a long-term prediction method for multivariate time series based on deep FCM, including obtaining a multivariate time series data set; performing standardization processing to obtain a multivariate time series standard data set; using a multidimensional Gaussian information granule design method based on a reasonable granularity principle to perform equidistant overlapping segmentation to obtain a multivariate time series segmentation data set; predicting the vector data of concept nodes in all time windows to perform long-term prediction of the multivariate time series; training parameters to obtain a deep dynamic vector fuzzy cognitive graph model; obtaining a convergence condition, judging whether the link weight meets the convergence condition, if it meets the condition, inputting the multivariate time series to be predicted into the deep dynamic vector fuzzy cognitive graph model to obtain a prediction result, and if it does not meet the condition, retraining the link weight. The present invention can effectively mine the long-term dependency between data, and has significantly improved the accuracy of fuzzy decision-making and time series prediction, and the present invention has interpretability.

Description

Technical Field

[0001] The present invention belongs to the field of fuzzy decision making and time series prediction, and specifically discloses a multivariate time series long-term prediction method based on deep FCM. Background Art

[0002] Fuzzy cognitive map is a powerful and effective soft computing tool that can be used for modeling and prediction of complex systems. It is interpretable and is therefore widely used in many fields, such as modeling and prediction of time series, industrial control, program formulation and decision-making, and classification. A fuzzy cognitive map is a directed network with feedback loops consisting of concept nodes and signed weights. It represents a dynamic system that changes over time, where concept nodes represent specific variables and attributes, and signed weights represent the causal relationship between nodes.

[0003] In the field of time prediction, the problem of multivariate long-term time series prediction has always been a hot topic of research. Due to the long-term dependence of the data of multivariate long-term time series prediction problems, the difficulty in characterizing seasonality, and the difficulty in determining statistical characteristics, the problem of multivariate long-term time series prediction has not been effectively solved. At present, the commonly used multivariate long-term time series prediction methods include statistical analysis learning, machine learning learning, and deep learning learning. Among them, the deep learning method is widely used due to its excellent prediction ability, but this method belongs to a "black box" model. The deep learning method has poor interpretability and high complexity, and the deep learning method ignores the influence relationship between variables. Fuzzy cognitive maps show excellent modeling capabilities in the field of multivariate time series prediction. The interpretability of fuzzy cognitive maps can play a key decision-making role in engineering, meteorology and other fields, but its defects are also very obvious. The weight relationship between the concept nodes of fuzzy cognitive maps is linear and monotonic. In actual situations, the relationship between concept nodes will change with time, while the relationship between concept nodes of traditional fuzzy cognitive maps is fixed. In time series modeling, traditional fuzzy cognitive maps only rely on the information of the previous moment, which makes the information feature extraction ability insufficient. These defects also lead to the weak modeling ability of fuzzy cognitive maps for long-term time series prediction tasks. Therefore, overcoming the inherent defects of fuzzy cognitive maps, improving the prediction accuracy of fuzzy cognitive maps in multivariate long-term time series, and ensuring the interpretability of multivariate long-term time series prediction methods are urgent issues to be solved in the field of fuzzy decision-making. Summary of the invention

[0004] In order to solve the problems of poor interpretability, high complexity and neglect of the influence relationship between variables in traditional multivariate long-term time series prediction methods in the existing fuzzy decision-making and time series prediction fields, as well as the problems of linear monotonicity of concept nodes in traditional fuzzy cognitive graphs in multivariate long-term time series prediction, poor long-term time series prediction accuracy and low interpretability, the present invention proposes a multivariate time series long-term prediction method based on deep FCM.

[0005] The present invention provides a multivariate time series long-term prediction method based on deep FCM, comprising the following steps:

[0006] S1. Acquire a multivariate time series data set of the system, wherein the multivariate time series data set includes a plurality of multivariate time series, each of which includes N attribute feature data and 4 time feature data, wherein the time feature data includes annual feature data, monthly feature data, daily feature data and hourly feature data;

[0007] S2. Fuzzifying the multivariate time series data set to obtain a multivariate time series fuzzy data set consisting of a plurality of fuzzified multivariate time series, wherein the fuzzified multivariate time series includes a plurality of variables, and the variables include annual feature fuzzy data, monthly feature fuzzy data, daily feature fuzzy data, hourly feature fuzzy data, and attribute feature fuzzy data;

[0008] S3. Based on the multidimensional Gaussian information granule design method of the reasonable granularity principle, the fuzzy multivariate time series in the multivariate time series fuzzy data set is equidistantly overlapped and segmented to obtain multiple time windows, and a multivariate time series segmentation data set composed of multiple time windows is obtained;

[0009] S4. Constructing a deep dynamic vector fuzzy cognitive map, including: constructing a dynamic vector fuzzy cognitive map, taking each of the attribute feature data and time feature data in the time window Δt1 in the multivariate time series segmentation data set as a concept node of the dynamic vector fuzzy cognitive map, predicting the vector data of the concept node in the next time window Δt2 through the dynamic vector fuzzy cognitive map, constructing a high-order dynamic vector fuzzy cognitive map, predicting the vector data of the concept nodes in all time windows after the time window Δt2 through the high-order dynamic vector fuzzy cognitive map, and before predicting the vector data in the last time window, performing correction prediction through the cross dynamic vector fuzzy cognitive map, and obtaining all predicted time windows after correction and inspection;

[0010] S5. Defuzzify and denormalize the multivariate time series in the prediction time window, and use the gradient descent algorithm to linearly transform the coefficient w of the principal vector p. p , the coefficient w when linearly transforming from vector q q, the link weight w between concept nodes v and unknown influencing factors u to obtain a trained deep dynamic vector fuzzy cognitive graph model;

[0011] S6. Obtain the convergence condition of the dynamic vector fuzzy cognitive map by the compression mapping principle, and determine the link weight w between the concept nodes of the deep dynamic vector fuzzy cognitive map model v Whether the convergence condition is met, if it is met, the deep dynamic vector fuzzy cognitive graph model is output and step S7 is performed, if it is not met, return to step S4 to randomly initialize and retrain the link weight w v ;

[0012] S7. Input the multivariate time series to be predicted into the deep dynamic vector fuzzy cognitive map model to obtain a prediction result.

[0013] According to a multivariate time series long-term prediction method based on deep FCM in some embodiments of the present application, in step S1, the length of the multivariate time series data set is L={t a1 ,t a2 ,...,t am}, the multivariate time series dataset As shown in formula (1):

[0014]

[0015] in, Represents annual characteristic data, t i ∈(t a1 ,t a2 ,...,t am ), Represents monthly characteristic data, represents daily characteristic data, Represents characteristic data, Represents attribute feature data, b∈(1,2,...,N).

[0016] According to a multivariate time series long-term prediction method based on deep FCM in some embodiments of the present application, in step S2, each attribute feature data and time feature data in the multivariate time series data set is processed using z-score, as shown in formula (2):

[0017]

[0018] Where μ is the mean of the multivariate time series data set, μ = [μ year μ month μ date μ hourμ1 μ2 ...μ N ], σ is the variance of the multivariate time series data set, σ = [σ year σ month σ date σ hour σ1 σ2 ... σ N ], Represents a multivariate time series dataset after z-score processing;

[0019] The annual feature data, monthly feature data, daily feature data and hourly feature data are normalized respectively, and the normalization range is [-0.5 0.5]. The multivariate time series data set after z-score processing The data in is fuzzified to obtain the multivariate time series fuzzy data set As shown in formula (3):

[0020]

[0021] The multivariate time series fuzzy data set is shown in formula (4):

[0022]

[0023] in, represents the fuzzy data of annual features, t i ∈(t a1 ,t a2 ,...,t am ), represents the fuzzy data of monthly features, represents the daily feature fuzzy data, When representing feature fuzzy data, Represents attribute feature fuzzy data, b∈(1,2,...,N).

[0024] According to a multivariate time series long-term prediction method based on deep FCM in some embodiments of the present application, in step S3, the equidistant overlapping segmentation includes enumerating the segmentation lengths of all time windows, and obtaining the optimal time window length by a grid search method, wherein the grid search method includes obtaining the average coverage and average specificity corresponding to each time window length, and the average coverage is shown in formula (5):

[0025]

[0026] Among them, G1,...,G d represents the sequence on each time window after segmentation, d represents the number of segmentations of the time window, k∈(1,2,3…d), L represents the length of the multivariate time series dataset, l represents the length of the time window, and n represents the length of the overlapping time windows.

[0027] Coverage(G k ) represents coverage, and the coverage is shown in formula (6):

[0028]

[0029] Where M represents the sampling times of the multivariate time series fuzzy dataset, D is the multivariate time series segmentation dataset, and f(G k ) is the Gaussian membership function of the multivariate variable, and the Gaussian membership function of the multivariate variable is shown in formula (7):

[0030]

[0031] Among them, μ k represents the mean value of the variable in time window k, ∑ k represents the covariance matrix between variables in time window k, ∑ k As shown in formula (8):

[0032]

[0033] Among them, cov(x'1,x' N+4 ) represents the variables x'1 and x' in time window k N+4 The covariance of

[0034] The average specificity is shown in formula (9):

[0035]

[0036] Among them, SP(G k ) is the specificity, and the specificity is shown in formula (10):

[0037]

[0038] Among them, λ i represents the eigenvalues ​​of the covariance matrix of the variables in time window k, Represents the covariance matrix between the variables of the multivariate time series fuzzy dataset, the covariance matrix of the multivariate time series fuzzy dataset As shown in formula (11):

[0039]

[0040] Among them, cov(x1,x N+4) represents the variables x1 and x in the multivariate time series fuzzy dataset N+4 The covariance of

[0041] The time window length corresponding to the maximum product of the average coverage and the average specificity is output as the optimal time window length.

[0042] According to a multivariate time series long-term prediction method based on deep FCM in some embodiments of the present application, in step S4, the dynamic vector fuzzy cognitive map is as shown in formula (12):

[0043]

[0044] Among them, A i (Δt2) represents the vector data predicted by the i-th concept node in the next time window Δt2, Δt2 = [t l-n+1 ,t l-n+2 ,...t 2l-n ], l represents the length of the time window, A j (Δt1) represents the vector data of the j-th concept node in the time window Δt1, Δt1 = [t1, t2, ... t l ], Indicates A j (Δt1) and A i The link weight between (Δt2), u i (Δt1) represents the unknown factor influencing variable of the i-th concept node in the time window Δt1, α ij Represents the vector data of the dynamic coefficient between the i-th concept node and the j-th concept node in the time window Δt1, α ij As shown in formula (13):

[0045]

[0046] in, represents the principal vector transformation matrix, Represents a transformation matrix from a vector;

[0047] The activation function of the dynamic vector fuzzy cognitive map is a sigmoid function, as shown in formula (14):

[0048]

[0049] Among them, λ represents the formula inclination, α represents the dynamic coefficient matrix, and w represents the weight matrix. represents the Hadamard product, A represents the concept node matrix on the time window Δt1, U represents the unknown factor influencing variable matrix,

[0050] The Hadamard product of the dynamic coefficient matrix and the weight matrix is ​​shown in formula (15):

[0051]

[0052] The concept node matrix A on the time window Δt1 is shown in formula (16):

[0053] A=[A1(Δt1) A2(Δt1) ... A N+4 (Δt1)] (16)

[0054] The unknown factor influence variable matrix U is shown in formula (17):

[0055] U=[u1(Δt1) u2(Δt1) ... u N+4 (Δt1)] (17)

[0056] The high-order dynamic vector fuzzy cognitive map is shown in formula (18):

[0057]

[0058] Among them, A i (Δt x ) represents the i-th concept node in the time window Δt x The predicted vector data, A j (Δt x-1 ) represents the jth concept node in the time window Δt x-1 Vector data on Indicates A j (Δt x-1 ) and A i (Δt x ), A j (Δt x-2 ) represents the jth concept node in the time window Δt x-2 Vector data on Indicates A j (Δt x-2 ) and A i (Δt x ), A j (Δt x-Ω ) represents the jth concept node in the time window Δt x-Ω Vector data on Indicates A j (Δt x-Ω ) and A i (Δt x ), u i (Δtx-1 ) represents the i-th concept node in the time window Δt xΔ1 Unknown factors affect the variables.

[0059] According to a multivariate time series long-term prediction method based on deep FCM in some embodiments of the present application, in step S4, the correction prediction uses the predicted multivariate time series overlapping the last time window and the second to last time window as the correction flag, and increases the vector dimension of the correction flag by filling zeros to obtain a correction sequence with the same length as the time window. The cross dynamic vector fuzzy cognitive map is shown in formula (19):

[0060]

[0061] Among them, A i (Δt d ) represents the i-th concept node in the time window Δt d The predicted vector data, A j (Δt dΔ1 ) represents the jth concept node in the time window Δt dΔ1 Vector data on Indicates A i (Δt d ) and A j (Δt d-1 ), u i (Δt d-1 ) represents the i-th concept node in the time window Δt d-1 The unknown factors on the variables, α ij ′ represents the correction sequence Δt SF The vector data of the i-th concept node and the time window Δt d-1 The vector data of the dynamic coefficients between the j-th concept nodes, α ij ′ is shown in formula (20):

[0062]

[0063] Among them, A i (Δt SF ) represents the calibration sequence Δt SF The vector data of the i-th concept node, Denotes the correction sequence Δt SF The principal vector transformation matrix, Represents the time window Δt d-1 The vector transformation matrix of the j-th concept node;

[0064] The activation function of the cross dynamic vector fuzzy cognitive map is a sigmoid function.

[0065] According to a multivariate time series long-term prediction method based on deep FCM in some embodiments of the present application, in step S5, the multivariate time series in the prediction time window is defuzzified and denormalized, as described in formula (21):

[0066]

[0067] in, represents the multivariate time series after defuzzification and denormalization, represents a multivariate time series in the forecast time window,

[0068] The coefficient w of the linear transformation of the main vector p is obtained by the gradient descent algorithm in the field of deep learning p , the coefficient w when linearly transforming from vector q q , the link weight w between concept nodes v And unknown influencing factors u are trained, and the MSE loss function is used, as shown in formula (22):

[0069]

[0070] Among them, len represents the length of the prediction result sequence, Indicates t i The prediction results at the moment, Indicates t i The true value of the moment.

[0071] According to a multivariate time series long-term prediction method based on deep FCM in some embodiments of the present application, in step S6, the convergence condition of the dynamic vector fuzzy cognitive map obtained by the compression mapping principle includes randomly taking out the concept values ​​of two states in the reasoning process of the dynamic vector fuzzy cognitive map or the high-order dynamic vector fuzzy cognitive map, and obtaining them by the compression mapping principle as shown in formula (23):

[0072] ||G(A)-G(A')||≤c||A-A'|| (23)

[0073] Where A and A' represent the concept values ​​of the two states in the dynamic vector fuzzy cognitive map reasoning process, c is a constant and c < 1, and the expression of G is shown in formula (24):

[0074]

[0075] Among them, u i Represents the unknown factor influencing variable of the i-th concept node, i∈(1,2,3…N+4), α i represents the dynamic coefficient matrix between the i-th concept node and the concept nodes in the same time window, λi =[α i1 α i2 ... α iN+4 ], represents the link weight matrix between the i-th concept node and the concept node in the previous time window,

[0076] We get formula (25):

[0077]

[0078] According to the Cauchy inequality, we get formula (26):

[0079]

[0080] Combining formula (25) with formula (26) yields formula (27):

[0081]

[0082] because And c'≤λ / 4, we get formula (28):

[0083]

[0084] According to the compatibility of vector norm and matrix norm, we get formula (29):

[0085]

[0086] According to the principle of softmax mechanism, ||α i || 2 ≤1, we get formula (30):

[0087]

[0088] The convergence condition is shown in formula (31):

[0089]

[0090] Among them, l represents the length of the current time window, g∈(1,2,…,l).

[0091] The present invention proposes a multivariate time series long-term prediction method based on deep FCM, which is interpretable. The method processes vector data and has better feature extraction capability and reasoning calculation efficiency. The reasoning sequence of dynamic vector fuzzy cognitive map and high-order dynamic vector fuzzy cognitive map effectively retains the time series information, improves the calculation efficiency and prediction accuracy. The weight relationship between each concept node is nonlinear, and the inferred result is more in line with the actual situation. The causal relationship between concept nodes can change with the change of input data. The method can also effectively mine the long-term dependency relationship between data, and has significantly improved the fuzzy decision-making and time series prediction accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 It is a flowchart of a multivariate time series long-term prediction method based on deep FCM in Example 1 of the present invention;

[0093] Figure 2 A schematic diagram of equidistant overlapping segmentation of a multivariate time series fuzzy data set in Example 1 of the present invention;

[0094] Figure 3 Schematic diagram of the process structure of the deep dynamic vector fuzzy cognitive map in Example 2 of the present invention;

[0095] Figure 4 Schematic diagram of the basic structure of the dynamic vector fuzzy cognitive map in Example 2 of the present invention;

[0096] Figure 5 A schematic diagram of the basic structure of a cross-dynamic vector fuzzy cognitive graph in Example 2 of the present invention;

[0097] Figure 6 This is the interpretability heat map of the WTH dataset in Example 3 of the present invention. DETAILED DESCRIPTION

[0098] The following embodiments of the present invention are described in further detail in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0099] Example 1

[0100] This embodiment provides a multivariate time series long-term prediction method based on deep FCM, such as Figure 1 As shown, the following steps are included:

[0101] S1. Obtaining a systematic multivariate time series dataset The multivariate time series data set includes multiple multivariate time series, each of which includes N attribute feature data and 4 time feature data. The time feature data includes annual feature data, monthly feature data, daily feature data and hourly feature data.

[0102] Specifically, the length of the multivariate time series data set is L = {t a1 ,t a2 ,...,t am}, Multivariate time series dataset As shown in formula (1):

[0103]

[0104] in, Represents annual characteristic data, t i ∈(t a1 ,t a2 ,...,t am ), Represents monthly characteristic data, represents daily characteristic data, Represents characteristic data, Represents attribute feature data, b∈(1,2,...,N).

[0105] S2. Fuzzify the multivariate time series data set to obtain a multivariate time series fuzzy data set consisting of multiple fuzzy multivariate time series, the fuzzy multivariate time series includes multiple variables, and the variables include annual feature fuzzy data, monthly feature fuzzy data, daily feature fuzzy data, hour feature fuzzy data and attribute feature fuzzy data;

[0106] Specifically, z-score is used to process each attribute feature data and time feature data in the multivariate time series data set, as shown in formula (2):

[0107]

[0108] Where μ is the mean of the multivariate time series data set, μ = [μ year μ month μ date μ hour μ1 μ2 ... μ N ], σ is the variance of the multivariate time series data set, σ = [σ year σ month σ date σ hour σ1 σ2 ... σ N ], Represents a multivariate time series dataset after z-score processing;

[0109] The annual feature data, monthly feature data, daily feature data and hourly feature data are normalized respectively, and the normalization range is [-0.5 0.5]. The multivariate time series data set after z-score normalization The data in is fuzzified to obtain a multivariate time series fuzzy data set As shown in formula (3):

[0110]

[0111] The multivariate time series fuzzy data set is shown in formula (4):

[0112]

[0113] in, represents the fuzzy data of annual features, t i ∈(t a1 ,t a2 ,...,t am ), represents the fuzzy data of monthly features, represents the daily feature fuzzy data, When representing feature fuzzy data, Represents attribute feature fuzzy data, b∈(1,2,...,N).

[0114] S3. Based on the principle of reasonable granularity, the multidimensional Gaussian information granule design method performs equidistant overlapping segmentation on the fuzzy multivariate time series in the multivariate time series fuzzy data set to obtain multiple time windows, such as Figure 2 As shown, a multivariate time series segmentation dataset consisting of multiple time windows is obtained;

[0115] When performing equal-distance overlapping segmentation of the fuzzy multivariate time series in the multivariate time series fuzzy data set, two indicators need to be considered, namely coverage and specificity. When the coverage is high, the specificity will be low, and vice versa. Therefore, the maximum product of average coverage and average specificity is defined as the optimal comprehensive indicator of information granulation.

[0116] The equidistant overlapping segmentation includes enumerating the segmentation lengths of all time windows, and obtaining the optimal time window length through the grid search method. The grid search method includes obtaining the average coverage and average specificity corresponding to each time window length, thereby obtaining the time window length corresponding to the maximum product of the average coverage and the average specificity as the optimal time window length. The average coverage is shown in formula (5):

[0117]

[0118] Among them, G1,...,G drepresents the sequence on each time window after segmentation, d represents the number of segmentations of the time window, k∈(1,2,3…d), L represents the length of the multivariate time series dataset, l represents the length of the time window, and n represents the length of the overlapping time windows.

[0119] Coverage(G k ) represents coverage, which is shown in formula (6):

[0120]

[0121] Where M represents the sampling times of the multivariate time series fuzzy dataset, D is the multivariate time series segmentation dataset, and f(G k ) is the Gaussian membership function of the multivariate variable. The Gaussian membership function of the multivariate variable is shown in formula (7):

[0122]

[0123] Among them, μ k represents the mean value of the variable in time window k, ∑ k represents the covariance matrix between variables in time window k, ∑ k As shown in formula (8):

[0124]

[0125] Among them, cov(x'1,x' N+4 ) represents the variables x'1 and x' in time window k N+4 The covariance of

[0126] The average specificity is shown in formula (9):

[0127]

[0128] Among them, SP(G k ) is the specificity, which is shown in formula (10):

[0129]

[0130] Among them, λ i represents the eigenvalues ​​of the covariance matrix of the variables in time window k, Represents the covariance matrix between the variables of the multivariate time series fuzzy dataset, the covariance matrix of the multivariate time series fuzzy dataset As shown in formula (11):

[0131]

[0132] Among them, cov(x1,x N+4 ) represents the variables x1 and x in the multivariate time series fuzzy dataset N+4 The covariance of

[0133] The time window length corresponding to the maximum product of average coverage and average specificity is output as the optimal time window length.

[0134] S4. Constructing a deep dynamic vector fuzzy cognitive map, including: constructing a dynamic vector fuzzy cognitive map, taking each attribute feature data and time feature data in the time window Δt1 in the multivariate time series segmentation data set as a concept node of the dynamic vector fuzzy cognitive map, the dynamic vector fuzzy cognitive map has a total of N+4 concept nodes in the time window Δt1, predicting the vector data of the concept node in the next time window Δt2 through the dynamic vector fuzzy cognitive map, constructing a high-order dynamic vector fuzzy cognitive map, predicting the vector data of the concept node in all time windows after the time window Δt2 through the high-order dynamic vector fuzzy cognitive map, and before predicting the vector data in the last time window, performing correction prediction through the cross dynamic vector fuzzy cognitive map, and obtaining all predicted time windows after correction test;

[0135] Specifically, the dynamic vector fuzzy cognitive map is shown in formula (12):

[0136]

[0137] Among them, A i (Δt2) represents the vector data predicted by the i-th concept node in the next time window Δt2, Δt2 = [t l-n+1 ,t l-n+2 ,...t 2l-n ], l represents the length of the time window, A j (Δt1) represents the vector data of the j-th concept node in the time window Δt1, Δt1 = [t1, t2, ... t l ], Indicates A j (Δt1) and A i The link weight between (Δt2), u i (Δt1) represents the unknown factor influencing variable of the i-th concept node in the time window Δt1, α ij Represents the vector data of the dynamic coefficient between the i-th concept node and the j-th concept node in the time window Δt1, α ij As shown in formula (13):

[0138]

[0139] in, represents the principal vector transformation matrix, Represents a transformation matrix from a vector;

[0140] The activation function of the dynamic vector fuzzy cognitive map is the sigmoid function, as shown in formula (14):

[0141]

[0142] Among them, λ represents the formula inclination, α represents the dynamic coefficient matrix, and w represents the weight matrix. represents the Hadamard product, A represents the concept node matrix on the time window Δt1, U represents the unknown factor influencing variable matrix,

[0143] The Hadamard product of the dynamic coefficient matrix and the weight matrix is ​​shown in formula (15):

[0144]

[0145] The conceptual node matrix A on the time window Δt1 is shown in formula (16):

[0146] A=[A1(Δt1) A2(Δt1) ... A N+4 (Δt1)] (16)

[0147] The unknown factors affecting the variable matrix U is shown in formula (17):

[0148] U=[u1(Δt1) u2(Δt1) ... u N+4 (Δt1)] (17)

[0149] The high-order dynamic vector fuzzy cognitive map is shown in formula (18):

[0150]

[0151] Among them, A i (Δt x ) represents the i-th concept node in the time window Δt x The predicted vector data, A j (Δt x-1 ) represents the jth concept node in the time window Δt x-1 Vector data on Indicates A j (Δt x-1 ) and A i (Δt x ), A j (Δt x-2) represents the jth concept node in the time window Δt x-2 Vector data on Indicates A j (Δt x-2 ) and A i (Δt x ), A j (Δt x-Ω ) represents the jth concept node in the time window Δt x-Ω Vector data on Indicates A j (Δt x-Ω ) and A i (Δt x ), u i (Δt x-1 ) represents the i-th concept node in the time window Δt x-1 Unknown factors affect the variables.

[0152] The correction prediction takes the predicted multivariate time series of the last time window overlapping the second to last time window as the correction flag, and increases the vector dimension of the correction flag by filling zeros to obtain a correction sequence with the same length as the time window. The cross-dynamic vector fuzzy cognitive map calculates the correlation between the correction sequence and the historical moment data to obtain the dynamic coefficient. The cross-dynamic vector fuzzy cognitive map is shown in formula (19):

[0153]

[0154] Among them, A i (Δt d ) represents the i-th concept node in the time window Δt d The predicted vector data, A j (Δt d-1 ) represents the jth concept node in the time window Δt d-1 Vector data on Indicates A i (Δt d ) and A j (Δt d-1 ), u i (Δt d-1 ) represents the i-th concept node in the time window Δt d-1 The unknown factors on the variables, α ij ′ represents the correction sequence Δt SF The vector data of the i-th concept node and the time window Δt d-1 The vector data of the dynamic coefficients between the j-th concept nodes, α ij ′ is shown in formula (20):

[0155]

[0156] Among them, A i (Δt SF ) represents the calibration sequence Δt SF The vector data of the i-th concept node, Denotes the correction sequence Δt SF The principal vector transformation matrix, Represents the time window Δt d-1 The vector transformation matrix of the j-th concept node;

[0157] The activation function of the cross dynamic vector fuzzy cognitive map is the sigmoid function.

[0158] The dynamic vector fuzzy cognitive map proposed in this embodiment has a causal relationship between feature data that changes dynamically over time. Unlike the traditional fuzzy cognitive map, the dynamic vector fuzzy cognitive map can process serialized data, that is, the input data of the dynamic vector fuzzy cognitive map is vector data, and the predicted output of the dynamic vector fuzzy cognitive map is also vector data. The variables within a time window under the dynamic vector fuzzy cognitive map can be predicted and modeled. The dynamic vector fuzzy cognitive map splits the weight relationship between concept nodes into two parts, namely the dynamic coefficient and the link weight. Compared with the fixed link weight form, it can more flexibly represent the causal relationship between nodes, and the link weight is still fixed after training, which is unique and interpretable. Specifically, taking one of the concept nodes as an example, the concept node generates a main vector p and a slave vector q after two linear transformations. The similarity between the two concept nodes is explored by calculating the inner product of the main vector p of the concept node to be solved and the slave vector q of other concept nodes. The calculation result of the inner product is the dynamic coefficient α between the concept nodes after softmax. The weight between the two concept nodes with greater similarity is given a larger dynamic coefficient α; in the correction prediction link, the vector values ​​of each concept node in the correction sequence are linearly transformed to obtain the main vector p, and the time window Δt d-1 The vector values ​​of each concept node are obtained from the vector q through linear transformation, and the remaining calculation steps are the same as the dynamic vector fuzzy cognitive map. The correction prediction link achieves both the prediction purpose and the correction effect by crossing the dynamic vector fuzzy cognitive map, and also improves the prediction accuracy.

[0159] S5. Defuzzify and denormalize the multivariate time series in the prediction time window, and use the gradient descent algorithm to linearly transform the coefficient w of the principal vector p. p , the coefficient w when linearly transforming from vector q q , the link weight w between concept nodes vAnd unknown influencing factors u are trained to obtain a deep dynamic vector fuzzy cognitive graph model;

[0160] Specifically, the gradient descent algorithm may be an Adam gradient descent algorithm;

[0161] All predicted time series are defuzzified and denormalized, as shown in formula (21):

[0162]

[0163] in, represents the multivariate time series after defuzzification and denormalization, represents a multivariate time series in the forecast time window,

[0164] The coefficient w of the linear transformation of the main vector p is obtained by the gradient descent algorithm in the field of deep learning p , the coefficient w when linearly transforming from vector q q , the link weight w between concept nodes v And unknown influencing factors u are trained, and the MSE loss function is used, as shown in formula (22):

[0165]

[0166] Among them, len represents the length of the prediction result sequence, Indicates t i The prediction results at the moment, Indicates t i The true value of the moment.

[0167] S6. Obtain the convergence condition of the dynamic vector fuzzy cognitive map through the compression mapping principle, and determine the link weights w between the concept nodes of the deep dynamic vector fuzzy cognitive map model v Whether the convergence condition is met, if it is met, the deep dynamic vector fuzzy cognitive graph model is output and step S7 is performed, if not, it returns to step S4 and randomly initializes and retrains the link weight w v ;

[0168] Since the deep dynamic vector fuzzy cognitive map model has a unique solution, the convergence condition of the dynamic vector fuzzy cognitive map obtained by the compression mapping principle includes randomly taking out the concept values ​​of two states in the dynamic vector fuzzy cognitive map reasoning process, which is obtained by the compression mapping principle as shown in formula (23):

[0169] ||G(A)-G(A')||≤c||A-A'|| (23)

[0170] Where A and A' represent the concept values ​​of the two states in the dynamic vector fuzzy cognitive map reasoning process, c is a constant and c<1, and the expression of G is shown in formula (24):

[0171]

[0172] Among them, u i Represents the unknown factor influencing variable of the i-th concept node, i∈(1,2,3…N+4), α i represents the dynamic coefficient matrix between the i-th concept node and the concept nodes in the same time window, α i =[α i1 α i2 ... α iN+4 ], represents the link weight matrix between the i-th concept node and the concept node in the previous time window,

[0173] We get formula (25):

[0174]

[0175] According to the Cauchy inequality, we get formula (26):

[0176]

[0177] Combining formula (25) with formula (26) yields formula (27):

[0178]

[0179] because And c'≤λ / 4, we get formula (28):

[0180]

[0181] According to the compatibility of vector norm and matrix norm, we get formula (29):

[0182]

[0183] According to the principle of softmax mechanism, ||α i || 2 ≤1, we get formula (30):

[0184]

[0185] The convergence condition is shown in formula (31):

[0186]

[0187] Among them, l represents the length of the current time window, g∈(1,2,…,l).

[0188] S7. Segment the multivariate time series to be predicted based on the multidimensional Gaussian information granule design method of the reasonable granularity principle to obtain multiple time windows, determine the time window to be tested, and input it into the deep dynamic vector fuzzy cognitive map model to obtain the prediction result.

[0189] Example 2

[0190] This embodiment discloses a multivariate time series long-term prediction method based on deep FCM, comprising the following steps:

[0191] S1. Get the multivariate time series dataset x of the system s (t), the multivariate time series data set used in this embodiment is WTH (Weather), which collects meteorological data of a place in the United States from 2010 to 2013. The multivariate time series data set includes multiple multivariate time series, each of which includes N attribute feature data and 4 time feature data. The WTH data set includes 12 attribute feature data. The sampling frequency of the WTH data set is 1 hour, and the time range of the data set collection is four years. The time feature data includes annual feature data, monthly feature data, daily feature data and hourly feature data;

[0192] S2. Fuzzify the multivariate time series data set to obtain a multivariate time series fuzzy data set consisting of multiple fuzzy multivariate time series, the fuzzy multivariate time series includes multiple variables, and the variables include annual feature fuzzy data, monthly feature fuzzy data, daily feature fuzzy data, hour feature fuzzy data and attribute feature fuzzy data;

[0193] S3. Based on the multidimensional Gaussian information granule design method of the reasonable granularity principle, the fuzzy multivariate time series in the multivariate time series fuzzy data set is equidistantly overlapped to obtain multiple time windows, and a multivariate time series segmentation data set composed of multiple time windows is obtained;

[0194] Set the length of each time window to be less than or equal to l ax , the grid search method is used to solve the optimal segmentation result of multidimensional Gaussian information particles. The fuzzy multivariate time series after segmentation is G = {G1,...,G x ,...,G d}, that is, the multivariate time series fuzzy dataset is divided into d time windows, where the data in the xth time window is Assume that the length of the overlapping time windows between time windows is l a1 (l a1 <l a4). In this embodiment, the length of the fuzzy multivariate time series in each time window is 4, and the length of the overlapping time window between time windows is 1, so the input is The prediction result sequence is

[0195] S4. Construct a deep dynamic vector fuzzy cognitive map, such as Figure 3 As shown in FIG. 1 , the method includes: constructing a dynamic vector fuzzy cognitive map (DV-FCM), taking each attribute feature data and time feature data in the time window Δt1 in the multivariate time series segmentation data set as a concept node of the dynamic vector fuzzy cognitive map, and the initial state of the concept node is Assign weight values ​​to different concept nodes, such as Figure 4 As shown, is the link weight between concept node 1 and concept node 2. Next, the dynamic coefficient of each link weight value is calculated. Figure 4 For example, when exploring the relationship between all concept nodes on the time window Δt1 and the concept node 1 of the time window Δt2, the q vector of the concept node 1 of the time window Δt1 is inner-producted with the p vector of each node of the time window Δt1 and softmax is performed on each calculation result to obtain the dynamic coefficient matrix α. The dynamic coefficient matrix α is inner-producted with the weight value matrix w to obtain the dynamic weight value matrix. The dynamic weight value is multiplied by the concept node and added with the external unknown factors of the concept node 1 on the time window Δt1. Finally, the vector value of each concept node on the time window Δt2 can be obtained through the dynamic vector fuzzy cognitive map. The inferred vector value of each concept node on the time window Δt2 is input into the fully connected layer to amplify the main influencing factors and reduce the secondary influencing factors to predict. Figure 3 The data in the time window of part ②, i.e., the concept node

[0196] By extracting features from historical information through high-order dynamic vector fuzzy cognitive maps, it is possible to predict Figure 3 Concept nodes in part ③

[0197] Since long-term time series forecasts will have errors, the concept nodes in the last time window are estimated. The correction prediction link is used. The correction prediction link uses a cross dynamic vector fuzzy cognitive map, such as Figure 5 As shown, the forecast multivariate time series with the last time window overlapped with the second-to-last time window is corrected As the input of the correction prediction link, the input of the correction prediction link Figure 3The fourth part is called the correction flag. The vector dimension of the correction flag is increased by filling with zeros to obtain a correction sequence with the same length as the time window, as shown in formula (32):

[0198]

[0199] Another part of the input to the correction prediction phase comes from Figure 3 The purpose of part ③ is to explore the relationship between the data of the last time window and historical information, that is, Figure 3 Parts ④ and ③ are transformed into the main vector p and the slave vector q respectively through linear transformation. When Δt4={t a10 ,t a11 ,t a12 ,t a13}, the time window Δt3 predicted by the high-order dynamic vector fuzzy cognitive map is Δt3 = {t a7 ,t a8 ,t a9 ,t a10 The vector value of the concept node 1 of} is transformed into the main vector p through linear transformation, and the vector values ​​of each node of the correction flag are transformed into the slave vector q through linear transformation. The dynamic coefficient matrix α can be obtained through inner product and softmax calculation. The dynamic weight value matrix can be obtained by taking the inner product of the dynamic coefficient matrix α and the weight value matrix w. The dynamic weight value is multiplied by the concept node and added with the external unknown factors of the concept node 1 in the time window Δt3. Finally, the vector concept value of the concept node 1 in the time window Δt4 can be obtained through the DV-FCM inference formula. This operation not only achieves the purpose of prediction but also achieves the effect of correction, and improves the prediction accuracy.

[0200] Specifically, the dynamic vector fuzzy cognitive map is shown in formula (33):

[0201]

[0202] Among them, A i (Δt2) represents the vector data predicted by the i-th concept node in the next time window Δt2, Δt2 = [t l-n+1 ,t l-n+2 ,...t 2l-n ], l represents the length of the time window, A j (Δt1) represents the vector data of the j-th concept node in the time window Δt1, Δt1 = [t1, t2, ... t l ], Indicates A j (Δt1) and A i The link weight between (Δt2), u i(Δt1) represents the unknown factor influencing variable of the i-th concept node in the time window Δt1, n represents the number of concept nodes, α ij Represents the vector data of the dynamic coefficient between the i-th concept node and the j-th concept node in the time window Δt1, α ij As shown in formula (34):

[0203]

[0204] in, represents the principal vector transformation matrix, Represents a transformation matrix from a vector;

[0205] The activation function of the dynamic vector fuzzy cognitive map is the sigmoid function, as shown in formula (35):

[0206]

[0207] Among them, λ represents the formula inclination, α represents the dynamic coefficient matrix, and w represents the weight matrix. represents the Hadamard product, A represents the concept node matrix on the time window Δt1, U represents the unknown factor influencing variable matrix,

[0208] The Hadamard product of the dynamic coefficient matrix and the weight matrix is ​​shown in formula (36):

[0209]

[0210] The conceptual node matrix A on the time window Δt1 is shown in formula (37):

[0211] A=[A1(Δt1) A2(Δt1) ... A N+4 (Δt1)] (37)

[0212] The unknown factor influencing variable matrix U is shown in formula (38):

[0213] U=[u1(Δt1) u2(Δt1) ... u N+4 (Δt1)] (38)

[0214] The high-order dynamic vector fuzzy cognitive map is shown in formula (39):

[0215]

[0216] Among them, A i (Δt x ) represents the i-th concept node in the time window Δt x The predicted vector data, A j (Δtx-1 ) represents the jth concept node in the time window Δt x-1 Vector data on Indicates A j (Δt x-1 ) and A i (Δt x ), A j (Δt x-2 ) represents the jth concept node in the time window Δt x-2 Vector data on Indicates A j (Δt x-2 ) and A i (Δt x ), A j (Δt x-Ω ) represents the jth concept node in the time window Δt x-Ω Vector data on Indicates A j (Δt x-Ω ) and A i (Δt x ), u i (Δt x-1 ) represents the i-th concept node in the time window Δt x-1 Unknown factors affect the variables.

[0217] S5. Defuzzify and denormalize the multivariate time series in the prediction time window, and use the gradient descent algorithm to linearly transform the coefficient w of the principal vector p. p , the coefficient w when linearly transforming from vector q q , the link weight w between concept nodes v and unknown influencing factors u to obtain a deep dynamic vector fuzzy cognitive graph model. Specifically, the gradient descent algorithm may be an Adam gradient descent algorithm.

[0218] All predicted time series are defuzzified and denormalized, as shown in formula (40):

[0219]

[0220] in, represents the multivariate time series after defuzzification and denormalization, represents a multivariate time series in the forecast time window,

[0221] The coefficient w of the linear transformation of the main vector p is obtained by the gradient descent algorithm in the field of deep learning p , the coefficient w when linearly transforming from vector q q, the link weight w between concept nodes v and unknown influencing factors u for training, using the MSE loss function, as shown in formula (41):

[0222]

[0223] Among them, l a9 Indicates the length of the prediction result sequence, Indicates t i The prediction results at the moment, Indicates t i The true value of the moment.

[0224] S6. Obtain the convergence condition of the dynamic vector fuzzy cognitive map through the compression mapping principle, and determine the link weights w between the concept nodes of the deep dynamic vector fuzzy cognitive map model v Whether the convergence condition is met, if it is met, the deep dynamic vector fuzzy cognitive graph model is output and step S7 is performed, if not, it returns to step S4 and randomly initializes and retrains the link weight w v ;

[0225] Since the deep dynamic vector fuzzy cognitive graph model has a unique solution,

[0226] The convergence condition of the dynamic vector fuzzy cognitive map obtained by the compression mapping principle includes randomly taking out the concept values ​​of two states in the reasoning process of the dynamic vector fuzzy cognitive map, which is obtained by the compression mapping principle as shown in formula (42):

[0227] ||G(A)-G(A')||≤c||A-A'|| (42)

[0228] Where A and A' represent the concept values ​​of the two states in the dynamic vector fuzzy cognitive map reasoning process, c is a constant and c < 1, and the expression of G is shown in formula (43):

[0229]

[0230] Among them, u i Represents the unknown factor influencing variable of the i-th concept node, i∈(1,2,3…N+4), α i represents the dynamic coefficient matrix between the i-th concept node and the concept nodes in the same time window, λ i =[α i1 α i2 ... α iN+4 ], represents the link weight matrix between the i-th concept node and the concept node in the previous time window,

[0231] We get formula (44):

[0232]

[0233] According to the Cauchy inequality, we get formula (45):

[0234]

[0235] We get formula (46):

[0236]

[0237] After rearranging, we get formula (47):

[0238]

[0239] because And c'≤λ / 4, we get formula (48):

[0240]

[0241] According to the compatibility of vector norm and matrix norm, we get formula (49):

[0242]

[0243] According to the principle of softmax mechanism, ||λ i || 2 ≤1, we get formula (50):

[0244]

[0245] The convergence condition is shown in formula (51):

[0246]

[0247] Among them, l represents the length of the current time window, g∈(1,2,…,l).

[0248] S7. Input the multivariate time series to be predicted into the deep dynamic vector fuzzy cognitive graph model to obtain the prediction result.

[0249] Example 3

[0250] This example uses seven real-world multivariate time series data sets to verify the multivariate time series long-term prediction method based on deep FCM of the present invention. The seven real-world multivariate time series data sets include:

[0251] 1) WTH (Weather): This dataset collects weather data from 2010 to 2013 in a certain place in the United States, with a sampling frequency of 1 hour;

[0252] 2) ER (Exchange Rate): This dataset collects the exchange rates of eight countries from 1990 to 2016;

[0253] 3) ECL (Electricity Consuming Load): This dataset collects the electricity consumption (Kwh) of 321 users in a certain area;

[0254] 4) ETTh1 (Electricity Transformer Temperature hour 1): This dataset collects data from a power station transformer in A, China, with a sampling frequency of 1h;

[0255] 5) ETTh2 (Electricity Transformer Temperature hour 2): This dataset collects data from a power station transformer in China B, with a sampling frequency of 1h;

[0256] 6) ETTm1 (Electricity Transformer Temperature minute 1): This dataset collects data from a power station transformer in A, China, with a sampling frequency of 1 minute.

[0257] 7) ETTm2 (Electricity Transformer Temperature minute 2): This dataset collects data on a transformer in a power station in B, China, with a sampling frequency of 1 minute.

[0258] This embodiment uses six commonly used long-term time series prediction algorithms to compare the prediction performance with the multivariate time series long-term prediction method based on deep FCM (Dynamic Vector Deep Fuzzy Cognitive Map, DV-DFCM) of the present invention, verifying the superiority of the multivariate time series long-term prediction method based on deep FCM (Dynamic Vector Deep Fuzzy Cognitive Map, DV-DFCM) of the present invention. The six long-term time series prediction algorithms used for comparison include:

[0259] 1) GA-FCM: The weight matrix of the classic FCM is solved by the GA algorithm, which can predict multivariate time series;

[0260] 2) LSTM: This algorithm predicts multivariate long-term time series by using LSTM network;

[0261] 3) SARIMA: This algorithm adds seasonal factors to ARIMA and is suitable for seasonal data sets and can predict univariate data. This baseline predicts each univariate data in the multivariate time series separately, thereby achieving the prediction of multivariate time series;

[0262] 4) ELR: This algorithm is an improved learning algorithm based on feedforward neural network. It replaces the gradient descent method by solving a system of equations, which improves the speed and accuracy of network learning, thereby predicting multivariate time series.

[0263] 5) CNN: This algorithm uses CNN network to predict multivariate time series, and the features and labels of the data serve as the input and output of the network.

[0264] Next, this example compares the prediction performance of the seven algorithms under seven real-world multivariate time series data sets. The best results under each data set are marked in bold. The prediction lengths of the five data sets WTH, ER, ECL, ETTh1 and ETTh2 are 168, 336, 720 respectively, and the prediction lengths of the two data sets ETTm1 and ETTm2 are 96, 288, 672 respectively. The performance indicator for comparison is the mean square error MSE. The specific results are shown in Table 1:

[0265] Table 1 Comparison of mean square error (MSE) between the multivariate time series long-term prediction method based on deep FCM of the present invention and other algorithms

[0266]

[0267] It can be seen from Table 1 that the multivariate time series long-term prediction method based on deep FCM of the present invention has a smaller error when processing multivariate long-term time series prediction tasks, and the prediction accuracy is higher.

[0268] Next, an example is used to illustrate the interpretability of the multivariate time series long-term prediction method based on deep FCM of the present invention. Regarding the interpretability of meteorological data prediction, this embodiment uses the WTH dataset for illustration. The WTH dataset has 12 features and a sampling frequency of one hour. Figure 6As shown, the influence relationship between the variables in the time window Δt1 and the time window Δt2 is displayed. By analyzing the learning results of WTH weight values, it can be concluded that the main variables affecting Relative Humidity (RH) in time window Δt2 are Dry Bulb Farenheit (DBF), Dry Bulb Celsius (DBC) and Wind Speed ​​(WS) in time window Δt1. The link weight value between Dry Bulb Farenheit (DBF) in time window Δt1 and Relative Humidity (RH) in time window Δt2 is -0.8524, the link weight value between Dry Bulb Celsius (DBC) in time window Δt1 and Relative Humidity (RH) in time window Δt2 is -0.473, and the link weight value between Wind Speed ​​(WS) in time window Δt1 and Relative Humidity (RH) in time window Δt2 is 0.516. It can be seen that Dry Bulb Farenheit (DBF) in time window Δt1 and Dry Bulb Celsius (DBC) in time window Δt1 have an important influence on Relative Humidity (RH) in time window Δt2. The influence of Humidity (RH) is negatively correlated and has a large impact, which is consistent with the actual situation, that is, the higher the climate temperature, the lower the humidity, while the influence of WindSpeed ​​(WS) in time window Δt1 on Relative Humidity (RH) in time window Δt2 is positive. It is speculated that the wind passes through the area with high humidity, which leads to the positive correlation between wind speed and humidity in the area. In addition to the 12 meteorological variables in the data set, there are other key factors that will also affect variables such as temperature and air pressure, such as precipitation, altitude, etc. These variables are all attributed to unknown factors affecting variables.

[0269] The embodiments of the present invention are given for the purpose of illustration and description, and are not intended to be exhaustive or to limit the invention to the disclosed forms. Many modifications and variations will be apparent to those of ordinary skill in the art. The embodiments are selected and described in order to better illustrate the principles and practical applications of the present invention and to enable those of ordinary skill in the art to understand the present invention and thereby design various embodiments with various modifications suitable for specific uses.

Claims

1. A multivariate time series long-term prediction method based on deep FCM, characterized in that: The steps include: S1. Acquire a multivariate time series data set of the system, wherein the multivariate time series data set is a WTH data set, and the WTH data set collects meteorological data. The multivariate time series data set includes multiple multivariate time series, and each of the multivariate time series includes N attribute feature data and 4 time feature data. The time feature data includes annual feature data, monthly feature data, daily feature data, and hourly feature data. The attribute feature data includes Visibility, Dry Bulb Farenheit, Dry Bulb Celsius, Wet Bulb Farenheit, Dew Point Farenheit, Dew Point Celsius, Relative Humidity, Wind Speed, Wind Direction, Station Pressure, Altimeter, and Wet Bulb Celsius. Unknown factors influencing variables include precipitation and altitude. S2. Fuzzifying the multivariate time series data set to obtain a multivariate time series fuzzy data set consisting of a plurality of fuzzified multivariate time series, wherein the fuzzified multivariate time series includes a plurality of variables, and the variables include annual feature fuzzy data, monthly feature fuzzy data, daily feature fuzzy data, hourly feature fuzzy data, and attribute feature fuzzy data; S3. Based on the multidimensional Gaussian information granule design method of the reasonable granularity principle, the fuzzy multivariate time series in the multivariate time series fuzzy data set is equidistantly overlapped and segmented to obtain multiple time windows, and a multivariate time series segmentation data set composed of multiple time windows is obtained; S4. Constructing a deep dynamic vector fuzzy cognitive map, including: constructing a dynamic vector fuzzy cognitive map, taking each of the attribute feature data and time feature data in the time window Δt1 in the multivariate time series segmentation data set as a concept node of the dynamic vector fuzzy cognitive map, predicting the vector data of the concept node in the next time window Δt2 through the dynamic vector fuzzy cognitive map, constructing a high-order dynamic vector fuzzy cognitive map, predicting the vector data of the concept nodes in all time windows after the time window Δt2 through the high-order dynamic vector fuzzy cognitive map, and before predicting the vector data in the last time window, performing correction prediction through the cross dynamic vector fuzzy cognitive map, and obtaining all predicted time windows after correction and inspection; S5. Defuzzify and denormalize the multivariate time series in the prediction time window, and use the gradient descent algorithm to linearly transform the coefficient w of the principal vector p. p , the coefficient w when linearly transforming from vector q q , the link weight w between concept nodes v and unknown influencing factors u to obtain a trained deep dynamic vector fuzzy cognitive graph model; S6. Obtain the convergence condition of the dynamic vector fuzzy cognitive map by the compression mapping principle, and determine the link weight w between the concept nodes of the deep dynamic vector fuzzy cognitive map model v Whether the convergence condition is met, if it is met, the deep dynamic vector fuzzy cognitive graph model is output and step S7 is performed, if it is not met, return to step S4 to randomly initialize and retrain the link weight w v ; S7. Input the multivariate time series to be predicted into the deep dynamic vector fuzzy cognitive map model to obtain a prediction result.

2. The multivariate time series long-term prediction method based on deep FCM according to claim 1 is characterized in that: In step S1, the length of the multivariate time series data set is L={t a1 ,t a2 ,...,t am }, the multivariate time series dataset As shown in formula (1): in, Represents annual characteristic data, t i ∈(t a1 ,t a2 ,...,t am ), Represents monthly characteristic data, represents daily characteristic data, Represents characteristic data, Represents attribute feature data, b∈(1,2,...,N).

3. The multivariate time series long-term prediction method based on deep FCM according to claim 2 is characterized in that: In step S2, each attribute feature data and time feature data in the multivariate time series data set is processed using z-score, as shown in formula (2): Where μ is the mean of the multivariate time series data set, μ = [μ year μ month μ date μ hour μ1 μ2 ... μ N ], σ is the variance of the multivariate time series data set, σ = [σ year σ month σ date σ hour σ1 σ2 ... σ N ], Represents a multivariate time series dataset after z-score processing; The annual feature data, monthly feature data, daily feature data and hourly feature data are normalized respectively, and the normalization range is [-0.5 0.5]. The multivariate time series data set after z-score processing The data in is fuzzified to obtain the multivariate time series fuzzy data set As shown in formula (3): The multivariate time series fuzzy data set is shown in formula (4): in, represents the fuzzy data of annual features, t i ∈(t a1 ,t a2 ,...,t am ), represents the fuzzy data of monthly features, represents the daily feature fuzzy data, When representing feature fuzzy data, Represents attribute feature fuzzy data, b∈(1,2,...,N).

4. The multivariate time series long-term prediction method based on deep FCM according to claim 3 is characterized in that: In step S3, the equidistant overlapping segmentation includes enumerating the segmentation lengths of all time windows, and obtaining the optimal time window length by a grid search method. The grid search method includes obtaining the average coverage and average specificity corresponding to each time window length. The average coverage is shown in formula (5): Among them, G1,...,G d represents the sequence on each time window after segmentation, d represents the number of segmentations of the time window, k∈(1,2,3…d), L represents the length of the multivariate time series dataset, l represents the length of the time window, and n represents the length of the overlapping time windows. Coverage(G k ) represents coverage, and the coverage is shown in formula (6): Where M represents the sampling times of the multivariate time series fuzzy dataset, D is the multivariate time series segmentation dataset, and f(G k ) is the Gaussian membership function of the multivariate variable, and the Gaussian membership function of the multivariate variable is shown in formula (7): Among them, μ k represents the mean of the variable in time window k, Σ k represents the covariance matrix between variables in time window k, Σ k As shown in formula (8): Among them, cov(x1′,x′ N+4 ) represents the variables x1′ and x′ in time window k N+4 The covariance of The average specificity is shown in formula (9): Among them, SP(G k ) is the specificity, and the specificity is shown in formula (10): Among them, λ i represents the eigenvalues ​​of the covariance matrix of the variables in time window k, Represents the covariance matrix between the variables of the multivariate time series fuzzy dataset, the covariance matrix of the multivariate time series fuzzy dataset As shown in formula (11): Among them, cov(x1,x N+4 ) represents the variables x1 and x in the multivariate time series fuzzy dataset N+4 The covariance of The time window length corresponding to the maximum product of the average coverage and the average specificity is output as the optimal time window length.

5. The multivariate time series long-term prediction method based on deep FCM according to claim 4 is characterized in that: In step S4, the dynamic vector fuzzy cognitive map is as shown in formula (12): Among them, A i (Δt2) represents the vector data predicted by the i-th concept node in the next time window Δt2, Δt2 = [t l-n+1 ,t l-n+2 ,...t 2l-n ], l represents the length of the time window, A j (Δt1) represents the vector data of the j-th concept node in the time window Δt1, Δt1 = [t1, t2, ... t l ], Indicates A j (Δt1) and A i The link weight between (Δt2), u i (Δt1) represents the unknown factor influencing variable of the i-th concept node in the time window Δt1, α ij Represents the vector data of the dynamic coefficient between the i-th concept node and the j-th concept node in the time window Δt1, α ij As shown in formula (13): in, represents the principal vector transformation matrix, Represents a transformation matrix from a vector; The activation function of the dynamic vector fuzzy cognitive map is a sigmoid function, as shown in formula (14): Among them, λ represents the formula inclination, α represents the dynamic coefficient matrix, and w represents the weight matrix. represents the Hadamard product, A represents the concept node matrix on the time window Δt1, U represents the unknown factor influencing variable matrix, The Hadamard product of the dynamic coefficient matrix and the weight matrix is ​​shown in formula (15): The concept node matrix A on the time window Δt1 is shown in formula (16): A=[A1(Δt1)A2(Δt1)...A N+4 (Δt1)](16) The unknown factor influence variable matrix U is shown in formula (17): U=[u1(Δt1)u2(Δt1)...u N+4 (Δt1)](17) The high-order dynamic vector fuzzy cognitive map is shown in formula (18): Among them, A i (Δt x ) represents the i-th concept node in the time window Δt x The predicted vector data, A j (Δt x-1 ) represents the jth concept node in the time window Δt x-1 Vector data on Indicates A j (Δt x-1 ) and A i (Δt x ), A j (Δt x-2 ) represents the jth concept node in the time window Δt x-2 Vector data on Indicates A j (Δt x-2 ) and A i (Δt x ), A j (Δt x-Ω ) represents the jth concept node in the time window Δt x-Ω Vector data on Indicates A j (Δt x-Ω ) and A i (Δt x ), u i (Δt x-1 ) represents the i-th concept node in the time window Δt x-1 Unknown factors affect the variables.

6. A multivariate time series long-term prediction method based on deep FCM according to claim 5, characterized in that: In step S4, the correction prediction uses the predicted multivariate time series of the last time window overlapping the second to last time window as the correction flag, and increases the vector dimension of the correction flag by filling zeros to obtain a correction sequence with the same length as the time window. The cross dynamic vector fuzzy cognitive map is shown in formula (19): Among them, A i (Δt d ) represents the i-th concept node in the time window Δt d The predicted vector data, A j (Δt d-1 ) represents the jth concept node in the time window Δt d-1 Vector data on Indicates A i (Δt d ) and A j (Δt d-1 ), u i (Δt d-1 ) represents the i-th concept node in the time window Δt d-1 The unknown factors on the variables, α ij ′ represents the correction sequence Δt SF The vector data of the i-th concept node and the time window Δt d-1 The vector data of the dynamic coefficients between the j-th concept nodes, α ij ′ is shown in formula (20): Among them, A i (Δt SF ) represents the calibration sequence Δt SF The vector data of the i-th concept node, Denotes the correction sequence Δt SF The principal vector transformation matrix, Represents the time window Δt d-1 The vector transformation matrix of the j-th concept node; The activation function of the cross dynamic vector fuzzy cognitive map is a sigmoid function.

7. The method for long-term prediction of multivariate time series based on deep FCM according to claim 6, characterized in that: In step S5, the multivariate time series in the prediction time window is defuzzified and denormalized, as described in formula (21): in, represents the multivariate time series after defuzzification and denormalization, represents a multivariate time series in the forecast time window, The coefficient w of the linear transformation of the main vector p is obtained by the gradient descent algorithm in the field of deep learning p , the coefficient w when linearly transforming from vector q q , the link weight w between concept nodes v And unknown influencing factors u are trained, and the MSE loss function is used, as shown in formula (22): Among them, len represents the length of the prediction result sequence, Indicates t i The prediction results at the moment, Indicates t i The true value of the moment.

8. The method for long-term prediction of multivariate time series based on deep FCM according to claim 7, characterized in that: In step S6, the convergence condition of obtaining the dynamic vector fuzzy cognitive map by the compression mapping principle includes randomly taking out the concept values ​​of two states in the reasoning process of the dynamic vector fuzzy cognitive map or the high-order dynamic vector fuzzy cognitive map, and obtaining the following as shown in formula (23) by the compression mapping principle: ||G(A)-G(A′)||≤c||AA′||(23) Where A and A′ represent the concept values ​​of the two states in the dynamic vector fuzzy cognitive map reasoning process, c is a constant and c < 1, and the expression of G is shown in formula (24): Among them, u i Represents the unknown factor influencing variable of the i-th concept node, i∈(1,2,3…N+4), α i represents the dynamic coefficient matrix between the i-th concept node and the concept nodes in the same time window, α i =[α i1 α i2 ... α iN+4 ], represents the link weight matrix between the i-th concept node and the concept node in the previous time window, We get formula (25): According to the Cauchy inequality, we get formula (26): Combining formula (25) with formula (26) yields formula (27): because And c′≤λ / 4, we get formula (28): According to the compatibility of vector norm and matrix norm, we get formula (29): According to the principle of softmax mechanism, ||α i || 2 ≤1, we get formula (30): The convergence condition is shown in formula (31): Among them, l represents the length of the current time window, g∈(1,2,…,l).

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