A Fluid Pipeline Flow Prediction Method Based on Adaptive Fuzzy Spectral Clustering and Hybrid Kernel Least Squares Support Vector Machine

Abstract

The present invention belongs to the field of fluid pipeline flow prediction, and specifically relates to a fluid pipeline flow prediction method based on adaptive fuzzy spectral clustering and hybrid kernel least squares support vector machine, including: obtaining a non-stationary fluid pipeline flow sequence, decomposing the non-stationary fluid pipeline flow sequence by using a VMD model to obtain stationary subsequences; performing clustering on all the stationary subsequences by using adaptive fuzzy spectral clustering; inputting the clustered sequences into a fluid pipeline flow prediction model of a hybrid kernel least squares support vector machine to obtain a fluid pipeline flow prediction result; the present invention uses an improved spectral clustering algorithm to perform feature clustering on the subsequences, divides them into three decomposition components with different amplitude-frequency characteristics, then predicts each type of component according to three kernel functions of Gaussian kernel, polynomial kernel and linear kernel, and then reconstructs the prediction results, improving the accuracy of flow prediction.

Description

Technical Field

[0001] The present invention belongs to the field of fluid pipeline flow prediction, and particularly relates to a fluid pipeline flow prediction method based on adaptive fuzzy spectral clustering and hybrid kernel least squares support vector machine. Background Art

[0002] Fluid pipelines are one of the important infrastructures for urban resource transportation. Ensuring the stable operation of fluid pipelines is of great significance for urban construction, environmental protection, and improving residents' living standards. Among them, pipeline flow is a key parameter for measuring the inner wall pressure of the pipeline and preventing problems such as pipeline breakage. By monitoring the real-time flow to achieve accurate prediction, it is beneficial to master the pipeline transportation status, implement effective management, reduce potential safety hazards, and ensure the orderly progress of urban construction.

[0003] By installing flow sensors on fluid pipelines, the flow values of pipeline transportation at each time point can be obtained, and then a fluid pipeline flow sequence is formed. It can be seen that the fluid pipeline flow sequence essentially belongs to a time series and also has characteristics such as non-linearity and non-stationarity. These uncertain characteristics often bring great difficulties to prediction analysis. Dai et al. used empirical mode decomposition (EMD) to decompose the initial flow sequence into different frequencies, converting the original sequence into a series of stationary data sequence components, and finally verified that the proposed method is superior to the non-decomposed time series model in terms of various error indicators. Zhu et al. proposed a flow prediction model combining EMD and particle swarm optimization (PSO) optimized least squares support vector machine, which can effectively improve the prediction accuracy of the model. However, only one type of kernel function is used for prediction analysis, and the adaptability of each decomposed component to different kernel functions is not considered. Ding et al. proposed a least squares support vector machine (LSSVM) time series prediction model based on multiple kernel functions, using the fuzzy C-means algorithm to perform feature clustering on the maximum wavelet decomposition component to construct a hybrid kernel LSSVM prediction model. However, this method is only applied to the decomposition and clustering of small samples, and the effectiveness of this method applied to large-scale sample clustering cannot be verified.

[0004] Spectral clustering (SC) is a classic clustering method based on graph theory. It has become a research hotspot in the field of data mining in recent years because it can handle high-dimensional data well and can show superior clustering benefits on data sets of arbitrary shapes. The similarity matrix is ​​the core of the spectral clustering algorithm. Considering that the construction of the traditional spectral clustering similarity matrix lacks certain robustness and has low construction quality, related studies have proposed a large number of improved spectral clustering algorithms to address these defects. Luo et al. modeled spectral clustering as a constrained multi-objective optimization problem, constructed a similarity matrix using a sparse representation method, and finally verified the effectiveness of the method through a real data set of image segmentation. Cao et al. proposed an efficient approximate spectral clustering method, which improved the performance of spectral clustering on a small representative data set by constructing a sparse similarity graph. In addition, traditional spectral clustering mainly uses the Gaussian kernel function method in the construction of the similarity matrix, which has the problem of difficulty in determining the scale parameter. Nie et al. proposed an adaptive neighborhood method to construct the similarity matrix of spectral clustering. By assigning the optimal neighbor based on the local distance to each data point, the similarity matrix is ​​adaptively learned, avoiding the problem of difficulty in determining the Gaussian kernel function parameter. Subsequently, they also considered the problem that spectral clustering is sensitive to the fixed similarity matrix of the original data, and proposed an entropy regularized adaptive neighborhood unsupervised clustering model (ERCAN) to synchronously update the similarity matrix and clustering results. However, the above studies ignored the limitation that spectral clustering is essentially hard clustering, and lacked consideration of the global distribution of the target data set on the basis of adaptive neighborhood. These problems are detrimental to the construction quality of the spectral clustering similarity matrix, and it is difficult to accurately cluster some samples located in special distribution areas (such as samples in densely populated areas or outliers, etc.). Summary of the invention

[0005] In order to solve the problems existing in the above prior art, the present invention proposes a fluid pipeline flow prediction method based on adaptive fuzzy spectral clustering and hybrid kernel least squares support vector machine, the method comprising:

[0006] S1: Obtain non-stationary fluid pipeline flow sequence;

[0007] S2: VMD model is used to decompose the non-stationary fluid pipeline flow sequence to obtain a stationary subsequence;

[0008] S3: Adaptive fuzzy spectral clustering is used to cluster all stationary subsequences;

[0009] S4: inputting the clustered sequence into the fluid pipeline flow prediction model of the hybrid kernel least squares support vector machine to obtain the fluid pipeline flow prediction result;

[0010] S5: Control the flow rate according to the fluid pipeline flow prediction result.

[0011] Preferably, the process of decomposing the initial non-stationary fluid pipeline flow rate sequence using the VMD model includes:

[0012] S21: Initialize the amplitude of the model estimation mode Center frequency Lagrange multiplier and the number of iterations n = 0;

[0013] S22: Let n←n + 1, and update the amplitude and center frequency of the mode using the amplitude update formula and the center frequency update formula respectively;

[0014] S23: Update the Lagrange multiplier according to the updated amplitude and center frequency;

[0015] S24: Decompose the input sequence according to the updated Lagrange multiplier;

[0016] S25: Calculate the discrimination accuracy ε according to the decomposition result. If ε > 0, output the stationary sequence components {u1(t), u2(t),..., u k (t)}, obtain k modal components and their center frequencies, otherwise return to step S22.

[0017] Furthermore, the formulas for updating the amplitude and center frequency of the mode using the amplitude update formula and the center frequency update formula respectively include:

[0018]

[0019]

[0020] Furthermore, the formula for updating the Lagrange multiplier is:

[0021]

[0022] Preferably, the process of clustering all the stationary subsequences using adaptive fuzzy spectral clustering includes:

[0023] S31: Initialize the membership matrix, the number of clusters, the cluster centers, the connection probability, and the value of the weighted exponent m, and set the maximum number of iterations;

[0024] S32: Construct the objective function of AFSC;

[0025] S33: Solve the objective function of AFSC using the alternating update method and the substitution method to obtain the optimal similarity measure s between pairwise subsequences ij ;

[0026] S34: Construct the similarity matrix S according to the optimal similarity measure result;

[0027] S35: Construct a normalized Laplacian matrix L according to the similarity matrix S;

[0028] S36: Calculate the eigenvectors corresponding to the first k minimum eigenvalues of L;

[0029] S37: Use the K-means algorithm to cluster the above eigenvectors to obtain the final clustering result of the stationary subsequences {u1(t), u2(t),..., u k (t)}.

[0030] Furthermore, the objective function is:

[0031]

[0032]

[0033] where s ij represents the connection probability between the i-th sample and the j-th sample, μ ij represents the fuzzy membership degree of the i-th sample belonging to the j-th cluster, α is the regularization coefficient, c j represents the initial clustering center, F is the indicator matrix, L S is the similarity matrix composed of connection probabilities, and λ1 and λ2 represent the weight coefficients for measuring global and local influences.

[0034] Furthermore, the process of calculating the optimal parameters of the objective function by using the alternating update method and the substitution method includes:

[0035] S321: Fix c, s ij and F, simplify the objective function according to the fixed parameters; use the Lagrangian function to optimize the simplified objective function and solve it to obtain μ;

[0036] S322: Fix μ, s ij and F, simplify the objective function according to the fixed parameters; take the partial derivative of the simplified objective function and set the partial derivative function equal to 0 to calculate c;

[0037] S323: Fix c, μ and F, set intermediate parameters, simplify the objective function according to the fixed parameters and the intermediate parameters; perform 2-norm transformation on the simplified objective function; solve the transformed function to obtain α;

[0038] S324: Fix c, μ and s ij , simplify the objective function according to the fixed parameters and solve the simplified function to obtain F.

[0039] Advantages of the present invention:

[0040] The present invention proposes an improved spectral clustering algorithm based on fuzzy membership and adaptive neighborhood function. This method uses the idea of adaptive neighborhood to determine the similarity measure to avoid the problem of difficult determination of parameters in traditional spectral clustering. On the other hand, this method combines the idea of fuzzy membership, extends spectral clustering to soft clustering, breaks away from the limitation of the non - zero - or - one division criterion, and increases the consideration of the global distribution of samples, improving the construction quality of the similarity matrix. According to the amplitude - frequency characteristics of the sequence, the present invention uses the improved spectral clustering algorithm to perform feature clustering on subsequences, divides them into three decomposition components with different amplitude - frequency characteristics, then constructs a hybrid - kernel LSSVM fluid pipeline flow prediction model according to the adaptability of three kernel functions, namely Gaussian kernel, polynomial kernel and linear kernel, for each type of component, and performs data reconstruction to obtain the final prediction result, making the prediction result more accurate. Brief Description of the Drawings

[0041] Appendix Figure 1 is the overall flowchart of the solution in the embodiment of the present invention;

[0042] Appendix Figure 2 is the flowchart of the AFSC algorithm in the embodiment of the present invention. Detailed Embodiment

[0043] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0044] A fluid pipeline flow prediction method based on adaptive fuzzy spectral clustering and hybrid - kernel least - squares support vector machine. For a non - stationary initial fluid pipeline flow sequence, first, the variational mode decomposition (VMD) is used to decompose the sequence into multiple stationary subsequences. Then, an improved spectral clustering algorithm (AFSC) based on fuzzy membership and adaptive neighborhood function is adopted. This method uses the idea of adaptive neighborhood to determine the similarity measure to avoid the problem of difficult determination of parameters in traditional spectral clustering, and this method combines the idea of fuzzy membership, extends spectral clustering to soft clustering, breaks away from the limitation of the non - zero - or - one division criterion, increases the consideration of the global distribution of samples, and improves the construction quality of the similarity matrix. For the VMD decomposition result, according to the amplitude - frequency characteristics of the sequence, the above - mentioned improved algorithm is used to perform feature clustering on the subsequences, and they are divided into three decomposition components with different amplitude - frequency characteristics. Finally, according to the adaptability of three kernel functions, namely Gaussian kernel, polynomial kernel and linear kernel, for each type of component, a hybrid - kernel LSSVM fluid pipeline flow prediction model is constructed, and data reconstruction is performed to obtain the final prediction result; the fluid pipeline flow is controlled according to the prediction result.

[0045] A fluid pipeline flow prediction method based on adaptive fuzzy spectral clustering and hybrid kernel least squares support vector machine, as Figure 1 shown, the method includes:

[0046] S1: Obtain the non-stationary fluid pipeline flow sequence;

[0047] S2: Decompose the non-stationary fluid pipeline flow sequence using the VMD model to obtain stationary subsequences;

[0048] S3: Cluster all the stationary subsequences using adaptive fuzzy spectral clustering;

[0049] S4: Input the clustered sequence into the fluid pipeline flow prediction model of the hybrid kernel least squares support vector machine to obtain the fluid pipeline flow prediction result;

[0050] S5: Control the flow according to the fluid pipeline flow prediction result.

[0051] The non-stationary fluid pipeline flow sequence is obtained according to the fluid pipeline flow modeling. The construction of the fluid pipeline flow model is a simulation of the flow sequence in the real fluid pipeline environment, which can accurately reflect the essential characteristics of the actual flow. Represent the fluid pipeline flow at time t as X t ∈R N×P , where P represents the flow parameters, including the characteristic attributes of the flow, and N represents the number of time points. According to the statistical results of the historical flow data at N time points, for the fluid pipeline flow data with a time step of T Use the correlation prediction model to predict the flow data for the next T f time steps

[0052] In this embodiment, due to the adverse effect of the non-stationarity of the initial fluid pipeline flow sequence on the prediction accuracy, the present application uses the VMD decomposition algorithm to perform stationary processing on the original sequence. The algorithm establishes a constrained variational problem and aims to find the solution, decomposing the initial flow sequence into a finite number of subsequences. The VMD model is constructed as follows:

[0053] Set the initial flow sequence X(t) to be decomposed into k components, then the corresponding constrained variational model is expressed as:

[0054]

[0055] where ω k represents the center frequency of the k-th mode function, K represents the decomposition layer number, represents the partial derivative operation, δ(t) represents the unit impulse function, and u k (t) represents the mode component.

[0056] Taking the optimal solution of the constrained problem as the solution goal, a Lagrange multiplier λ(t) and a quadratic penalty factor α are added to the constrained variational model to transform the constrained problem into an unconstrained variational problem. Since the reconstruction accuracy of the signal needs to be strictly controlled, the constraint on λ(t) is considered to be extended, and the extended expression is:

[0057]

[0058] where <.> represents the extended expression of the constraint on λ(t).

[0059] The multiplicative operator alternating direction algorithm is introduced to solve the unconstrained variational problem, and the component center frequency and mode are updated to obtain the optimal solution of the model. The expressions for updating the center frequency and the estimated mode in the frequency domain are:

[0060]

[0061]

[0062] where and represent the amplitude and center frequency of the (n + 1)-th mode respectively, represents the instantaneous frequency, represents the modal function u i 's frequency, represents the spectrum of λ, α represents the penalty factor, ω k represents the center frequency, represents the modal function u k 's frequency.

[0063] Specifically, the process of decomposing the initial non-stationary fluid pipeline flow rate sequence using the VMD model includes:

[0064] S21: Initialize the amplitude of the model estimated mode center frequency Lagrange multiplier and the iteration number n = 0;

[0065] S22: Let n ← n + 1, and update the amplitude and center frequency of the mode using the amplitude update formula and the center frequency update formula respectively;

[0066] S23: Update the Lagrange multiplier according to the updated amplitude and center frequency;

[0067] S24: Decompose the input sequence according to the updated Lagrange multiplier;

[0068] S25: Calculate the discrimination accuracy ε according to the decomposition result. If ε > 0, output the stationary sequence components {u1(t), u2(t),..., u k (t)}, obtain k modal components and their center frequencies; otherwise, return to step S22.

[0069] In this embodiment, adaptive fuzzy spectral clustering is used to cluster all stationary subsequences. The essence of spectral clustering is the evolution based on K-means clustering and belongs to the category of hard clustering. Hard clustering means that a sample can only belong to one category, which deviates from the objective facts and is not conducive to applications in datasets with complex sample structures and uneven distributions. Most traditional spectral clustering methods use the full connection method, that is, the method of using the Gaussian kernel function to obtain the pairwise similarity between samples. However, the scale parameter in the Gaussian kernel function often needs to be set manually, and its value is extremely sensitive to the distribution of the original data samples. The adaptive neighborhood idea can well satisfy the local distribution of data, but the determination of the connection probability lacks consideration of the global distribution of samples. For some samples located in areas with high density or outliers located at the edge positions, etc., the connection probability cannot be well determined, thus further affecting the construction of the similarity matrix.

[0070] To solve the problems of the above traditional clustering, obtain a more accurate connection probability, that is, similarity measure, and then construct a more robust similarity matrix, this application designs an improved spectral clustering algorithm (AFSC) based on fuzzy membership and adaptive neighborhood function. First, replace the similarity measure in the original spectral clustering objective function with the connection probability and perform Laplace transform to establish a connection for the subsequent improvement part. Then, based on the adaptive neighborhood and the spectral clustering objective function, introduce the idea of membership, consider the membership of each sample point located in different distribution regions to each initial clustering center, add a global perspective to the determination of the connection probability, and improve the construction quality of the similarity matrix. Finally, the result of AFSC, that is, the similarity measure, is derived through the alternating update method and the substitution method, and the final similarity matrix is constructed using this result.

[0071] The AFSC algorithm process is as Figure 2 shown, and the specific objective function is expressed as:

[0072]

[0073] where s ij represents the connection probability between the i-th sample and the j-th sample, μ ij represents the fuzzy membership of the i-th sample belonging to the j-th cluster, α is the regularization coefficient, c j represents the initial clustering center, F is the indicator matrix, L S is the similarity matrix composed of connection probabilities, and λ1 and λ2 represent the weight coefficients for measuring the global and local influences.

[0074] According to the properties of the Laplace function, Tr(F T L S F) can be equivalently replaced by the following form:

[0075]

[0076] According to the equivalent replacement formula of Tr(F T L S F), formula (6) is transformed, and its transformed expression is:

[0077]

[0078] From problem (8), it can be seen that the connection probability s i between the target sample x ij and its nearest neighbor points can be comprehensively obtained through the spectral clustering component, membership function component, and adaptive neighborhood function component of the objective function in problem (8). s ij As a bridge connecting these three components, the result obtained in this way can better satisfy the global and local structures of the target dataset.

[0079] Specifically, the influence of the connection probability in the adaptive neighborhood method is added to the update of the membership degree, that is, the local distribution of the samples is considered, making the update result more accurate. In contrast, for the traditional adaptive neighborhood function Through this construction method, for some samples located in special distribution regions, such as samples in high-density regions and samples in edge discrete regions, when updating the connection probability s ij the membership degree of the target sample to the initial clustering center is considered, that is, the global distribution of the samples is considered. The final updated result of s ij obtained in the above way, and the constructed similarity matrix is more robust and better satisfies the true structure of the data.

[0080] In this embodiment, the alternating update method and the substitution method are used to calculate the optimal parameters of the objective function; specifically including:

[0081] S321: Fix c, s ij and F, simplify the objective function according to the fixed parameters; use the Lagrangian function to optimize the simplified objective function and solve it to obtain μ. The specific process is as follows:

[0082] The formula after simplifying the objective function according to the fixed parameters is:

[0083]

[0084]

[0085] Among them, n represents the number of samples, r represents the number of cluster centers, and s ij represents the connection probability, represents the membership degree, and x i represents the i-th sample, and c j represents the j-th cluster center, represents the sum of the membership degrees of the i-th sample to all cluster centers.

[0086] Using the Lagrange multiplier method, the constraint 0 ≤ μ ij ≤ 1 is scaled into the objective function, and the Lagrangian function is expressed as follows:

[0087]

[0088] Among them, η ≥ 0 is the Lagrange multiplier.

[0089] Let λ1 = 1, and take the partial derivative of μ in problem (10) ij and set it to 0. Its expression is:

[0090]

[0091] Also from it can be obtained that:

[0092]

[0093] Substitute equation (12) into equation (11) to get:

[0094]

[0095] Among them, m represents the weighting exponent, characterizing the degree of fuzzification. The best range is [1, 2.5], and generally 2 is appropriate. x i represents the i-th sample.

[0096] S322: Fix μ, s ij and F, simplify the objective function according to the fixed parameters; take the partial derivative of the simplified objective function and set the partial derivative function equal to 0 to calculate c.

[0097] Rewrite problem (8) according to the fixed parameters as:

[0098]

[0099] Let λ1 = 1, and take the partial derivative of c in equation (15) j and set it to 0:

[0100]

[0101] Solve for c according to the above formula.

[0102] S323: Fix c, μ, and F, set intermediate parameters, simplify the objective function based on the fixed parameters and intermediate parameters; perform a 2-norm transformation on the simplified objective function; solve the transformed function to obtain α.

[0103] According to the fixed parameters, problem (8) can be written as:

[0104]

[0105] Let Then equation (16) becomes the following form:

[0106]

[0107] Let Then equation (17) can be expressed as the following form:

[0108]

[0109] Perform a 2-norm transformation on equation (18):

[0110]

[0111] Then from problem (19), the Lagrangian function can be obtained as:

[0112]

[0113] where η2≥0, η3≥0 are Lagrange multipliers.

[0114] Use the standard Karush-Kuhn-Tucker (KKT) conditions to solve problem (20) and obtain the following results:

[0115]

[0116] Finally, combining the results obtained from equation (21), we define the regularization coefficient α. From the constraint and equation (21), we have:

[0117]

[0118] From equation (21), we also know that s ik > 0, s i,k+1 = 0, then we have:

[0119]

[0120] Substitute equation (22) into equation (23) to get:

[0121]

[0122] Through the defined range of the regularization coefficient α above, we use the average value of α1, α2, …, α n as the final α, which is expressed as follows:

[0123]

[0124] S324: Fix c, μ, and s ij , simplify the objective function according to the fixed parameters, and solve the simplified function to obtain F.

[0125] Write problem (8) according to the fixed parameters as:

[0126]

[0127] The optimal solution F of problem (26) consists of the c eigenvectors corresponding to the first c smallest eigenvalues of L S , which is consistent with the relaxation optimization process of spectral clustering.

[0128] Apply the proposed improved algorithm AFSC to the clustering of VMD decomposition components; use the VMD decomposition components {u1(t), u2(t),..., u k (t)} as the target data set, and regard the components as individual randomly distributed sample points; select the amplitude and frequency characteristics of each sample point as the sample feature set to perform feature clustering. Since the low-frequency components with high amplitudes represent the change trends of these components, and the high-frequency components with low amplitudes represent the details containing noise, these components should be divided into at least 3 categories, including: high-frequency low-amplitude components, medium-frequency medium-amplitude components, and low-frequency high-amplitude components.

[0129] In this paper, LSSVM is used to construct a fluid pipeline flow prediction model for each flow sequence component. LSSVM has the advantages of simple solution and high operation efficiency, and it contains a large number of kernel functions that can flexibly handle various nonlinear regression problems. Its model construction is as follows:

[0130] Let the sample set of the fluid pipeline flow decomposition components be where u i is the input vector (the flow data at each time point in the flow sequence component), y i is its output value, m is the sample size, R n represents the set of n-dimensional real numbers, and R represents the set of real numbers.

[0131] The regression prediction expression of LSSVM is shown as follows:

[0132]

[0133] where, αi where \( \mathbf{w} \) represents the weight vector, \( b \) represents the bias, and \( K(\mathbf{u}, \mathbf{u'} ) \) represents the kernel function, which is the inner product in the high-dimensional feature space. In this paper, three kernel functions, namely the Gaussian kernel, the linear kernel, and the polynomial kernel, are mainly used, and their corresponding expressions are as follows: i

[0134]

[0135] where \( K \) GAU represents the Gaussian kernel, \( \sigma \) represents the kernel function parameter, \( K \) POL represents the polynomial kernel, and \( K \) LIN represents the linear kernel, and \( T \) represents the transpose.

[0136] The Gaussian kernel is representative of local kernel functions. Such kernel functions can effectively extract information near sample points and have strong learning ability, but weak generalization ability. The polynomial kernel function and the linear kernel function are representative of global kernel functions. They have strong generalization ability for sample points at a distance and can obtain global information far from the sample points, but their learning ability for data in a small neighborhood near the sample points is weak. For high-frequency sequence components, the overall change trend is complex and the autocorrelation is weak, so it is suitable to use the LSSVM with local kernel functions for prediction analysis. For low-frequency sequence components, which represent the overall change trend of the original sequence and have strong autocorrelation, it is suitable to use the LSSVM with global kernel functions for prediction analysis. Therefore, according to the clustering results of AFSC, we construct a Gaussian kernel LSSVM prediction model for high-frequency and low-amplitude components, a polynomial kernel LSSVM prediction model for medium-frequency and medium-amplitude components, and a linear kernel LSSVM prediction model for low-frequency and high-amplitude components. Substituting Equation (28) into Equation (27), the hybrid kernel LSSVM prediction model is obtained as follows:

[0137]

[0138] where \( f_1(\mathbf{u}) \), \( f_2(\mathbf{u}) \), and \( f_3(\mathbf{u}) \) are the prediction functions for the high-frequency and low-amplitude component sequence, the medium-frequency and medium-amplitude component sequence, and the low-frequency and high-amplitude component sequence, respectively. Finally, by adding up the prediction results of the three prediction functions, that is, data reconstruction, the final predicted result of the fluid pipeline flow rate is obtained.

[0139] The above-described embodiments further illustrate the object, technical solution, and advantages of the present invention. It should be understood that the above-described embodiments are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made to the present invention within the spirit and principle of the present invention shall be included in the protection scope of the present invention.​

Claims

1. A fluid pipeline flow prediction method based on adaptive fuzzy spectral clustering and hybrid kernel least squares support vector machine, characterized in that, Including: S1: Obtain the non-stationary fluid pipeline flow rate sequence; S2: Decompose the non-stationary fluid pipeline flow rate sequence using the VMD model to obtain stationary subsequences; specifically including: S21: Initialize the amplitude of the model estimation mode Center frequency Lagrange multiplier And the number of iterations n = 0; S22: Let n←n + 1, and update the amplitude and central frequency of the mode using the amplitude update formula and the central frequency update formula respectively; S23: Update the Lagrange multiplier according to the updated amplitude and central frequency; S24: Decompose the input sequence according to the updated Lagrange multiplier; S25: Calculate the discrimination accuracy ε according to the decomposition result. If ε > 0, output the stationary sequence components {u1(t), u2(t),..., u k (t)}, and obtain k modal components and their center frequencies; otherwise, return to step S22; S3: Cluster all the stationary subsequences using adaptive fuzzy spectral clustering; specifically including: S31: Initialize the membership matrix, the number of clusters, the cluster centers, the connection probability, and the value of the weighted exponent m, and set the maximum number of iterations; S32: Construct the objective function of AFSC; the expression of the objective function is: where s ij represents the connection probability between the i-th sample and the j-th sample, μ ij represents the fuzzy membership of the i-th sample belonging to the j-th cluster, α is the regularization coefficient, c j represents the initial clustering center, F is the indicator matrix, L S is the similarity matrix composed of connection probabilities, and λ1 and λ2 represent the weight coefficients for measuring global and local influence; S33: Solve the objective function of AFSC by using the alternating update method and the substitution method to obtain the optimal similarity measure s between paired subsequences ij ; S34: Construct the similarity matrix S according to the optimal similarity measurement result; S35: Construct the normalized Laplacian matrix L according to the similarity matrix S; S36: Calculate the eigenvectors corresponding to the first k smallest eigenvalues of L; S37: Cluster the above eigenvectors using the K-means algorithm to obtain the stationary subsequences {u1(t), u2(t),..., u k (t)}; the final clustering result S4: Input the clustered sequence into the fluid pipeline flow rate prediction model of the hybrid kernel least squares support vector machine to obtain the fluid pipeline flow rate prediction result; S5: Control the flow rate according to the fluid pipeline flow rate prediction result.

2. The fluid pipeline flow prediction method based on adaptive fuzzy spectral clustering and hybrid kernel least squares support vector machine according to claim 1, wherein The formulas for updating the amplitude and central frequency of the mode using the amplitude update formula and the central frequency update formula respectively include: Among them, represents the updated spectrum, ω represents the center frequency, represents the instantaneous frequency, represents the frequency of the mode function u i of, represents the spectrum of λ, α represents the penalty factor, ω represents the center frequency, ω k represents the center frequency, represents the updated center frequency, represents the frequency of the mode function u k of.

3. A fluid pipeline flow prediction method based on adaptive fuzzy spectral clustering and hybrid kernel least squares support vector machine according to claim 1, characterized in that, The formula for updating the Lagrange multiplier is: Among them, represents the spectrum of λ after update, represents the instantaneous frequency, represents the updated spectrum.

4. A fluid pipeline flow prediction method based on adaptive fuzzy spectral clustering and hybrid kernel least squares support vector machine according to claim 1, characterized in that, The process of calculating the optimal parameters of the objective function using the alternating update method and the substitution method includes: S321: Fix c and s ij and F, simplify the objective function according to the fixed parameters; use the Lagrangian function to optimize the simplified objective function and solve it to obtain μ; S322: Fix μ and s ij And F, simplify the objective function according to the fixed parameters; take the partial derivative of the simplified objective function and set the partial derivative function equal to 0 to calculate c; S323: Fix c, μ, and F, set intermediate parameters, simplify the objective function according to the fixed parameters and the intermediate parameters; perform 2-norm transformation on the simplified objective function; solve the transformed function to obtain α; S324: Fix c, μ, and s ij , simplify the objective function according to the fixed parameters, and solve the simplified function to obtain F.

5. A fluid pipeline flow prediction method based on adaptive fuzzy spectral clustering and hybrid kernel least squares support vector machine according to claim 1, characterized in that, The process of processing the clustered sequence using the fluid pipeline flow rate prediction model of the hybrid kernel least squares support vector machine includes: The fluid pipeline flow rate prediction model of the hybrid kernel least squares support vector machine includes the Gaussian kernel LSSVM prediction model, the polynomial kernel LSSVM prediction model, and the linear kernel LSSVM prediction model; The input sequence includes high-frequency low-amplitude components, medium-frequency medium-amplitude components, and low-frequency high-amplitude components; Input the high-frequency low-amplitude components into the Gaussian kernel LSSVM prediction model for flow rate prediction, input the medium-frequency medium-amplitude components into the polynomial kernel LSSVM prediction model for flow rate prediction, and input the low-frequency high-amplitude components into the linear kernel LSSVM prediction model for flow rate prediction; Accumulate and reconstruct the prediction results of the three types of prediction models to obtain the final prediction result of the fluid pipeline flow rate.

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