Submarine cable temperature rapid calculation method based on support vector regression

Abstract

The invention discloses a submarine cable temperature rapid calculation method based on support vector regression. The method comprises the following steps: S1, determining a sample space of submarine cable temperature and obtaining a sample working condition data set; s2, calculating a node temperature column vector of each sample working condition based on the submarine cable simulation calculation model, forming a snapshot matrix, and obtaining a base vector and a POD modal coefficient matrix of the submarine cable temperature field reduced-order model according to the snapshot matrix; s3, constructing a support vector regression model between the sample working condition and the POD modal coefficient matrix, and obtaining a corresponding POD modal coefficient according to the input test working condition; and S4, reconstructing a submarine cable temperature field reduced-order model according to the basis vector and the POD modal coefficient. According to the method, the calculation speed is increased to the second level, the temperature change of the submarine cable can be reflected in real time, and compared with traditional finite element multi-physics field coupling calculation, the method has remarkable advantages in calculation speed and precision.

Description

Technical Field

[0001] The present invention belongs to the technical field of calculating the temperature distribution of submarine cables, and specifically relates to a method for quickly calculating the temperature of submarine cables based on support vector regression. Background Art

[0002] As the power collection and transmission system of offshore wind farms, submarine cables also play an important role in island power supply, independent grid interconnection, power supply for offshore oil platforms, and short-distance power transmission across rivers and straits. The temperature condition of submarine cables is closely related to their operating status. Therefore, how to efficiently and accurately determine the temperature distribution of submarine cables and evaluate their operating status based on this has become an urgent problem to be solved. Although traditional numerical simulation techniques (such as finite element analysis, finite volume analysis, etc.) have made certain progress in solving the calculation problem of the electrothermal field of submarine cables, due to the high degrees of freedom involved in these methods and the need for discretization processing in both spatial and temporal dimensions, this results in a huge amount of calculation, and the calculation time may be as long as several hours, which cannot meet the real-time requirements of the digital twin model.

[0003] In order to improve the calculation speed while maintaining the accuracy of traditional numerical calculation methods, researchers at home and abroad have proposed using machine learning techniques to construct digital twin models of electrical equipment. However, the current research on digital twin models of the electrothermal field of power equipment is still in its infancy, and there is relatively little research on the temperature reduction model of submarine cables. Summary of the Invention

[0004] The purpose of the invention is to overcome the disadvantages and deficiencies existing in the prior art, and provide a method for quickly calculating the temperature of submarine cables based on support vector regression, which can realize the quick calculation of the temperature of submarine cables and improve the calculation accuracy and efficiency.

[0005] The purpose of the present invention is achieved by the following technical solutions: A method for quickly calculating the temperature of submarine cables based on support vector regression includes the steps:

[0006] S1. Determine the sample space of the temperature of the submarine cable and obtain the sample working condition data set of the temperature of the submarine cable;

[0007] S2. Calculate the nodal temperature column vectors of each sample working condition based on the submarine cable simulation calculation model, form a snapshot matrix with the nodal temperature column vectors, and obtain the basis vectors U′ and the POD modal coefficient matrix α of the temperature field reduction model of the submarine cable according to the snapshot matrix;

[0008] S3. Construct a support vector regression model between the sample working conditions and the POD modal coefficient matrix α, and obtain the corresponding POD modal coefficient α′ of the input test working condition based on the support vector regression model;

[0009] S4. Reconstruct the reduced-order model of the submarine cable temperature field according to the basis vectors U' and the POD modal coefficients α'.

[0010] Preferably, step S1 specifically includes: selecting the three most significant factors affecting the temperature of the submarine cable, including the current-carrying capacity, seawater temperature, and seawater velocity, presetting the value ranges of each factor to form a sample space, and then obtaining a sample working condition data set through the Latin hypercube sampling method.

[0011] Preferably, step S2 specifically includes:

[0012] S21. Form a snapshot matrix by arranging the node temperature column vectors:

[0013] X = [x 1 , x 2 , …, x n , Equation (1),

[0014] where X is the snapshot matrix, and let x i be the node temperature column vector, i ∈ [1, n];

[0015] S22. Perform singular value decomposition on the snapshot matrix:

[0016] X = U·Σ·V T , Equation (2),

[0017] where U = (ψ 1 , ψ 2 , … ψ n ), Σ = diag(λ 1 , λ 2 , … λ n ),

[0018] In the formula, U is the eigenvector matrix, ψ i is the eigenvector, Σ is the diagonal matrix, λ i is the eigenvalue corresponding to the eigenvector, and V T is the right orthogonal matrix;

[0019] S23. Arrange the eigenvalues λ i from largest to smallest, and select the eigenvectors corresponding to the first m eigenvalues to form the basis vectors U' of the reduced-order model of the submarine cable temperature field, where m ≤ n:

[0020] U' = (ψ 1 , ψ 2 , … ψ m ), Equation (3);

[0021] S24. Select the first m-order diagonal matrix ∑' and the first m-order right orthogonal matrix V' and obtain the POD modal coefficient matrix α:

[0022] α = V'·∑', Equation (4).

[0023] Preferably, in step S3, the construction of the support vector regression model includes the following steps:

[0024] S31. Set feature variables and target variables: Use the current-carrying capacity, seawater temperature, and seawater velocity as feature variables, and use the POD mode coefficient matrix as the target variable;

[0025] S32. Initialize the model hyperparameters: Set initial values for the model hyperparameters including the kernel function, regularization parameter, and tolerance rate parameter;

[0026] S33. Preliminary training: Use the initial parameters to perform preliminary training on the sample working condition data to obtain an initial support vector regression model;

[0027] S34. Hyperparameter tuning: Select the optimal hyperparameter combination through grid search and cross-validation;

[0028] S35. Model evaluation: Use the mean squared error MSE as the evaluation index to select the optimal parameters;

[0029] S36. Retrain the model: Retrain the model using the optimal parameters to finally obtain an optimized support vector regression model.

[0030] Preferably, in step S4, the expression of the reduced-order model for reconstructing the submarine cable temperature field is:

[0031] x = U'α', Equation (5),

[0032] where x represents the column vector of the submarine cable temperature under the input sample working conditions.

[0033] Preferably, the initial values in step S32 specifically include: the initial value of the kernel function is the Gaussian kernel radial basis function, the initial value of the regularization parameter is 1, and the initial value of the tolerance rate parameter is 0.1.

[0034] Preferably, step S34 specifically includes the following steps:

[0035] S341. Search through grid search within the specified hyperparameter range to find the optimal hyperparameter combination;

[0036] where the value range of the kernel function is set to the linear kernel, polynomial kernel, and radial basis kernel function, the value range of the regularization parameter is [0.1, 10], and the value range of the tolerance rate is [0.1, 0.3], and a hyperparameter grid is formed;

[0037] S342. For the performance of each hyperparameter combination in the hyperparameter network, perform k-fold cross-validation using the sample space training set: divide the training set into k subsets, each time select one of the subsets as the validation set, and the remaining k - 1 subsets as the training set, and train k models.

[0038] Preferably, in step S35, the expression of the mean square error MSE is:

[0039]

[0040] where y i is the actual value, is the predicted value, n is the number of samples, and select the hyperparameter combination that minimizes the mean square error MSE as the optimal parameter.

[0041] Preferably, the first m eigenvalues need to satisfy:

[0042]

[0043] Preferably, the construction of the submarine cable simulation calculation model specifically includes:

[0044] Use the finite element method to model the 35kV three-core submarine cable, and consider the influence of the seabed soil and seawater; set the geometric model size of the 35kV three-core submarine cable; set the initial temperature of each layer of the cable and the environment to 25°C, and set the geometric model boundary to thermal insulation with a normal heat flux density of 0.

[0045] The present invention has the following advantages and effects compared with the prior art:

[0046] (1) The present invention provides a method for quickly calculating the temperature of a submarine cable based on support vector regression. By reducing the order model, the complex multi-physical field problem is simplified into a low-dimensional regression problem. By introducing the support vector regression model SVR and combining it with the reduced order model of the submarine cable temperature field, the mapping relationship between the input working conditions (current-carrying capacity, seawater temperature, seawater velocity) and the target variable (POD modal coefficient) is fitted to achieve the rapid calculation of the submarine cable temperature, and the calculation speed is increased to the second level, which can reflect the temperature change of the submarine cable in real time. Compared with the traditional finite element multi-physical field coupling calculation, this method has significant advantages in both calculation speed and accuracy, and can meet the requirements of digital twin applications for real-time and accuracy. This method is not only applicable to the calculation of the submarine cable temperature, but also provides an efficient solution for digital twin, and has a wide application prospect.

[0047] (2) The support vector regression model with Gaussian kernel radial basis function introduced in the present invention can transform the non - linear problem into a linear problem in a high - dimensional space for solution, can more accurately describe the relationship between the current - carrying capacity, seawater temperature, seawater velocity and POD modal coefficients (that is, fit the data more precisely), and can improve the accuracy of the algorithm. Description of the Drawings

[0048] Figure 1 It is a schematic flow chart of a method for quickly calculating the temperature of submarine cables based on support vector regression according to the present invention.

[0049] Figure 2 It is a schematic structural diagram of a 35kV three - core submarine cable finite - element model in the embodiment.

[0050] Figure 3 It is a schematic flow chart of the construction and training of the support vector regression model of the present invention. Detailed Embodiments

[0051] The present invention will be further described in detail below in conjunction with the embodiments and the drawings, but the embodiments of the present invention are not limited thereto.

[0052] Embodiment 1

[0053] As Figure 1 shown, it is a schematic flow chart of a method for quickly calculating the temperature of submarine cables based on support vector regression, including the steps:

[0054] S1. Determine the sample space of the submarine cable temperature and obtain the sample condition data set of the submarine cable temperature;

[0055] Step S1 specifically includes: Select the three most significant factors affecting the submarine cable temperature, including the current - carrying capacity, seawater temperature and seawater velocity, and preset the value ranges of each factor to form a sample space, and then obtain the sample condition data set through the Latin hypercube sampling method.

[0056] Specifically, in this embodiment, the value ranges specifically include: the current - carrying capacity I ∈ [200, 700] A, the seawater temperature T ∈ [3, 30] °C, and the seawater velocity V ∈ [0, 1] m / s. Among them, the method of obtaining the sample condition data set through the Latin hypercube sampling method includes: evenly dividing the sample space intervals of the three dimensions of the current - carrying capacity, seawater temperature, and seawater velocity into N layers, randomly taking values in each layer, and then randomly matching the values taken in each layer from each dimension to form N three - dimensional sample sampling points.

[0057] S2. Calculate the node temperature column vectors of each sample condition based on the submarine cable simulation calculation model, form a snapshot matrix with the node temperature column vectors, and obtain the basis vector U′ and the POD modal coefficient matrix α of the submarine cable temperature field reduced - order model according to the snapshot matrix;

[0058] Step S2 specifically includes:

[0059] S21. Form a snapshot matrix by using the column vectors of the temperatures of each node:

[0060] X = [x 1 , x 2 , …, x n , Equation (1),

[0061] where X is the snapshot matrix, and let x i be the column vector of the node temperature, and i ∈ [1, n];

[0062] S22. Perform singular value decomposition on the snapshot matrix:

[0063] X = U·Σ·V T , Equation (2),

[0064] where U = (ψ 1 , ψ 2 , … ψ n ), Σ = diag(λ 1 , λ 2 , … λ n ),

[0065] In the formula, U is the eigenvector matrix, ψ i is the eigenvector, Σ is the diagonal matrix, λ i is the eigenvalue corresponding to the eigenvector, and V T is the right orthogonal matrix;

[0066] S23. Arrange the eigenvalues λ i in descending order, and select the eigenvectors corresponding to the first m eigenvalues to form the basis vectors U' of the reduced-order model of the submarine cable temperature field, where m ≤ n:

[0067] U' = (ψ 1 , ψ 2 , … ψ m ), Equation (3);

[0068] S24. Select the first m-order diagonal matrix ∑′ and the first m-order right orthogonal matrix V′ and obtain the POD modal coefficient matrix α:

[0069] α = V′·∑′, Equation (4).

[0070] In this embodiment, in order to meet the requirements of the downgraded calculation accuracy, the first m eigenvalues need to satisfy:

[0071]

[0072] Specifically, in this embodiment, the construction of the submarine cable simulation calculation model specifically includes: using the finite element method to model a 35 kV three-core submarine cable and considering the influence of submarine soil and seawater; the geometric model dimensions of the 35 kV three-core submarine cable include a core diameter of 26.2 mm, an insulation layer thickness of 24.0 mm, a shielding layer thickness of 2.9 mm, an armor thickness of 5.6 mm, an inner sheath thickness of 2.9 mm, and an outer sheath thickness of 3.5 mm; the length of the submarine cable simulation calculation model is 5 m, the width is 2 m, and the height is 6 m, where the water layer height is 2 m and the soil layer height is 4 m; the 35 kV three-core submarine cable is buried, and the burial depth is 2 m; the initial temperature of each layer of the cable and the environment is set to 25 °C, and the geometric model boundary is set to thermal insulation with a normal heat flux density of 0. The cable used is of model

[0073] HYJYF41-F26 / 35ky3×70mm 2 +2×36B1, and the structural schematic diagram of the 35 kV three-core submarine cable finite element model is shown in Figure 2 as

[0074] S3. Construct a support vector regression model between the sample working conditions and the POD modal coefficient matrix α, and obtain the POD modal coefficient α' corresponding to the input test working conditions based on the support vector regression model;

[0075] In step S3, the construction of the support vector regression model includes the following steps:

[0076] S31. Set the characteristic variables and target variables: use the current-carrying capacity, seawater temperature, and seawater velocity as the characteristic variables, and the POD modal coefficient as the target variable;

[0077] S32. Initialize the model hyperparameters: set initial values for the model hyperparameters including the kernel function, regularization parameter, and error tolerance parameter; among them, the initial value of the kernel function is the Gaussian kernel radial basis function, the initial value of the regularization parameter is 1, and the initial value of the error tolerance parameter is 0.1.

[0078] S33. Preliminary training: use the initial parameters to perform preliminary training on the sample working condition data to obtain an initial support vector regression model;

[0079] S34. Hyperparameter tuning: select the optimal combination of hyperparameters through grid search and cross-validation;

[0080] Step S34 specifically includes the following steps:

[0081] S341. Search through grid search for the optimal combination of hyperparameters within the specified hyperparameter range;

[0082] Among them, the value range of the kernel function is set as linear kernel, polynomial kernel, and radial basis kernel function, the value range of the regularization parameter is [0.1, 10], the value range of the error tolerance rate is [0.1, 0.3], and a hyperparameter network is formed;

[0083] S342. For the performance of each hyperparameter combination in the hyperparameter network, use the sample space training set for k-fold cross-validation: divide the training set into k subsets, each time select one of the subsets as the validation set, and the remaining k - 1 subsets as the training set, and train k models.

[0084] S35. Model evaluation: Use the mean square error MSE as the evaluation index and select the optimal parameters:

[0085] The expression of the mean square error MSE is:

[0086]

[0087] where y i is the actual value, is the predicted value, n is the number of samples, and select the hyperparameter combination that minimizes the mean square error MSE as the optimal parameter.

[0088] S36. Retrain the model: Retrain the model using the optimal parameters to finally obtain an optimized support vector regression model.

[0089] Specifically, as Figure 3 shown is the schematic diagram of the construction and training process of the support vector regression model in the present invention. In this embodiment, the introduction of the support vector regression model with Gaussian kernel radial basis function can more accurately fit the data, and optimize the hyperparameters through grid search and cross-validation, further improving the prediction accuracy of the model.

[0090] S4. Reconstruct the reduced-order model of the submarine cable temperature field according to the basis vector U' obtained in step S2 and the POD modal coefficient α' obtained in step S3. The expression of the reconstructed reduced-order model of the submarine cable temperature field is:

[0091] x = U'α', Equation (5),

[0092] where x represents the column vector of the submarine cable temperature under the input sample working conditions, realizing the rapid calculation of the submarine cable temperature.

[0093] In summary, the present invention provides a rapid calculation method for the temperature of submarine cables based on support vector regression. By means of a reduced-order model, complex multi-physical field problems are simplified into low-dimensional regression problems. By introducing the support vector regression model SVR and combining it with the reduced-order model of the submarine cable temperature field, that is, taking the POD modal coefficients as the target variables, the SVR model is used to establish the mapping relationship between the input features (current-carrying capacity, seawater temperature, seawater velocity) and the target variables, and the calculation speed is increased to the second level, which can reflect the temperature change of the submarine cable in real time. Compared with the traditional finite element multi-physical field coupling calculation, this method has significant advantages in both calculation speed and accuracy, and can meet the requirements of digital twin applications for real-time performance and accuracy. This method is not only applicable to the temperature calculation of submarine cables, but also provides an efficient solution for digital twins, with broad application prospects.

[0094] The above embodiments are preferred embodiments of the present invention and cannot limit the present invention. Any other changes or other equivalent replacement methods made without departing from the technical solutions of the present invention are included in the protection scope of the present invention.

Claims

1. A method for rapid calculation of submarine cable temperature based on support vector regression, characterized in that: Includes steps: S1. Determine the sample space of the submarine cable temperature and obtain a sample operating condition data set of the submarine cable temperature; S2. Calculate the node temperature column vector of each sample working condition based on the submarine cable simulation calculation model, form each node temperature column vector into a snapshot matrix, and obtain the basis vector U′ and POD modal coefficient matrix α of the submarine cable temperature field reduction model according to the snapshot matrix; S3, constructing a support vector regression model between the sample working condition and the POD modal coefficient matrix α, and obtaining the POD modal coefficient α′ corresponding to the input test working condition based on the support vector regression model; S4. Reconstruct the reduced-order model of the submarine cable temperature field based on the basis vector U' and the POD modal coefficient α'.

2. A method for rapid calculation of submarine cable temperature based on support vector regression according to claim 1, characterized in that: Step S1 specifically includes: selecting the three most significant factors affecting the temperature of the submarine cable, including current carrying capacity, seawater temperature and seawater velocity, and presetting the value range of each factor to form a sample space, and then obtaining a sample operating condition data set through the Latin hypercube sampling method.

3. The method for rapid calculation of submarine cable temperature based on support vector regression according to claim 1 is characterized in that: Step S2 specifically includes: S21. The temperature column vectors of each node are combined into a snapshot matrix: X=[x1,x2,…,x n ], formula (1), Among them, X is the snapshot matrix, let x i is the node temperature column vector, i∈[1,n]; S22. Perform singular value decomposition on the snapshot matrix: X = U Σ V T , Equation (2), Where, U=(ψ1,ψ2,…ψ n ),Σ=diag(λ1,λ2,…λ n ), Where U is the eigenvector matrix, ψ i is the eigenvector, Σ is a diagonal matrix, λ i is the eigenvalue corresponding to the eigenvector, V T is a right orthogonal matrix; S23, the eigenvalue λ i Arrange from large to small, and select the eigenvectors corresponding to the first m eigenvalues ​​to form the basis vector U' of the reduced-order model of the submarine cable temperature field, where m≤n: U'=(ψ1,ψ2,…ψ m ), expression(3); S24. Select the first m-order diagonal matrix Σ′ and the first m-order right orthogonal matrix V′ and obtain the POD modal coefficient matrix α: α=V′·∑′, formula (4).

4. The method for rapid calculation of submarine cable temperature based on support vector regression according to claim 2 is characterized in that: In step S3, the construction of the support vector regression model includes the following steps: S31, setting characteristic variables and target variables: taking current carrying capacity, seawater temperature and seawater velocity as characteristic variables, and taking POD modal coefficient matrix as target variable; S32, initializing model hyperparameters: setting initial values ​​for model hyperparameters including kernel function, regularization parameter and fault tolerance parameter; S33, preliminary training: using initial parameters to perform preliminary training on sample operating condition data to obtain an initial support vector regression model; S34, Hyperparameter tuning: Select the optimal hyperparameter combination through network search and cross-validation; S35. Model evaluation: Use mean square error (MSE) as the evaluation indicator and select the optimal parameters: S36. Retrain model: Retrain the model using the optimal parameters to finally obtain an optimized support vector regression model.

5. The method for rapid calculation of submarine cable temperature based on support vector regression according to claim 1 is characterized in that: The expression of the reduced-order model of the submarine cable temperature field reconstructed in step S4 is: x=U′α′, formula (5), Where x represents the column vector of the submarine cable temperature under the input sample conditions.

6. A method for rapid calculation of submarine cable temperature based on support vector regression according to claim 4, characterized in that: The initial values ​​in step S32 specifically include: the initial value of the kernel function is a Gaussian kernel radial basis function, the initial value of the regularization parameter is 1, and the initial value of the fault tolerance parameter is 0.

1.

7. A method for rapid calculation of submarine cable temperature based on support vector regression according to claim 4, characterized in that: Step S34 specifically includes the following steps: S341. Finding the optimal hyperparameter combination within the specified hyperparameter range through network search; The kernel function is set to have a value range of linear kernel, polynomial kernel, and radial basis kernel function, the regularization parameter is set to have a value range of [0.1, 10], the tolerance rate is set to have a value range of [0.1, 0.3], and a hyperparameter network is formed; S342. For the performance of each hyperparameter combination in the hyperparameter network, use the sample space training set to perform k-fold cross validation: divide the training set into k subsets, select one of the subsets as the validation set each time, and the remaining k-1 subsets as the training set, and train k models.

8. The method for rapid calculation of submarine cable temperature based on support vector regression according to claim 4 is characterized in that: In step S35, the expression of the mean square error MSE is: Among them, y i is the actual value, is the predicted value, n is the number of samples, and the hyperparameter combination that minimizes the mean square error MSE is selected as the optimal parameter.

9. The method for rapid calculation of submarine cable temperature based on support vector regression according to claim 3 is characterized in that: The first m eigenvalues ​​must satisfy:

10. The method for rapid calculation of submarine cable temperature based on support vector regression according to claim 1, characterized in that: The construction of the submarine cable simulation calculation model specifically includes: The 35kV three-core submarine cable was modeled using the finite element method, and the influence of submarine soil and seawater was considered. The geometric model size of the 35kV three-core submarine cable was set. The initial temperature of each layer of the cable and the environment was set to 25℃, the boundary of the geometric model was set to thermal insulation, and the normal heat flux density was set to 0.

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