XLPE insulating layer structure uncertainty quantitative design method based on thermoelectric characteristics of high-voltage direct-current submarine cable

Abstract

An XLPE insulating layer structure uncertainty quantitative design method based on thermoelectric characteristics of a high-voltage direct-current submarine cable belongs to the field of high-voltage direct-current submarine cable design, and comprises the following steps: constructing an electromagnetic-thermal multi-physics field coupling model based on a physical equation, and obtaining electric field intensity and temperature field data with real physical significance; a Kriging agent model is established, a nonlinear mapping relation between design parameters and physical field response is fitted, the calculation efficiency is improved to more than thousands of times of that of a traditional model, and the prediction error is lower than 0.01; key variables are screened through Morris screening and Sobol sensitivity analysis, uncertainty risks are quantified in combination with kernel density estimation, an optimal structure design value is obtained through iterative optimization, failure probability return-to-zero is achieved, submarine cable operation safety and economical efficiency are considered, cost waste caused by excessive design is avoided, physical model and data driving advantages are fused, the design result credibility is high, and the design efficiency is high. The method can be directly applied to engineering design of the XLPE insulating layer of the high-voltage direct-current submarine cable in deep and far sea.

Description

Technical Field

[0001] This invention relates to the field of power transmission technology, and in particular to an uncertainty quantification design method for XLPE insulation layer structure based on the thermoelectric properties of high-voltage DC submarine cables. Background Technology

[0002] High-voltage direct current submarine cables serve as the core carrier for cross-regional energy interconnection in deep-sea areas, and their operational reliability directly determines the efficiency of the entire power transmission system. Cross-linked polyethylene (XLPE) insulation, as a core component of submarine cables, has its structural design and performance evaluation as key factors affecting the power transmission performance and economy of deep-sea wind power systems.

[0003] Currently, the design and performance evaluation of high-voltage direct current (HVDC) submarine cables in deep-sea wind power systems mainly rely on traditional methods, including deterministic design based on empirical formulas, experimental design methods with iterative adjustments based on equivalent experiments, and evaluation of the current-carrying capacity of submarine cables based on equivalent thermal circuit methods or simulation analysis. However, these methods all have significant drawbacks and cannot meet the requirements of modern deep-sea wind power systems for high efficiency, high precision, low cost, and high reliability in submarine cable design.

[0004] Deterministic design methods based on empirical formulas rely on empirical relationships summarized from past engineering practices to design insulation layers. They calculate key design parameters such as insulation layer thickness and material selection by inputting basic parameters (e.g., voltage level, current capacity). However, this method lacks in-depth analysis of complex physical processes under specific operating conditions and fails to fully consider the random uncertainties caused by manufacturing and assembly errors and the complex working environment of deep-sea environments. This often results in overly conservative design results or potential failure risks. Furthermore, its reliance on qualitative analysis and empirical judgment makes it difficult to quantitatively assess the thermoelectric failure risk of the insulation layer, thus limiting the reliability and practicality of the design results.

[0005] The equivalent experimental design method simulates the actual working environment and repeatedly tests and adjusts submarine cable samples to optimize the insulation layer structure. However, it requires a large number of physical experiments, which is not only time-consuming but also generates huge design and R&D costs, making it extremely uneconomical. Furthermore, it is difficult to fully cover all possible random uncertainties, and the experimental results may still have some deviations.

[0006] The equivalent thermal circuit method establishes an equivalent thermal circuit model of submarine cables based on thermoelectric analogy theory, simulates the heat dissipation process of submarine cables, and proposes an inversion algorithm for the conductor temperature of submarine cables based on the equivalent thermal circuit model, thereby evaluating the current carrying capacity of submarine cables. However, when dealing with different laying scenarios, this method treats the thermal parameters of the submarine cable body as constant parameters, ignoring the dynamic changes in the thermal parameters of the submarine cable body caused by changes in the laying environment, resulting in errors in the evaluation results. Furthermore, because the dynamic changes in the thermal parameters of the submarine cable body are ignored, the accuracy is limited when evaluating the current carrying capacity of submarine cables in complex laying environments.

[0007] Simulation analysis methods establish multi-physics coupled simulation models of submarine cables under typical laying scenarios based on real-world laying scenarios. These models are used to solve for the temperature distribution of the cable conductors under different laying scenarios, thereby evaluating the current-carrying capacity of the cable. However, multi-physics coupled simulation models involve large computational loads and long calculation times per run, making it difficult to meet the requirements of reliability design for massive sample sizes, resulting in extremely low design efficiency. Furthermore, to reduce computational costs, the models are often simplified, which may lead to discrepancies between simulation results and actual performance.

[0008] Furthermore, for example, CN119312608A discloses a method for evaluating the temperature stability of high-voltage DC cables based on XLPE conductivity. This method measures the DC current of XLPE insulation material at different temperatures through resistivity testing, calculates conductivity and temperature stability characterization indicators, and combines finite element analysis software to evaluate the temperature and thermal stability of the XLPE insulation material in high-voltage DC cables. However, resistivity testing requires specialized experimental equipment and conditions, resulting in high experimental costs, cumbersome experimental procedures, and long evaluation cycles, making it difficult to meet the needs of rapid design. Moreover, this method mainly focuses on the conductivity characteristics of XLPE material and fails to comprehensively consider the dynamic changes in thermal parameters of the overall submarine cable structure. Before the proposal of a submarine cable optimization and selection method that considers the dynamic changes in the thermal parameters of the submarine cable itself, traditional methods often ignored the dynamic changes in the thermal parameters of the submarine cable itself under different laying scenarios when considering submarine cable selection. The use of submarine cables of uniform specifications for design could lead to problems such as overheating or insufficient current carrying capacity during actual operation. Overly conservative designs could also lead to material waste and increased manufacturing costs, reducing the economic efficiency of the system.

[0009] To address the shortcomings and deficiencies of existing technologies, this invention proposes a submarine cable optimization and selection method that comprehensively considers the dynamic changes in the thermal parameters of the submarine cable itself, as well as an efficient temperature stability assessment method based on XLPE conductivity. This invention fully considers the influence of manufacturing and assembly errors and the random uncertainties of the complex working environment in deep-sea areas. By dynamically adjusting the thermal parameters of the submarine cable itself, it improves design accuracy and ensures the accuracy and reliability of the design results. It avoids the need for extensive physical experiments, significantly reducing design costs and time cycles through simulation analysis and optimization algorithms. It can quantitatively assess the thermoelectric failure risk of the insulation layer, providing a scientific basis for design optimization and avoiding cost waste caused by overly conservative designs. Combining the interpretability of the physical model and the efficiency of the data-driven model improves the credibility and practicality of the design results. By accurately assessing the current-carrying capacity and temperature stability of the submarine cable under different laying scenarios, it enhances the operational reliability of the submarine cable. This invention is of great significance for overcoming many shortcomings of traditional design methods and improving the design level and operational reliability of high-voltage DC submarine cables for deep-sea wind power systems. Summary of the Invention

[0010] The technical problem this invention aims to solve is to provide an uncertainty quantification design method for XLPE insulation layer structures based on the thermoelectric properties of high-voltage direct current (HVDC) submarine cables, addressing the issues of low accuracy, high cost, and lack of quantitative evaluation in the design of XLPE insulation layers for HVDC submarine cables (HVDC submarine cables) in deep-sea inter-regional energy interconnection. Specifically, existing empirical formula design methods and equivalent experimental design methods fail to fully consider the influence of manufacturing and assembly errors and the random uncertainties of the complex working environment in deep-sea areas, resulting in design failure risks and high design costs.

[0011] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: This paper presents an uncertainty quantification design method for XLPE (Cross-Linked Polyethylene) insulation layer structures based on the thermoelectric properties of high-voltage DC submarine cables. Through cascaded physical simulation, surrogate model construction, and uncertainty quantification analysis, a closed-loop design method is formed to achieve accurate optimization design of XLPE (Cross-Linked Polyethylene) layer structures. The specific technical solution includes three core processes: (I) Construction of electromagnetic-thermal multiphysics coupling model for high voltage DC submarine cables This model provides a data foundation with real physical meaning for subsequent designs. The specific steps are as follows: Model simplification: Based on the characteristic that the cross-sectional structure of the high voltage DC submarine cable is continuous and identical everywhere, the three-dimensional submarine cable is simplified into an infinitely long two-dimensional model that includes all the structures of each layer of the submarine cable. Constructing a two-dimensional Ampere's law model: Combining electromagnetic constitutive relations, a two-dimensional Ampere's law model is established for the steady-state operation of submarine cables. (1); In the formula, Represents the magnetic vector potential; Indicates magnetic permeability; This represents electrical conductivity, which is a function of temperature. The function, Represents electric potential, , , These are the three dimensions of a spatial coordinate system, used to characterize the position of the submarine cable's cross-section and length.

[0012] Forming a fully coupled set of equations: Solving for the electric potential based on the current continuity equation, establishing the solid-state heat transfer physical equations coupled with the electromagnetic field, thus forming a fully coupled set of electromagnetic-thermal multiphysics equations: (2); In the formula, The Hamiltonian operator is used to represent the divergence and gradient operations of a vector field. This indicates the internal heat source that generates Joule heating in a copper conductor; This represents the thermal conductivity.

[0013] Determine the internal heat source: The calculation form for the internal heat source is as follows: (3).

[0014] Electromagnetic field boundary conditions are defined as follows: considering current, fixed potential, and magnetic flux perpendicular to the boundary, the boundary conditions are: (4); In the formula, Indicates a current source term; Represents the normal vector; Indicates a fixed potential value; It represents the magnetic vector potential.

[0015] Setting temperature field boundary conditions: Considering thermally insulating boundaries and fixed temperature boundaries, the boundary conditions are as follows: (5); In the formula, It represents the constant external temperature value.

[0016] Mesh generation and shape function determination: The geometric domain of an infinitely long two-dimensional submarine cable section is meshed, and the shape function is determined based on the mesh type; Numerical solution: The Newton iteration method is used to numerically solve the fully coupled equations containing nonlinear terms to obtain the electric field intensity and temperature field distribution of the submarine cable.

[0017] (II) Construction of Kriging surrogate model for thermoelectric performance of high voltage DC submarine cable To address the low computational efficiency of multiphysics coupling models, a highly efficient and accurate Kriging surrogate model is constructed based on their simulation data. The steps are as follows: Determine core design parameters: Taking the thermoelectric performance of submarine cable as the design goal, select core design parameters and determine their value range. Core parameters include, but are not limited to, XLPE insulation layer thickness, XLPE insulation layer conductivity, XLPE insulation layer thermal conductivity, semi-conductive shielding layer thickness, voltage amplitude fluctuation, transmission power fluctuation, and alloy lead protective sheath thickness. Constructing the design sample point matrix: Using methods such as random sampling, uniform sampling, or Latin hypercube sampling, construct the design sample point matrix within the design scope. (11); In the formula, Represents the design variable matrix. Indicates the dimension of the variable. This indicates the matrix transpose.

[0018] Combined data sample matrix: Combine the sampled design variable matrices to form the data sample matrix S: (12); In the formula, Indicates the number of samples; Represents the real number field.

[0019] Determine the response value matrix: Construct the response value matrix using the electric field strength and temperature peak values ​​of the XLPE insulation layer as response indicators. : (13); In the formula, This represents the correspondence in response to electric field strength. This indicates the correspondence with temperature as the response.

[0020] Constructing a Kriging surrogate model: The true function is represented by a regression model and a Gaussian process. The model form is as follows: (14); In the formula, This represents the response value of the surrogate model, which is the predicted result of the electrothermal performance of the submarine cable; This is the transpose of the basis function term; Indicates the regression parameters; It is a Gaussian process.

[0021] Hyperparameter estimation: The hyperparameters of the Gaussian process are estimated using maximum likelihood estimation. The log-likelihood function is: (15); In the formula, Represents the natural logarithm operation; Represents variance. Represents the correlation matrix; Represents a polynomial matrix.

[0022] Solving the optimization problem: The Lagrange multiplier method is introduced to solve the constrained optimization problem, resulting in a surrogate model for predicting thermoelectric performance. (16); In the formula, This represents the predicted response value at the unknown prediction point. The design variable matrix representing the unknown prediction points; This represents the transpose of the odd function term representing the predicted location point. This represents the transpose of the correlation coefficient matrix between the predicted points and the sample points; The inverse matrix of the correlation coefficient matrix; This represents the variance parameter estimate of a Gaussian process, characterizing the uncertainty of the prediction results; Indicates all A vector, with dimensions matching the number of samples; Indicates all Transpose of a vector; yes Simplified representation; yes A simplified representation of .

[0023] Model training and prediction: The surrogate model is trained using sample data, and the unknown design variable matrix is ​​substituted into the model to obtain the response value; Model validation: Extract 10 to 20 sets of unknown design samples, compare the prediction results of the surrogate model with the simulation model results, and calculate the mean square error (MSE). Model optimization: If the MSE is greater than 0.01, increase the amount of sampled data and repeat steps 3 to 9 until the MSE meets the accuracy requirement (≤0.01).

[0024] (III) Uncertainty Quantification Design of XLPE Insulation Layer for High Voltage DC Submarine Cables The steps for uncertainty quantification and structural optimization based on the surrogate model are as follows: Sample point densification: Selecting XLPE insulation layer thickness and transmission power as design parameters, the sample points are densified within their design range, and the corresponding electric field strength and temperature field response values ​​are obtained through the proxy model; Fitting the response surface: Based on the refined design samples and response values, fit the response surface expression: (17); In the formula, Represents the variable of insulation layer thickness. Represents the transmission power variable. Represents the design function for electric field intensity. Represents the temperature design function. , , , , , These represent the fitting coefficients for different electric field intensity functions; , , , , , These represent the fitting coefficients for different temperature functions.

[0025] Design equations are constructed based on the design limits of electric field strength (below 30 kV / mm) and peak temperature (below 90 °C): (18).

[0026] Solving for deterministic design values: By solving the simultaneous design equations, the deterministic design value of the XLPE insulation layer thickness is obtained; Uncertainty variables were identified: the main design variables affecting the thermoelectric performance of the submarine cable were selected, including XLPE thickness, semiconductive shielding layer thickness, alloy lead layer thickness, MDPE protective sheath thickness, XLPE conductivity, XLPE thermal conductivity, and peak voltage, etc., whose uncertainty distribution satisfies Gaussian distribution or uniform distribution, with upper and lower bound fluctuation range of 0.1%~5%; Key variable selection: Key design variables were identified using the Morris screening method. The selection model was as follows: (6); (7); In the formula, Indicates the first The absolute average effect of the design variables; the larger the value, the greater the influence of the variables. Indicates the first The standard deviation of the effect values ​​of each design variable reflects the strength of nonlinearity or interaction. Indicates the first The design variable in the th... The average change of the variable along the trajectory; Indicates the length of the trajectory.

[0027] Sobol sensitivity analysis: Based on the screening results, Sobol sensitivity analysis is performed to accurately quantify the contribution rate of design variables, including first-order exponent estimation and total sensitivity exponent estimation. First-order sensitivity exponential estimation model: (8); The overall sensitivity index estimation model is as follows: (9); In the formula, Indicates the first The first-order sensitivity index of each design variable; , For two independent sample matrices, , ; Indicates the number of samples; For variable dimensions; Indicates will The first of the matrix Column replacement The first of the matrix A mixed matrix constructed from columns; Represents the sample matrix No. The response value of each sample; Represents the mixture matrix No. The response value of each sample; Indicates the first The overall sensitivity index of the design variables; Indicates will The first of the matrix Column replacement The first of the matrix A mixed matrix constructed from columns; Represents the mixture matrix No. The response value of the nth sample; The nth design variable and the first matrix The columns correspond.

[0028] Uncertainty Propagation and Optimization: This study investigates uncertainty propagation for design variables with Sobol exponents exceeding 0.1, and obtains the probability density function through kernel density estimation. (10); In the formula, For kernel functions; Indicates bandwidth; Indicates the number of samples; Indicates the sample response value; This indicates the predicted response value.

[0029] Estimate the failure probability, iteratively optimize the XLPE insulation layer thickness, and repeat the above process until the probability of the electric field strength and temperature exceeding the design limit is reduced to zero, thus obtaining the optimal design value.

[0030] The uncertainty quantification design method for XLPE insulation layer structure based on the thermoelectric properties of high-voltage DC submarine cables provided by this invention has the following beneficial effects: 1. This invention effectively solves the problem of uncontrollable failure risk caused by neglecting random uncertainty in traditional deterministic design. Through uncertainty quantification analysis, it comprehensively covers random factors such as manufacturing and assembly errors, material property deviations, and load fluctuations, reducing the probability of thermoelectric failure of XLPE insulation layer to zero and ensuring long-term stable operation of submarine cables in complex deep-sea environments.

[0031] 2. This invention overcomes the problems of high cost and low efficiency of experimental design and pure physical model simulation design. It introduces the Kriging surrogate model, which reduces the single calculation time from 150 seconds to 0.2 seconds (5000 sample data), greatly improving the design efficiency, while controlling the prediction error to be less than 0.01, ensuring the prediction accuracy.

[0032] 3. This invention solves the contradiction that pure data-driven models lack physical interpretability and pure physical models are difficult to handle high-dimensional uncertainty. It integrates the advantages of physical models and data-driven models, constructs a multi-physics coupling model based on real physical equations, ensures the accuracy of the physical meaning of sample data, and uses physical simulation data as the training basis for the surrogate model, so that the design results have both physical rationality and statistical robustness.

[0033] 4. This invention achieves a design result that balances safety and economy. It establishes reliability constraints based on failure probability, replacing the traditional conservative safety factor design. It obtains the optimal XLPE insulation layer thickness while ensuring zero failure risk, avoiding material waste caused by over-design and reducing the manufacturing cost of submarine cables.

[0034] 5. This invention effectively reduces reliance on physical experiments and lowers R&D costs. It obtains massive amounts of sample data by combining physical simulation with proxy models, eliminating the need for repeated adjustments through numerous equivalent experiments and avoiding the huge R&D costs and cycle losses associated with experimental design methods.

[0035] 6. The reliability of this invention is significantly improved. Through uncertainty quantification analysis, the failure risk caused by random factors such as manufacturing errors, material deviations, and load fluctuations is quantified, and the failure probability is reduced to zero, thus completely solving the potential failure problem of traditional deterministic design.

[0036] 7. This invention significantly improves design efficiency by introducing the Kriging proxy model, balancing efficiency and accuracy, and solving the problem of excessively high computational costs for pure physics models, making it possible to compute massive amounts of samples.

[0037] 8. This invention has outstanding economic advantages. It establishes reliability constraints based on failure probability, avoids material waste caused by traditional conservative design, and obtains the optimal insulation layer thickness under the premise of ensuring zero failure risk, thus significantly reducing the manufacturing cost of submarine cables.

[0038] 9. The design results of this invention have high reliability, combining the advantages of physical models and data-driven approaches. The design results have both physical rationality and statistical robustness, and can be directly applied to engineering practice, reducing the difficulty of technology implementation.

[0039] 10. This invention has strong applicability. The core design parameters cover the key performance parameters and operating condition parameters of the XLPE insulation layer. The parameter range and design limits can be adjusted according to actual engineering needs. It is suitable for the design of XLPE insulation layers for high-voltage DC submarine cables of different specifications and operating environments.

[0040] 11. This invention efficiently screens key variables, reduces optimization complexity, quickly eliminates design variables with minor impact through the Morris screening method, focuses on key parameters, and then accurately quantifies the contribution rate of variables through Sobol sensitivity analysis, thereby improving design efficiency.

[0041] 12. The variables in this invention have independent and controllable influences, and the optimization is highly targeted. The Sobol sensitivity analysis results show that the influence of key design variables is relatively independent, and single-parameter precise optimization can be performed. Optimization strategies are formulated for the dominant influence of voltage fluctuations on field strength and the key role of thermal conductivity on temperature.

[0042] 13. This invention adapts to complex working conditions, fully considering the influence of complex working conditions such as temperature fluctuations and load fluctuations in the deep sea environment. By incorporating the disturbance of environmental factors on design variables through uncertainty analysis, the optimized XLPE insulation layer structure has stronger environmental adaptability.

[0043] 14. This invention improves the traceability of design parameters. All design processes are based on clear physical equations, mathematical models and quantitative analysis results. The selection of core parameters, optimization logic and final values ​​are all supported by data, which facilitates subsequent adjustments and verification by engineering technicians.

[0044] 15. The present invention features precise and controllable iterative optimization with high design accuracy. Based on kernel density estimation, it quantifies the propagation law of uncertainty and continuously adjusts the structural parameters of the XLPE insulation layer through iterative optimization until the probability of the electric field strength and temperature exceeding the design limit is reduced to zero, thereby improving the matching accuracy between the insulation layer structure and the thermoelectric performance of the submarine cable.

[0045] 16. The invention has a complete technical closed loop and strong engineering applicability. It connects the three core processes of electromagnetic-thermal multiphysics modeling, Kriging surrogate model construction, and uncertainty quantification design, forming a strict technical closed loop. The design results can be directly applied to engineering practice without additional verification.

[0046] 17. This invention has strong resistance to environmental fluctuations, enabling the optimized XLPE insulation layer structure to stably meet the operational requirements of different water depths and temperature ranges, thereby improving the operational stability of submarine cables in complex environments.

[0047] 18. Compared with the equivalent experimental design method, the present invention significantly reduces the experimental sample size and testing time, significantly reduces the design cost, and at the same time ensures the authenticity and validity of the design data, thereby improving design efficiency and economic benefits. Attached Figure Description

[0048] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a design flowchart of the present invention; Figure 2 This is a diagram showing the electric field intensity distribution of the steady-state thermoelectric performance of the high-voltage DC submarine cable of this invention. Figure 3 This is a temperature field distribution diagram illustrating the steady-state thermoelectric performance of the high-voltage DC submarine cable of the present invention. Figure 4 This is the electric field strength prediction result of the proxy model of this invention; Figure 5 This is the temperature prediction result of the proxy model of this invention; Figure 6 This invention verifies the electric field strength of the proxy model results using simulation model results; Figure 7 This invention uses simulation model results to verify the temperature of the proxy model results; Figure 8 The influence of MOAT design parameters on field strength in this invention; Figure 9 The effect of MOAT design parameters on temperature was investigated in this invention. Figure 10 This is a flowchart of the Sobol analysis process of the present invention; Figure 11 The influence of sensitivity analysis of the design parameters of this invention on the field strength; Figure 12 The effect of sensitivity analysis of the design parameters of this invention on temperature; Figure 13 This is a graph showing the probability density function of the electric field intensity in this invention. Figure 14 This is a probability density function graph of the temperature peak value of the present invention. Detailed Implementation

[0049] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments: Example 1 This embodiment provides an uncertainty quantification design method for XLPE insulation layer structure based on the thermoelectric characteristics of high-voltage direct current (HVDC) submarine cables. First, an electromagnetic-thermal multiphysics coupling model of the HVDC submarine cable with practical physical significance is established, and initial sample points are obtained based on this model. Then, a surrogate model is used to fit the nonlinear mapping relationship between design parameters and physical field responses. The surrogate model and Monte Carlo method are integrated to achieve rapid statistical analysis of a large number of samples, quantifying the probability distribution characteristics of key performance indicators. Finally, reliability constraints are established based on the uncertainty quantification analysis results to achieve optimized design of the XLPE insulation layer structure of the HVDC submarine cable. The proposed method mainly includes three parts: electromagnetic-thermal multiphysics modeling, surrogate model construction, and uncertainty quantification design. The algorithm flowchart is shown below. Figure 1 As shown. The detailed weak signal extraction process is as follows: Process 1: Construction of Electromagnetic-Thermal Multiphysics Coupling Model for High Voltage Direct Current Submarine Cables The operating environment of high-voltage direct current (HVDC) submarine cables is quite extreme, making it difficult to directly measure the thermoelectric properties of the insulation layer. Therefore, obtaining the field strength and temperature of the XLPE layer in HVDC submarine cables through electromagnetic-thermal multiphysics coupling modeling is highly feasible and economical. The electromagnetic-thermal multiphysics coupling model of HVDC submarine cables is constructed based on actual physical equations and constrained by boundary conditions under the real operating conditions of the submarine cable. The calculation results have real physical meaning and serve as the data foundation for subsequent steps in constructing surrogate models and performing uncertainty quantification design. The detailed steps for constructing the electromagnetic-thermal multiphysics coupling model of HVDC submarine cables in this method are as follows: Step 1: Based on the characteristic that the cross-sectional structure of the high-voltage DC submarine cable is continuous and identical everywhere, the three-dimensional submarine cable is simplified into a two-dimensional model with infinite length. The model includes all the structures of each layer of the submarine cable.

[0050] Step 2: Construct a two-dimensional Ampere's law model for steady-state operation of submarine cables by combining electromagnetic constitutive relations: (1); In the formula, Represents the magnetic vector potential; Indicates magnetic permeability; This represents electrical conductivity, which is a function of temperature. The function, Represents electric potential, , , These are the three dimensions of a spatial coordinate system, used to characterize the position of the submarine cable's cross-section and length.

[0051] Step 3: Solve for the electric potential based on the current continuity equation, and establish the solid-state heat transfer physics equations coupled with the electromagnetic field, ultimately forming the electromagnetic-thermal multi-physics fully coupled equation set for simulating the thermoelectric performance of high-voltage DC submarine cables: (2); In the formula, The Hamiltonian operator is used to represent the divergence and gradient operations of a vector field. This indicates the internal heat source that generates Joule heating in a copper conductor; This represents the thermal conductivity.

[0052] Step 4: Identify the internal heat source in the electromagnetic-thermal multiphysics coupling equations. Temperature affects conductivity in the electromagnetic-thermal multiphysics coupling mechanism. The specific calculation method is as follows: (3).

[0053] Step 5: Based on the multiphysics coupling equations, considering current, fixed potential, and magnetic flux perpendicular boundaries, determine the electromagnetic field boundary conditions for calculating the thermoelectric performance of high-voltage DC submarine cables: (4); In the formula, Indicates a current source term; Represents the normal vector; Indicates a fixed potential value; It represents the magnetic vector potential.

[0054] In the boundary condition formula (4), J0 represents the current source term, and n represents the current source term.

[0055] Step 6: Based on the multiphysics coupling equations, considering thermal insulation boundaries and fixed temperature boundaries, determine the temperature field boundary conditions for calculating the thermoelectric performance of high-voltage DC submarine cables: (5); In the formula, It represents the constant external temperature value.

[0056] Step 7: Mesh the geometric domain of the infinitely long two-dimensional submarine cable section and determine the shape function based on the mesh type.

[0057] Step 8: The electromagnetic-thermal multiphysics fully coupled model of the HVDC submarine cable contains nonlinear terms. The Newton iteration method is used for numerical iteration to obtain the electric field strength and temperature field distribution of the HVDC submarine cable, such as... Figure 2 and Figure 3 As shown.

[0058] Process 2: Construction of a surrogate model for the thermoelectric performance of high-voltage direct current submarine cables While the electromagnetic-thermal multiphysics coupling model for HVDC submarine cables can accurately calculate the electric field strength and temperature field of the cable, its computational efficiency is low (for example, on a computer with an i7-12700F and 16GB of RAM, it takes approximately 150 seconds to calculate a single set of data). For uncertain quantitative analyses requiring large amounts of data (typically on the order of 10³ or higher), the direct application value of the HVDC submarine cable electromagnetic-thermal multiphysics coupling model is limited. To address this issue, a method is adopted to construct a surrogate model using computational results with practical physical meaning obtained from simulation models. The Kriging surrogate model is selected because it is an unbiased estimator, requires a small sample size, and achieves ultra-high computational efficiency. The detailed steps for constructing the HVDC submarine cable thermoelectric performance surrogate model in this method are as follows: Step 1: Taking the thermoelectric performance of the high voltage DC submarine cable as the design goal, select the value range of the core design parameters (core parameters include but are not limited to: XLPE insulation layer thickness, XLPE insulation layer conductivity, XLPE insulation layer thermal conductivity, semi-conductive shielding layer thickness, voltage amplitude fluctuation, transmission power fluctuation, alloy lead protective sheath thickness, etc.).

[0059] Step 2: Construct the design sample point matrix within the design scope using the selected sampling method (e.g., random sampling, uniform sampling, Latin hypercube sampling, etc.): (11); In the formula, Represents the design variable matrix. Indicates the dimension of the variable. This indicates the matrix transpose.

[0060] Step 3: Combine the design variable matrices obtained from the sampling to obtain the data sample matrix S, represented as follows: (12); In the formula, Indicates the number of samples; Represents the real number field.

[0061] Step 4: Focusing on the thermoelectric performance of the submarine cable during operation, the electric field strength and temperature peak of the XLPE insulation layer are used as the response value matrix y: (13); In the formula, This represents the correspondence in response to electric field strength. This indicates the correspondence with temperature as the response.

[0062] Step 5: Construct a Kriging surrogate model for the thermoelectric performance of high-voltage direct current submarine cables by representing the true function through regression models and Gaussian processes: (14); In the formula, This represents the response value of the surrogate model, which is the predicted result of the electrothermal performance of the submarine cable; This is the transpose of the basis function term; Indicates the regression parameters; It is a Gaussian process.

[0063] Step 6: In the Gaussian process of the Kriging surrogate model, maximum likelihood estimation is used to estimate the hyperparameters, obtaining their log-likelihood function. The format is: (15); In the formula, Represents the natural logarithm operation; Represents variance. Represents the correlation matrix; Represents a polynomial matrix.

[0064] Step 7: Introduce the Lagrange multiplier method to solve the constrained optimization problem, and finally obtain the surrogate model for predicting the thermoelectric performance of high-voltage direct current submarine cables as follows: (16); In the formula, This represents the predicted response value at the unknown prediction point. The design variable matrix representing the unknown prediction points; This represents the transpose of the odd function term representing the predicted location point. This represents the transpose of the correlation coefficient matrix between the predicted points and the sample points; The inverse matrix of the correlation coefficient matrix; This represents the variance parameter estimate of a Gaussian process, characterizing the uncertainty of the prediction results; Indicates all A vector, with dimensions matching the number of samples; Indicates all Transpose of a vector; yes Simplified representation; yes A simplified representation of .

[0065] Step 8: After training the surrogate model using the sample data from formulas (12) and (13), the unknown design variable matrix for predicting the electric and temperature field response values ​​is substituted into the surrogate model for the thermoelectric performance of the high-voltage DC submarine cable to obtain the response values, such as... Figure 4 and Figure 5 As shown.

[0066] Step 9: Extract 10 to 20 sets of unknown design sample surrogate model prediction results and compare them with simulation model, and calculate MSE, such as Figure 6 and Figure 7 As shown.

[0067] Step 10: If the MSE between the surrogate model prediction of electric field intensity and temperature field and the simulation value is greater than 0.01, increase the amount of sampling data in Step 2, and then repeat the calculations in Steps 3 to 9.

[0068] Process 3: Uncertainty Quantification Design of XLPE Insulation Layer for High Voltage DC Submarine Cables Based on the expanded sample point data within the design scope using the surrogate model, and using the encrypted design and response values, combined with design limits, design equations are constructed to obtain a preliminary deterministic design. Subsequently, uncertainty quantification analysis is performed on the design variables affecting the thermoelectric performance of the submarine cable, mainly considering the influence of manufacturing and installation errors, material property deviations, and random uncertainties caused by load fluctuations. Finally, through repeated iterative optimization, the optimal design value of the XLPE insulation layer of the high-voltage DC submarine cable can be obtained. The detailed steps of the uncertainty quantification design of the XLPE insulation layer of the high-voltage DC submarine cable in this method are as follows: Step 1: In Step 1 of Process 2, select the XLPE insulation layer thickness and transmission power as design parameters, densify the sample points within the parameter design range, and obtain the response values ​​of the electric field strength and temperature field corresponding to the increased sample points through the constructed surrogate model.

[0069] Step 2: Based on the encrypted design samples and response values, fit the specific expression form of the response surface: (17); In the formula, Represents the variable of insulation layer thickness. Represents the transmission power variable. Represents the design function for electric field intensity. Represents the temperature design function. , , , , , These represent the fitting coefficients for different electric field intensity functions; , , , , , These represent the fitting coefficients for different temperature functions.

[0070] Step 3: Construct design equations for matching the XLPE insulation thickness and transmission power of high-voltage DC submarine cables based on the design limits of electric field strength and peak temperature (the design limits are taken as electric field strength below 30kV / mm and temperature below 90℃). (18).

[0071] Step 4: Solve the design equations from the previous step to obtain the deterministic design value of the XLPE layer thickness of the high-voltage DC submarine cable.

[0072] Step 5: After obtaining the deterministic design values, perform uncertainty quantification optimization design, calculate the probability of thermoelectric failure of the insulation layer, and optimize accordingly. Select the main design variables affecting the thermoelectric performance of the submarine cable, mainly considering the influence of manufacturing and installation errors, material property deviations, and random uncertainties caused by load fluctuations. These typically include XLPE thickness, semiconductive shielding layer thickness, alloy lead layer thickness, MDPE protective sheath thickness, XLPE conductivity, XLPE thermal conductivity, and peak voltage. The distribution of uncertainty should conform to a Gaussian or uniform distribution, and the upper and lower bounds can be determined according to the actual situation, typically within a fluctuation range of 0.1% to 5%.

[0073] Step 6: Different design variables have varying degrees of influence on the electric field strength and temperature field. First, the Morris screening method is used to determine the key design variables to reduce the computational cost of the high-dimensional DC submarine cable structure optimization model. The Morris screening model is as follows: (6); (7); In the formula, Indicates the first The absolute average effect of the design variables; the larger the value, the greater the influence of the variables. Indicates the first The standard deviation of the effect values ​​of each design variable reflects the strength of nonlinearity or interaction. Indicates the first The design variable in the th... The average change of the variable along the trajectory; Indicates the length of the trajectory.

[0074] The calculation results are as follows Figure 8 and Figure 9 As shown, the results indicate that voltage, XLPE insulation thickness, and thermal conductivity have significant effects on the electric field strength. The thermal conductivity of the insulation layer exhibits large differences in effect value across different perturbation directions, demonstrating a prominent nonlinear effect. Regarding the peak temperature, XLPE insulation thickness and thermal conductivity have a significant impact on the parameters of interest, with insulation thickness exhibiting a nonlinear or interactive effect. While the semiconductive shielding layer thickness has a relatively small impact on both the electric field strength and peak temperature, it shows some variability in the MOAT standard deviation or mean value; therefore, it will be retained in further quantitative analysis of its impact. The MDPE sheath thickness, alloy lead thickness, and XLPE insulation conductivity have relatively small effects on the electric field strength. Furthermore, the impact of voltage fluctuations on the steady-state peak temperature of the XLPE insulation layer is negligible; therefore, these design variables will be removed in the subsequent uncertainty analysis.

[0075] Step 7: Use the MOAT screening results to perform Sobol sensitivity analysis, further quantifying the contribution rate of the design variables. Sobol sensitivity analysis includes first-order exponent estimation and total sensitivity exponent estimation. Based on the Kriging surrogate model, the Monte Carlo method is used to estimate the Sobol exponent, first generating two independent sample matrices. , For the number of samples, then The first of the matrix Column replacement The first of the matrix Constructing a hybrid matrix from columns .

[0076] The first-order sensitivity exponent estimation model is as follows: (8); The overall sensitivity index estimation model is as follows: (9); In the formula, Indicates the first The first-order sensitivity index of each design variable; , For two independent sample matrices, , ; Indicates the number of samples; For variable dimensions; Indicates will The first of the matrix Column replacement The first of the matrix A mixed matrix constructed from columns; Represents the sample matrix No. The response value of each sample; Represents the mixture matrix No. The response value of each sample; Indicates the first The overall sensitivity index of the design variables; Indicates will The first of the matrix Column replacement The first of the matrix A mixed matrix constructed from columns; Represents the mixture matrix No. The response value of the nth sample; The nth design variable and the first matrix The columns correspond.

[0077] Sobol sensitivity analysis identifies key parameters through the overall sensitivity index, and then uses a first-order index to determine whether the variable can be used for single-parameter optimization or to study its interaction with other design variables. The analysis logic is as follows: Figure 10 As shown. The calculation results are as follows. Figure 11 and Figure 12As shown, the results indicate that for electric field strength and peak temperature, except for the semiconductive shielding layer thickness which has a relatively small impact, the Sobol exponents of all the studied design variables exceed 0.1, indicating further research value. The first-order sensitivity exponents of each design variable are equal to the total sensitivity exponent, suggesting that the influence of each design variable on the parameters of interest is relatively independent, and the interaction between variables can be disregarded. In electric field strength, voltage fluctuations account for more than 0.5% of the maximum field strength, followed by XLPE insulation layer thickness; therefore, optimizing the insulation layer thickness is necessary to mitigate the risks posed by voltage instability. In peak temperature, the thermal conductivity of the XLPE insulation layer has a significantly greater impact than other parameters, indicating that controlling the thermal conductivity is the most critical factor determining the steady-state operating temperature of the submarine cable. Combined with the MOAT (Morris One-at-A-Time, Morris screening method) results, the effects of changes in XLPE insulation layer thickness on both field strength and temperature are nonlinear.

[0078] Step 8: Conduct uncertainty propagation studies on design variables with Sobol exponents exceeding 0.1, quantify the probability of the impact of random uncertainty errors of design variables on field strength and temperature, and obtain the probability density function through kernel density estimation: (10); In the formula, For kernel functions; Indicates bandwidth; Indicates the number of samples; Indicates the sample response value; This indicates the predicted response value.

[0079] The probability density distribution is obtained as follows Figure 13 and Figure 14 As shown, integrating the probability density function of the electric field strength in the failure region, the estimated failure probability of the electric field strength exceeding the limit design value is 22.62%. This indicates that the original XLPE insulation layer thickness of the submarine cable has a significantly insufficient ability to withstand risks, therefore, its thickness needs to be increased in the optimization of the insulation layer structure. Figure 1 The design approach iteratively optimizes the thickness of the XLPE insulation layer by repeating all the above calculation processes. Finally, the optimal value of the XLPE insulation layer thickness can be obtained. The probability of the field strength and temperature in the insulation layer exceeding the design limit is reduced to zero, which balances design reliability and economy and avoids risky design and overprotection design.

[0080] In the preferred embodiment, the sampling method described in step 2.2 is any one of random sampling, uniform sampling, or Latin hypercube sampling. This setting ensures the representativeness and diversity of the sample and avoids the impact of sampling bias on the accuracy of the results. Random sampling is simple and easy to implement, uniform sampling can cover the area evenly, and Latin hypercube sampling can perform stratified and precise sampling; the appropriate method can be flexibly selected according to actual needs.

[0081] In the preferred embodiment, the electric field strength design limit mentioned in step 3.3 is below 30kV / mm, and the temperature design limit is below 90℃. These settings ensure that the equipment maintains stable performance during long-term operation, avoiding insulation breakdown caused by excessive electric field strength or material aging due to excessive temperature. At the same time, these design limits provide sufficient safety margin to cope with instantaneous fluctuations under extreme operating conditions.

[0082] In summary, the uncertainty quantification design method for XLPE insulation layer structure based on the thermoelectric properties of HVDC submarine cables proposed in this invention integrates physical simulation, surrogate models, and uncertainty quantification analysis. It forms a rigorous technical closed loop, combining electromagnetic-thermal multiphysics coupling simulation applied to HVDC submarine cables, efficient parameter mapping using the Kriging surrogate model, and quantification of engineering risks related to random uncertainties. Traditional deterministic design ignores manufacturing errors, material parameter fluctuations, and load fluctuations, leading to unknown and uncontrollable actual failure risks. The method proposed in this patent does not rely on experimental or empirical design formulas. It constructs a data-driven optimization design method starting from a model with practical physical meaning, offering advantages of high efficiency and high accuracy. This method ensures the reliability of HVDC submarine cables while avoiding excessive design costs, demonstrating strong practical application value.

[0083] This invention solves the problem of low efficiency in design by directly applying multi-physics coupling, and improves design feasibility. Traditional design relies on electromagnetic-thermal fully coupled models (such as formulas (2)-(5)) for direct simulation, which takes about 150 seconds per calculation (requiring a high-performance computer), while reliability design requires a large number of samples (>10³), resulting in excessive computational cost. This solution introduces the Kriging surrogate model (formulas (14)-(16)), trains the model with a small number of physical simulation samples, and abstracts the nonlinear mapping relationship into an efficient prediction tool (the calculation time for 5000 sample data is about 0.2 seconds). At the same time, the prediction error of the surrogate model is controlled to be less than 0.01, ensuring prediction accuracy.

[0084] This method achieves multi-objective collaborative optimization, ensuring that the design of high-voltage DC submarine cables balances safety and economy. Traditional deterministic design relies on conservative safety factors, which can easily lead to over-design (such as excessively thick insulation layers), increasing costs. This scheme establishes reliability constraints based on failure probability, and adjusts the thickness and repeats uncertainty propagation based on uncertainty quantification analysis until the failure probability reaches zero. Under the premise of ensuring zero failure risk, the optimal insulation layer thickness is obtained (…). Figure 13 and Figure 14 This avoids material waste and reduces the manufacturing cost of submarine cables.

[0085] This method differs from simple data-driven design (black box model) by integrating physical models with data-driven approaches, ensuring both accuracy and practicality, and resulting in highly reliable design results. It addresses the challenges of purely data-driven models lacking physical interpretability in high-voltage DC submarine cable insulation design, and purely physical models struggling to handle high-dimensional uncertainties. This scheme constructs an electromagnetic-thermal fully coupled model based on real physical equations, matching boundary conditions to accurately reflect actual working conditions, ensuring the physical meaning of sample data. The surrogate model is rigorously trained using physical simulation data, guaranteeing that the sample data used in uncertain quantification design inherits the true physical meaning attributes of the simulation data. The design results possess both physical rationality and statistical robustness, and can be directly applied to engineering practice.

Claims

1. A method for uncertain quantification design of XLPE insulation layer structure based on the thermoelectric properties of high-voltage DC submarine cables, characterized in that, Includes the following steps: Step 1: Construct an electromagnetic-thermal multiphysics coupling model for high-voltage DC submarine cables; Step 2: Construct a proxy model for the thermoelectric performance of high-voltage DC submarine cables based on the coupling model; Step 3: Based on the surrogate model, perform uncertainty quantification design of the XLPE insulation layer of the high-voltage DC submarine cable to obtain the optimal structural design value of the XLPE insulation layer.

2. The uncertainty quantification design method for XLPE insulation layer structure based on the thermoelectric properties of high-voltage DC submarine cables according to claim 1, characterized in that, The specific process of constructing the electromagnetic-thermal multiphysics coupling model of the high-voltage DC submarine cable in step 1 includes: Step 1.1: Based on the characteristic that the cross-sectional structure of the high-voltage DC submarine cable is continuous and identical everywhere, the three-dimensional submarine cable is simplified into an infinitely long two-dimensional model, which includes all the structures of each layer of the submarine cable; Step 1.2: Construct a two-dimensional Ampere's law model for steady-state operation of submarine cables by combining electromagnetic constitutive relations; Step 1.3: Solve for the electric potential based on the current continuity equation and establish the solid heat transfer physical equation of electromagnetic field coupling to form a fully coupled set of electromagnetic-thermal multiphysics equations. Step 1.4: Determine the internal heat sources in the fully coupled equation set; Step 1.5: Based on the fully coupled equations, considering the current, fixed potential, and magnetic flux perpendicular boundary, determine the electromagnetic field boundary conditions; Step 1.6: Based on the fully coupled equations, considering thermally insulating boundaries and fixed temperature boundaries, determine the temperature field boundary conditions; Step 1.7: Mesh the geometric domain of the infinitely long two-dimensional submarine cable section and determine the shape function based on the mesh type; Step 1.8: The Newton iteration method is used to numerically solve the fully coupled equations to obtain the electric field strength and temperature field distribution of the submarine cable.

3. The uncertainty quantification design method for XLPE insulation layer structure based on the thermoelectric properties of high-voltage DC submarine cables according to claim 2, characterized in that, The two-dimensional Ampere's law model mentioned in step 1.2 is as follows: （1）； In the formula, Represents the magnetic vector potential; Indicates magnetic permeability; This represents electrical conductivity, which is a function of temperature. The function, Represents electric potential, , , These are the three dimensions of the spatial coordinate system.

4. The uncertainty quantification design method for XLPE insulation layer structure based on the thermoelectric properties of high-voltage DC submarine cables according to claim 2, characterized in that, The electromagnetic-thermal multiphysics fully coupled equations mentioned in step 1.3 are as follows: （2）； In the formula, For Hamiltonian operators; This indicates the internal heat source in a copper conductor that generates Joule heating; This represents the thermal conductivity.

5. The uncertainty quantification design method for XLPE insulation layer structure based on the thermoelectric properties of high-voltage DC submarine cables according to claim 2, characterized in that, The calculation form of the internal heat source mentioned in step 1.4 is as follows: （3）。 6. The uncertainty quantification design method for XLPE insulation layer structure based on the thermoelectric properties of high-voltage DC submarine cables according to claim 2, characterized in that, The electromagnetic field boundary conditions described in step 1.5 are as follows: （4）； In the formula, Indicates a current source term; Represents the normal vector; Indicates a fixed potential value; It represents the magnetic vector potential.

7. The uncertainty quantification design method for XLPE insulation layer structure based on the thermoelectric properties of high-voltage DC submarine cables according to claim 2, characterized in that, The temperature field boundary conditions described in step 1.6 are as follows: （5）； In the formula, It represents the constant external temperature value.

8. The uncertainty quantification design method for XLPE insulation layer structure based on the thermoelectric properties of high-voltage DC submarine cables according to claim 1, characterized in that, The proxy model mentioned in step 2 is the Kriging proxy model. The specific process of constructing this proxy model includes: Step 2.1: Taking the thermoelectric performance of the high-voltage DC submarine cable as the design target, determine the value range of the core design parameters. The core design parameters include at least one of the following: XLPE insulation layer thickness, XLPE insulation layer conductivity, XLPE insulation layer thermal conductivity, semi-conductive shielding layer thickness, voltage amplitude fluctuation, transmission power fluctuation, and alloy lead protective sheath thickness. Step 2.2: Construct a design sample point matrix within the design scope using sampling methods; Step 2.3: Combine the sampled design variable matrices to obtain the data sample matrix; Step 2.4: Use the electric field strength and temperature peak value of the XLPE insulation layer as the response value matrix; Step 2.5: Construct the Kriging surrogate model by using a regression model and a Gaussian process to represent the true function; Step 2.6: Estimate the hyperparameters of the Gaussian process in the Kriging surrogate model using maximum likelihood estimation; Step 2.7: Introduce the Lagrange multiplier method to solve the constrained optimization problem and obtain a surrogate model for predicting the thermoelectric performance of high-voltage DC submarine cables; Step 2.8: Train the surrogate model using sample data, and substitute the unknown design variable matrix into the surrogate model to obtain the response value; Step 2.9: Extract 10 to 20 sets of unknown design samples, compare the prediction results of the surrogate model with the simulation model results, and calculate the mean square error (MSE). Step 2.10: If MSE is greater than 0.01, increase the amount of sampled data in step 2.2 and repeat steps 2.3 to 2.

9.

9. The uncertainty quantification design method for XLPE insulation layer structure based on the thermoelectric properties of high-voltage DC submarine cables according to claim 8, characterized in that: The sampling method described in step 2.2 is any one of random sampling, uniform sampling, or Latin hypercube sampling.

10. The uncertainty quantification design method for XLPE insulation layer structure based on the thermoelectric properties of high-voltage DC submarine cables according to claim 1, characterized in that, The specific process of uncertainty quantification design for the XLPE insulation layer of the high-voltage DC submarine cable in step 3 includes: Step 3.1: Select the XLPE insulation layer thickness and transmission power as design parameters, densify the sample points within the parameter design range, and obtain the response values ​​of electric field strength and temperature field corresponding to the increased sample points through the constructed surrogate model; Step 3.2: Based on the encrypted design sample and response value, fit the specific expression form of the response surface; Step 3.3: Based on the design limits of electric field strength and temperature peak, construct the design equations for matching the XLPE insulation layer thickness of high voltage DC submarine cable with transmission power; Step 3.4: Solve the design equations simultaneously to obtain the deterministic design value of the XLPE insulation layer thickness; Step 3.5: Select the main design variables that affect the thermoelectric performance of the submarine cable, considering the influence of manufacturing and installation errors, material property deviations, and random uncertainties caused by load fluctuations. The uncertainty distribution of the main design variables should satisfy a Gaussian distribution or a uniform distribution, with upper and lower bound fluctuations ranging from 0.1% to 5%. Step 3.6: Identify key design variables using the Morris screening method; Step 3.7: Perform Sobol sensitivity analysis based on Morris screening results to accurately quantify the contribution rate of design variables; Step 3.8: Conduct uncertainty propagation research on design variables with Sobol exponents exceeding 0.1, obtain the probability density function through kernel density estimation, estimate the failure probability, and iteratively optimize to obtain the optimal value of XLPE insulation layer thickness.

11. The uncertainty quantification design method for XLPE insulation layer structure based on the thermoelectric properties of high-voltage DC submarine cables according to claim 10, characterized in that: The electric field strength design limit mentioned in step 3.3 is below 30kV / mm, and the temperature design limit is below 90℃.

12. The uncertainty quantification design method for XLPE insulation layer structure based on the thermoelectric properties of high-voltage DC submarine cables according to claim 10, characterized in that, The Morris screening model described in step 3.6 is as follows: （6）； （7）； In the formula, Indicates the first The absolute average effect of each design variable; Indicates the first Standard deviation of the effect values ​​of each design variable; Indicates the first The design variable in the th... The average change of the variable along the trajectory; Indicates the length of the trajectory.

13. The uncertainty quantification design method for XLPE insulation layer structure based on the thermoelectric properties of high-voltage DC submarine cables according to claim 10, characterized in that, The Sobol sensitivity analysis described in step 3.7 includes first-order exponent estimation and total sensitivity exponent estimation. The first-order sensitivity exponent estimation model is as follows: （8）； The overall sensitivity index estimation model is as follows: （9）； In the formula, Indicates the first The first-order sensitivity index of each design variable; , For two independent sample matrices, , ; Indicates the number of samples; For variable dimensions; Indicates will The first of the matrix Column replacement The first of the matrix A mixed matrix constructed from columns; Represents the sample matrix No. The response value of each sample; Represents the mixture matrix No. The response value of each sample; Indicates the first The overall sensitivity index of the design variables; Indicates will The first of the matrix Column replacement The first of the matrix A mixed matrix constructed from columns; Represents the mixture matrix No. The response value of the nth sample; The nth design variable and the first matrix The columns correspond.

14. The uncertainty quantification design method for XLPE insulation layer structure based on the thermoelectric properties of high-voltage DC submarine cables according to claim 10, characterized in that, The probability density function for kernel density estimation described in step 3.8 is: （10）； In the formula, For kernel functions; Indicates bandwidth; Indicates the number of samples; Indicates the sample response value; This indicates the predicted response value.

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