Cable electrical performance simulation design method and system based on multi-objective optimization

Abstract

The invention relates to the technical field of multi-objective optimization, in particular to a cable electrical performance simulation design method and system based on multi-objective optimization. The method comprises the steps of constructing a low-fidelity model and a high-fidelity model, fusing and evaluating features based on feature sensitivity, and performing staged evaluation by using a non-dominated sorting genetic algorithm. According to the method, exploration is accelerated by using a low-fidelity model at an optimized initial algebra, and hierarchical non-dominated sorting and high-fidelity evaluation refinement solution sets are applied in a convergence stage. Meanwhile, a constraint dominating principle and a dynamic penalty function are integrated, and it is ensured that the generated Pareto optimal solution set is strictly located in a feasible region. The efficiency bottleneck between high-precision simulation and optimization iteration is effectively solved, and the optimization efficiency of complex cable design and the reliability of a final scheme are remarkably improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of multi-objective optimization, and particularly to a cable electrical performance simulation design method and system based on multi-objective optimization. BACKGROUND

[0002] Cable electrical performance optimization design is a complex computational aided design task, involving multiple conflicting objectives such as minimizing cost, maximizing performance, and meeting strict safety constraints. Especially in critical infrastructures such as nuclear power plants, the design scheme must meet extremely strict safety level redundancy and entity isolation constraints, which puts high requirements on the constraint handling ability of the algorithm.

[0003] In the prior art, the mainstream method to solve the multi-objective optimization problem of the cable is to couple a high-precision physical simulation model such as the finite element method with a multi-objective evolutionary algorithm such as the non-dominated sorting genetic algorithm. This method can objectively find the Pareto optimal solution set between cost, performance, and reliability. To improve computational efficiency, existing research has improved the core operators of the genetic algorithm, successfully shortening the number of iterations required for algorithm convergence from hundreds of generations to about one hundred generations, effectively improving the convergence speed. However, due to the huge time consumption required by high-fidelity finite element models for accurate calculation of physical quantities such as electric field and temperature field, a single simulation usually takes minutes. Although the number of iterations has been reduced, the entire optimization design cycle still takes several days or even weeks, which is far from meeting the requirements of modern engineering design for rapid iteration. In addition, the convergence efficiency and accuracy of existing algorithms are difficult to fully guarantee when dealing with complex engineering hard constraints such as strict safety redundancy and entity isolation in safety class cables for nuclear power plants.

[0004] In view of the deficiencies in the prior art described above, the core technical problem to be solved by the present application is: how to break through the computational efficiency bottleneck between high-fidelity physical simulation and multi-objective optimization algorithm iteration evaluation, significantly shorten the optimization cycle of cable design under the premise of ensuring the engineering accuracy of the optimization results, and effectively and strictly handle complex safety hard constraints?

[0005] To this end, a cable electrical performance simulation design method and system based on multi-objective optimization are proposed. SUMMARY

[0006] The present application aims to provide a cable electrical performance simulation design method and system based on multi-objective optimization, which solves the computational efficiency bottleneck between high-precision physical simulation and multi-objective optimization iteration evaluation by constructing a heterogeneous multi-fidelity model and evaluating feature fusion according to feature sensitivity, adopting a phased hierarchical non-dominated sorting strategy, and integrating constraint dominance principle and dynamic penalty function, ensures that the final solution set strictly meets the engineering hard constraints under the premise of ensuring design accuracy and convergence speed.

[0007] To achieve the above object, the present application provides the following technical solutions: A cable electrical performance simulation design method based on multi-objective optimization, comprising: A low-fidelity model and a high-fidelity model for evaluating the electrical performance of the cable are constructed, and the characteristic sensitivity of the design variables of the cable to the output results of the low-fidelity model and the high-fidelity model is calculated; the evaluation characteristics of the low-fidelity model and the high-fidelity model are fused according to the characteristic sensitivity to obtain the target function evaluation result of the current design scheme; The design variable population is initialized, and a non-dominated sorting genetic algorithm is used; in the initial number of optimization generations, the low-fidelity model is used for target function evaluation; in the convergence stage of optimization, the individuals located on the Pareto frontier are preferentially evaluated by the high-fidelity model; for all individuals in the population, hierarchical non-dominated sorting is performed, and in the convergence stage, the individuals evaluated by the high-fidelity model and the neighborhood solutions are selected as the population with higher priority for selection operation; The hard constraints of the cable design are modeled; in the optimization process, the constraint dominance principle is used to process the constraint violation individuals in the population; a dynamic penalty function is introduced, and the penalty strength is dynamically adjusted according to the optimization generation number and the constraint violation degree, so as to ensure that the generated Pareto solution set is located in the feasible region; The Pareto optimal solution set satisfying all hard constraints is output; and an optimal design scheme is selected from the Pareto optimal solution set according to a preset satisfaction function.

[0008] Preferably, the low-fidelity model and the high-fidelity model are specifically: The low-fidelity model uses an analytical formula and / or a simplified circuit model to evaluate the ohmic loss and the linear electrical performance indicators of the capacitance value of the cable; and the high-fidelity model uses the finite element method to calculate the electric field distribution, the temperature field distribution, and the thermal-electric-mechanical multi-physical field coupling nonlinear coupling performance indicators of the cable.

[0009] Preferably, the calculation of the characteristic sensitivity comprises: A preset small perturbation increment is applied to any design variable in the set of cable design variables; the low-fidelity model and the high-fidelity model are used to calculate the corresponding model output characteristic values before and after the perturbation of the design variable, respectively, to obtain the corresponding change amount of the model output characteristic values; the finite difference method is used to quantitatively obtain the characteristic sensitivity of the design variable by calculating the ratio of the small perturbation increment of the design variable to the corresponding change amount of the model output characteristic values; The characteristic sensitivities of all design variables are normalized to eliminate the dimensional influence.

[0010] Preferably, the fusion of the evaluation characteristics of the low-fidelity model and the high-fidelity model according to the characteristic sensitivity comprises the following steps: For each performance objective to be evaluated in the cable design scheme, an adaptive weighting coefficient is determined based on feature sensitivity; the adaptive weighting coefficient is positively correlated with the feature sensitivity of the design variables to the output of the high-fidelity model. Obtain the performance characteristic values ​​of the design scheme evaluated by the low-fidelity model and the high-fidelity model respectively; perform a weighted summation of the performance characteristic values ​​of the low-fidelity model and the high-fidelity model to obtain the fused characteristic value under the performance target to be evaluated; summarize the fused characteristic values ​​of all performance targets and the degree of violation of hard constraints to form the objective function evaluation result of the current design scheme.

[0011] Preferably, the violation degree of the hard constraint is a non-negative index used to quantify the degree to which the current design scheme does not meet the hard constraint. For each hard constraint, the individual violation degree is calculated: For constraints with a maximum value limit, the individual violation degree is equal to the difference between the actual calculated value and the maximum allowed threshold; if the actual calculated value does not exceed the maximum threshold, the violation degree is zero. For constraints with a minimum value limit, the individual violation degree is equal to the difference between the required minimum threshold and the actual calculated value; if the actual calculated value is not lower than the minimum threshold, the violation degree is zero. For logical and / or isolation constraints, the degree of individual violation is quantified by a logical decision; The total constraint violation rate of the design scheme is obtained by summing up the violation rates calculated from all individual hard constraints.

[0012] Preferably, the specific usage of the non-dominated sorting genetic algorithm includes the following steps: Based on the number of generations the evolutionary process has run, the population evaluation strategy is divided into an initial generation exploration phase and a convergence phase. In the initial generation exploration phase, the non-dominated sorting genetic algorithm uses the feature values ​​of a low-fidelity model when evaluating the objective function. In the convergence phase, the non-dominated sorting genetic algorithm uses the feature values ​​of a high-fidelity model when evaluating the objective function. During each generation of evolution, the current population is non-dominated sorted based on the total constraint violation degree and the objective function evaluation result. During the convergence phase, the non-dominated sorting genetic algorithm treats individuals that have been evaluated by the high-fidelity model and individuals in the neighborhood that have not yet been evaluated as high-priority populations during sorting and selection operations. Based on the non-dominated ranking results, an elite retention strategy is applied to select the next generation of parent populations; crossover and mutation operations are performed on the selected parent populations to generate new offspring populations, which then enter the next generation iteration evaluation.

[0013] Preferably, the specific methods for handling individuals in the population that violate constraints include: Before the selection operation is performed in the population, the constraint dominance principle is applied to rank the individuals. When the total constraint violation of two individuals is not equal, the design scheme with the lower total constraint violation is selected. A dynamic penalty function is introduced, which takes the total constraint violation as input and combines it with the current optimization algebra to calculate the dynamic penalty term. The dynamic penalty term is superimposed on the objective function value of the individual that violates the constraint to form a new objective function value; the objective function value after dynamic penalty correction is combined with the total constraint violation degree as the final evaluation basis for the individual in the selection operation.

[0014] A cable electrical performance simulation design system based on multi-objective optimization includes: Model Evaluation and Fusion Module: Constructs low-fidelity and high-fidelity models to evaluate the electrical performance of cables, calculates the feature sensitivity of cable design variables to the output results of the low-fidelity and high-fidelity models, and fuses the evaluation features of the low-fidelity and high-fidelity models based on the feature sensitivity to obtain the objective function evaluation results of the current design scheme. Evolutionary selection module: Initialize the design variable population using a non-dominated sorting genetic algorithm; in the initial generations of optimization, evaluate the objective function using a low-fidelity model; during the convergence phase of optimization, prioritize individuals located at the Pareto front for high-fidelity model evaluation; perform hierarchical non-dominated sorting on all individuals in the population, and during the convergence phase, select individuals evaluated by the high-fidelity model and their neighborhood solutions as higher-priority populations for selection operations; Hard constraint modeling module: Models the hard constraints of cable design; During the optimization process, the constraint dominance principle is used to handle constraint violation individuals in the population; A dynamic penalty function is introduced, and the penalty intensity is dynamically adjusted with the optimization algebra and the degree of constraint violation to ensure that the generated Pareto solution set is located within the feasible region; Output filtering module: Outputs a Pareto optimal solution set that satisfies all hard constraints; Selects the optimal design scheme from the Pareto optimal solution set according to a preset satisfaction function.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention achieves dynamic scheduling of computing resources by constructing a heterogeneous multi-fidelity model and performing evaluation feature fusion based on feature sensitivity. In the initial algebraic exploration phase of optimization, it primarily relies on a low-cost, fast low-fidelity model, while resources are concentrated on using a high-fidelity model for accurate evaluation during the convergence phase. This strategy effectively avoids the problem of time-consuming finite element simulations for all individuals in each generation, as in traditional methods, thereby significantly shortening the overall optimization design cycle from several days or weeks and greatly improving the rapid iteration capability of cable design.

[0016] 2. This invention does not simply replace a high-fidelity model with a low-fidelity model. Instead, it uses feature sensitivity to precisely guide the feature fusion weights of the two models, ensuring the rationality of the evaluation results. Simultaneously, the hierarchical non-dominated ranking strategy ensures that limited and valuable high-fidelity model evaluation resources are preferentially allocated to high-potential solutions located near the Pareto front. This mechanism guarantees that while significantly improving computational efficiency, the final Pareto optimal solution set still meets engineering design requirements in terms of accuracy of key indicators such as electrical performance and thermal field distribution.

[0017] 3. This invention dynamically adjusts the penalty intensity, allowing the algorithm to explore a wide area in the early stages of optimization, thus avoiding getting trapped in local optima. During the convergence phase, the dynamically enhanced penalty mechanism and constraint dominance principle force individuals to converge towards feasible regions that satisfy the constraints. This mechanism is particularly suitable for unconditionally satisfying strict hard constraints such as safety-level redundancy and physical isolation distances in the design of safety-grade cables for nuclear power plants, ensuring the engineering reliability and safety of the design scheme. Attached Figure Description

[0018] Figure 1 This is a flowchart of a cable electrical performance simulation design method based on multi-objective optimization proposed in this invention. Figure 2 This is a flowchart illustrating a cable electrical performance simulation design method based on multi-objective optimization proposed in this invention. Figure 3 This is a flowchart of the non-dominated sorting genetic algorithm proposed in this invention; Figure 4 This is a system structure diagram of a cable electrical performance simulation design system based on multi-objective optimization proposed in this invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] Example 1 Please see Figures 1 to 3 This invention provides a simulation design method and system for cable electrical performance based on multi-objective optimization, the technical solution of which is as follows: A simulation design method for cable electrical performance based on multi-objective optimization, such as... Figure 1 - Figure 2 As shown, it includes: Construct low-fidelity and high-fidelity models to evaluate the electrical performance of cables, and calculate the feature sensitivity of cable design variables to the output results of the low-fidelity and high-fidelity models; based on the feature sensitivity, fuse the evaluation features of the low-fidelity and high-fidelity models to obtain the objective function evaluation results of the current design scheme; Initialize the design variable population using a non-dominated sorting genetic algorithm; in the initial generation of optimization, use a low-fidelity model to evaluate the objective function; during the convergence phase of optimization, prioritize individuals located at the Pareto front for high-fidelity model evaluation; perform hierarchical non-dominated sorting on all individuals in the population, and during the convergence phase, select individuals evaluated by the high-fidelity model and their neighborhood solutions as higher-priority populations for selection operations. The hard constraints of the cable design are modeled; during the optimization process, the constraint dominance principle is used to handle individuals in the population that violate the constraints; a dynamic penalty function is introduced, and the penalty intensity is dynamically adjusted with the optimization algebra and the degree of constraint violation to ensure that the generated Pareto solution set is located within the feasible region. Output a Pareto optimal solution set that satisfies all hard constraints; select the optimal design scheme from the Pareto optimal solution set according to a preset satisfaction function.

[0021] Furthermore, the low-fidelity model and the high-fidelity model are specifically as follows: The low-fidelity model uses analytical formulas and / or simplified circuit models to evaluate the ohmic loss and capacitance linear electrical performance of the cable; the high-fidelity model uses the finite element method to calculate the electric field distribution, temperature field distribution, and thermoelectric mechanical multi-physics coupling nonlinear coupling performance of the cable.

[0022] The low-fidelity model can be constructed by equating the cable to a simplified circuit model with lumped or distributed parameters, consisting of the ohmic resistance of the conductor, the dielectric loss resistance of the insulation layer, and the distributed capacitance. The resistance and capacitance are calculated using analytical formulas based on geometric dimensions and material parameters. The high-fidelity model employs the finite element method, which involves two-dimensional geometric modeling of the cable cross-section, dividing it into quadrilateral / triangular meshes, applying potential boundary conditions at the conductor-insulation interface, and applying convective heat transfer boundary conditions at the outer sheath boundary to accurately calculate the electric and temperature field distributions.

[0023] This invention achieves a comprehensive and accurate evaluation of the linear electrical performance and thermo-mechanical coupling nonlinear performance of cables by constructing a heterogeneous evaluation system consisting of a low-fidelity analytical / simplified circuit model and a high-fidelity finite element model. This strategy utilizes a low-cost model to improve computational efficiency while employing a high-precision model to ensure the reliability of key indicators, significantly shortening the cable optimization design cycle and improving the quality of engineering design.

[0024] Furthermore, the calculation of the feature sensitivity includes: For any design variable in the cable design variable set, a preset small disturbance increment is applied; using the low-fidelity model and the high-fidelity model, the corresponding model output feature values ​​before and after the disturbance of the design variable are calculated respectively, and the corresponding change of the model output feature values ​​is obtained; using the finite difference method, the feature sensitivity of the design variable is quantified by calculating the ratio of the small disturbance increment of the design variable to the corresponding change of the model output feature values. The characteristic sensitivity of all design variables is normalized to eliminate the influence of dimensions.

[0025] The normalization of the feature sensitivity is achieved using methods such as max-min normalization or Z-score standardization, mapping the sensitivity value to the range of 0 to 1. For any performance target to be evaluated, the calculation of the adaptive weighting coefficient is positively correlated with the feature sensitivity of the design variables to the high-fidelity model output. Specifically, the adaptive weighting coefficient can be expressed as a monotonically increasing function based on the normalized high-fidelity model feature sensitivity value. For example, the normalized sensitivity value can be directly used as the weighting coefficient, or the square of the sensitivity value can be used as the weighting coefficient. The result is then mapped to the interval [0, 1] to ensure that features with higher sensitivity have greater weights in the high-fidelity model.

[0026] This embodiment employs the finite difference method to accurately quantify the feature sensitivity of design variables to the outputs of low-fidelity and high-fidelity models, providing a scientific basis for model fusion. By normalizing the sensitivity, the influence of different design variable dimensions on the evaluation results is effectively eliminated, ensuring the objectivity and accuracy of the weights. Based on this sensitivity information, adaptive weighting coefficients can dynamically allocate the evaluation weights of the high-fidelity model, ensuring that the fused feature values ​​more accurately reflect the physical factors that have the greatest impact on the design objective, thereby significantly improving the accuracy and convergence efficiency of multi-objective optimization search.

[0027] Furthermore, the fusion of evaluation features from the low-fidelity model and the high-fidelity model based on feature sensitivity specifically includes the following steps: For each performance objective to be evaluated in the cable design scheme, an adaptive weighting coefficient is determined based on feature sensitivity; the adaptive weighting coefficient is positively correlated with the feature sensitivity of the design variables to the output of the high-fidelity model. Obtain the performance characteristic values ​​of the design scheme evaluated by the low-fidelity model and the high-fidelity model respectively; perform a weighted summation of the performance characteristic values ​​of the low-fidelity model and the high-fidelity model to obtain the fused characteristic value under the performance target to be evaluated; summarize the fused characteristic values ​​of all performance targets and the degree of violation of hard constraints to form the objective function evaluation result of the current design scheme.

[0028] The adaptive weighting coefficients The calculation is based on the normalized high-fidelity model feature sensitivity. To clearly represent the positive correlation mathematically and to increase the weight of highly sensitive variables, Can be adopted The quantization calculation is performed using the monotonically increasing power function form.

[0029] Specifically, for any design variable, its adaptive weighting coefficient The relationship can be determined by the following formula: ; in: It is the normalized value of the sensitivity of the design variables to the high-fidelity model output features of the current performance target to be evaluated, and its range is [0, 1]. This is a preset exponential parameter greater than or equal to 1 (e.g., p=1 or p=2). The setting of this parameter reflects the degree of enhancement to the high-sensitivity feature. When... When =1, Directly equal to They exhibit a linear positive correlation. When >1 (e.g.) =2), equal The power value of the value exhibits a non-linear positive correlation, which gives higher weights to features with high sensitivity.

[0030] The fusion of the performance characteristic values ​​is performed for the same performance objective (e.g., total loss). Let... For the first The feature values ​​of each performance objective are obtained by evaluating them using a low-fidelity model. For the first The feature values ​​of each performance objective are obtained through evaluation using a high-fidelity model. Before performing a weighted summation, it must be ensured that... and They have the same physical dimensions (e.g., both are cable losses or both are material usage, etc.). If their dimensions are different, one or both characteristic values ​​should be normalized or their dimensions transformed.

[0031] The fusion feature value The calculation formula is: ; in These are adaptive weighting coefficients based on feature sensitivity.

[0032] The specific operation of summarizing the fused characteristic values ​​of all performance objectives and the degree of violation of hard constraints to form the objective function evaluation result of the current design scheme is as follows: The fusion feature value of all performance targets This forms a multidimensional objective function vector.

[0033] ; Where M represents the number of performance objectives. The degree of violation of hard constraints. It is an independent non-negative scalar, obtained by summing the violations of all individual hard constraints.

[0034] In non-dominated sorting genetic algorithms, the optimization objective remains a multi-objective function vector. The principle of constraint and dominance uses independent... This helps determine the dominance relationship between two individuals, without reducing a multi-objective problem to a single-objective problem. Specifically, individuals For individuals The determination of dominance is based on and Independent comparisons ensure that the algorithm outputs a multi-objective Pareto optimal solution set.

[0035] This embodiment achieves a dynamic balance between the efficiency of the low-fidelity model and the accuracy of the high-fidelity model by determining adaptive weighting coefficients based on feature sensitivity. This weighted summation feature fusion mechanism ensures that the calculated fused feature values ​​objectively and accurately reflect the true impact of design variables on performance objectives. By summarizing the multi-objective performance fusion values ​​with hard constraint violation degrees to form a unified evaluation result, the evaluation process of the optimization algorithm is greatly simplified, the efficiency and accuracy of iterative evaluation are improved, and a solid foundation is laid for the efficient application of multi-objective evolutionary algorithms in complex engineering design.

[0036] Furthermore, the design variable population consists of a set of variables constituting the cable geometry and material parameters. The design variables include at least the following key parameters and their allowed value ranges (boundary constraints): conductor diameter The allowed range is (For example, 10.0mm to 30.0mm).

[0037] Insulation layer thickness The allowed range is (For example, 5.0mm to 15.0mm).

[0038] Semiconducting layer conductivity The allowed range is (For example, 1) Up to 10 The initial design variable population is specifically generated by using Latin hypercube sampling or uniform random sampling within the above-mentioned allowed value range to generate N individuals, thereby ensuring that the initial population has good diversity.

[0039] Furthermore, the violation degree of the hard constraint is a non-negative index used to quantify the extent to which the current design scheme does not satisfy the hard constraint. For each hard constraint, the individual violation degree is calculated: For constraints with a maximum value limit, the individual violation degree is equal to the difference between the actual calculated value and the maximum allowed threshold; if the actual calculated value does not exceed the maximum threshold, the violation degree is zero. For constraints with a minimum value limit, the individual violation degree is equal to the difference between the required minimum threshold and the actual calculated value; if the actual calculated value is not lower than the minimum threshold, the violation degree is zero. For logical and / or isolation constraints, the degree of individual violation is quantified by a logical decision; The total constraint violation rate of the design scheme is obtained by summing up the violation rates calculated from all individual hard constraints.

[0040] The hard constraints of cable design refer to the engineering safety and performance indicators that must be strictly met in actual operation, and their set includes, but is not limited to, the following: Maximum operating electric field strength constraint: Electric field strength at any point inside the insulation layer The electric field strength shall not exceed the allowable design strength of the material. ,Right now .

[0041] Maximum operating temperature constraint: Temperature at any point inside the conductor and insulation layer The operating temperature must not exceed the long-term allowable operating temperature of the material. ,Right now .

[0042] Minimum mechanical stress constraint: Ensures the minimum bending or tensile stress that the cable must withstand during installation and operation. Meet minimum requirements ,Right now The degree of individual violation is determined based on the constraints. Calculate, its value is equal to .

[0043] This embodiment explicitly models core engineering hard constraints such as maximum operating electric field strength and maximum operating temperature, and accurately quantifies the violation degree of individual and total constraints. This provides a rigorous basis for feasibility judgment of the optimization algorithm. This effectively ensures that the multi-objective evolutionary algorithm can reliably converge to the feasible region that fully satisfies all safety and performance requirements, greatly improving the engineering safety and reliability of the final cable design scheme.

[0044] Furthermore, such as Figure 3 As shown, the specific usage of the non-dominated sorting genetic algorithm includes the following steps: Based on the number of generations the evolutionary process has run, the population evaluation strategy is divided into an initial generation exploration phase and a convergence phase. In the initial generation exploration phase, the non-dominated sorting genetic algorithm uses the feature values ​​of a low-fidelity model when evaluating the objective function. In the convergence phase, the non-dominated sorting genetic algorithm uses the feature values ​​of a high-fidelity model when evaluating the objective function. During each generation of evolution, the current population is non-dominated sorted based on the total constraint violation degree and the objective function evaluation result. During the convergence phase, the non-dominated sorting genetic algorithm treats individuals that have been evaluated by the high-fidelity model and individuals in the neighborhood that have not yet been evaluated as high-priority populations during sorting and selection operations. Based on the non-dominated ranking results, an elite retention strategy is applied to select the next generation of parent populations; crossover and mutation operations are performed on the selected parent populations to generate new offspring populations, which then enter the next generation iteration evaluation.

[0045] During the convergence phase, individuals that have been evaluated using the high-fidelity model and their neighborhoods are designated as a high-priority population. The neighborhood solution refers to all unevaluated individuals in the design variable space whose Euclidean distance to the evaluated high-fidelity model individuals is less than a preset threshold. The hierarchical non-dominated sorting ensures that, during elite retention and selection operations, these high-precision solutions and their neighborhoods have a higher probability of entering the next generation of the parent population by assigning the high-priority population a virtual non-dominated level superior to the ordinary population, or by giving them higher priority in crowding calculations.

[0046] The preset threshold (i.e., neighborhood radius) is not a fixed constant, but is dynamically adjusted according to the optimization process and population density. The preset threshold can be set to a dynamic value to ensure that the number of individuals contained in the neighborhood is maintained at a preset proportion (e.g., not exceeding 2% to 5% of the current population size). If the number of individuals exceeds this proportion, the preset threshold is reduced; if the number of individuals is too small, the preset threshold is increased.

[0047] The evaluation switching strategy between the low-fidelity model and the high-fidelity model is determined algebraically based on the optimization process: Preset a switching algebra threshold When the current optimization algebra At this stage, which is the initial algebra phase, all individuals are evaluated using a low-fidelity model. At this point, the algorithm enters the convergence phase.

[0048] Switching Algebraic Thresholds The following principles should be followed: the number of generations in the initial exploration phase should be at least 20%-50% of the population size (N) to ensure that the low-fidelity model can explore sufficient design space. For typical cable design problems with a population size (N=100) and a design variable dimension (n=10), The number of generations can be set from 20 to 50. In addition, a dynamic judgment method can be adopted: when the fitness value of the best individual in the population changes by less than 1% over 5 consecutive generations, it is considered to have entered the convergence stage, at which point high-fidelity evaluation is switched.

[0049] This embodiment achieves efficient scheduling of computational resources by deeply integrating a non-dominated sorting genetic algorithm with a phased heterogeneous evaluation strategy. In the initial exploration phase, a low-fidelity model is used to quickly approximate the optimal region, while in the convergence phase, computational resources are concentrated on Pareto front individuals and their neighborhood solutions evaluated by the high-fidelity model, assigning them high priority. This dynamic switching and hierarchical sorting mechanism, while ensuring the accuracy of the final solution set, significantly reduces the number of computationally expensive finite element simulation calls, significantly improving the algorithm's convergence speed and overall optimization efficiency, and resolving the contradiction between accuracy and efficiency in complex engineering optimization.

[0050] Furthermore, the specific methods for handling individuals in the population who violate constraints include: Before the selection operation is performed in the population, the constraint dominance principle is applied to rank the individuals. When the total constraint violation of two individuals is not equal, the design scheme with the lower total constraint violation is selected. A dynamic penalty function is introduced, which takes the total constraint violation as input and combines it with the current optimization algebra to calculate the dynamic penalty term. The dynamic penalty term is superimposed on the objective function value of the individual that violates the constraint to form a new objective function value; the objective function value after dynamic penalty correction is combined with the total constraint violation degree as the final evaluation basis for the individual in the selection operation.

[0051] The specific processing logic of the constraint dominance principle first requires calculating each design scheme. Total constraint violation The total constraint violation rate The calculation method is as follows: sum the violation degrees of all individual hard constraints, i.e. ,in This represents the total number of hard constraints. For the first The degree of individual violation of the constraint. Next, by comparing two individuals... and Total constraint violation and objective function value To determine the dominance relationship: like and ,but Dominate (Feasible solutions dominate infeasible solutions).

[0052] like and ,and ,but Dominate (Infeasible solutions with lower violation degree dominate infeasible solutions with higher violation degree).

[0053] like =0, or >0, then and The dominance relationship between them depends on their Pareto dominance relationship in the objective function space, that is: if individuals All objective function values ​​are not inferior to individual values. And at least one objective function value is better than that of the individual. ,but Dominate .

[0054] The dynamic penalty function is designed to compute a dynamic penalty term, which can be in the form of multiplying a penalty coefficient that monotonically increases with the number of optimization algebras (e.g., grows linearly or exponentially with the number of algebras) by a monotonically increasing function of the total constraint violation (e.g., a linear or squared value of the violation). The strength of this penalty term is low in the early stages of optimization, allowing the algorithm to explore infeasible regions; in the later stages of optimization, the penalty strength gradually increases, forcing the population to converge to a feasible region that satisfies the hard constraints. This dynamic penalty term is superimposed on the objective function value of the individuals that violate the constraints, forming a new objective function value.

[0055] This invention constructs a robust and flexible constraint handling mechanism by combining the constraint dominance principle with a dynamic penalty function. The constraint dominance principle ensures that feasible solutions always take precedence over infeasible solutions during selection operations, and selects individuals with lower overall constraint violation rates among infeasible solutions, guaranteeing strict adherence to constraints and effective convergence of the algorithm. Simultaneously, the dynamic penalty function can dynamically adjust the penalty intensity based on the number of generations and the violation rate, allowing the algorithm to explore a wider design space in the early stages and strongly guide the population to converge to the feasible region in the later stages. This significantly improves the robustness of the optimization process, ensuring that the final Pareto solution set is a high-quality design scheme that strictly satisfies the hard engineering constraints.

[0056] Furthermore, the preset satisfaction function aims to transform the multi-objective optimization results into a single-objective decision, reflecting the design decision-maker's preferences. The satisfaction function can be the negative value of a distance function based on the ideal point; for example, a weighted Tchebycheff metric can be used as the distance function. This metric quantifies the distance by calculating the maximum weighted difference between all objective function values ​​and their respective ideal point values, where the weighting coefficients reflect the decision-maker's emphasis on each performance objective. The design scheme that minimizes this maximum weighted difference is the optimal design scheme.

[0057] By employing a weighted Tchebycheff metric as the satisfaction function, this method can accurately quantify the distance between the multi-objective Pareto solution set and the ideal point, and efficiently select the design scheme that best meets the actual engineering needs from the optimal solution set based on the decision-maker's preference weights (such as the degree of importance attached to cost or loss).

[0058] This invention provides an efficient and high-precision simulation design method for cable electrical performance. By constructing a heterogeneous multi-fidelity evaluation system and combining it with a feature sensitivity fusion mechanism, the accuracy of the objective function evaluation is ensured. During the optimization process, an algebraic-based phased switching strategy and hierarchical non-dominated sorting are employed to concentrate computational resources on high-potential solutions and their neighborhoods for high-precision refinement, thereby significantly shortening the optimization design cycle. Simultaneously, the algorithm applies a mechanism combining constraint dominance principles and dynamic penalty functions to rigorously and flexibly handle hard constraints such as maximum electric field strength and maximum temperature in cable design, ensuring that the final Pareto optimal solution set is a reliable scheme that fully meets engineering safety requirements. Furthermore, a satisfaction function provides decision-makers with the optimal design choice.

[0059] Example 2 This second embodiment details the specific process of applying the method of the present invention to the design optimization of a 10kV polyethylene XLPE insulated power cable.

[0060] The design optimization objectives include minimizing the total cable cost and minimizing power loss. Design variables include conductor radius. Insulation layer thickness and sheath thickness Key geometric parameters are all taken within strict engineering boundary constraints.

[0061] Hard constraints that must be satisfied The set includes: the maximum electric field strength within the insulation layer. The maximum operating temperature of the conductor must not exceed the allowable value for the material. The temperature must not exceed 90 degrees Celsius, and the minimum short-circuit current capacity is required. The preset requirements must be met.

[0062] The low-fidelity model uses simplified circuit models and analytical formulas to quickly evaluate linear electrical performance indicators of cables, such as ohmic loss and capacitance. The high-fidelity model uses the finite element method to construct a two-dimensional geometric model of the cable cross-section and mesh it for accurate calculation of the electric field distribution. Temperature field distribution The nonlinear performance indices of thermoelectric mechanical multiphysics coupling provide high-precision data for the verification of hard constraints.

[0063] During the evaluation phase, the finite difference method is used to accurately quantify the sensitivity of design variables to the features of the model output, and then normalization is performed. Adaptive weighting coefficients. The sensitivity value is determined directly based on the normalized high-fidelity model to ensure the fusion of feature values. It can accurately reflect the physical factors that have the greatest impact on nonlinear coupling indicators.

[0064] The optimization process uses a non-dominated sorting genetic algorithm and employs a threshold based on the number of generations switched. A phased evaluation strategy. In the initial exploration phase... A low-fidelity model is used for evaluation to accelerate the algorithm's approximation of the optimal region. Entering the convergence phase... Then, high-fidelity model evaluation is prioritized for individuals located at the Pareto frontier.

[0065] During the convergence phase, a hierarchical non-dominated sort is applied, which treats individuals of the evaluated high-fidelity model and their neighborhood solutions with Euclidean distances less than a preset threshold as high-priority populations and assigns them higher virtual non-dominated levels to ensure the rapid convergence of the high-precision solution set.

[0066] The constraint handling mechanism combines the constraint dominance principle with a dynamic penalty function. The total constraint violation rate of the design scheme is... It is achieved by summing the violations of all individual hard constraints. The constraint dominance principle ensures that the constraint with the lower total violation is selected first. A penalty term is introduced by the dynamic penalty function. Its strength increases with the number of optimization algebras. Linearly increasing, and related to the total constraint violation degree Multiplying the squared values ​​of the penalties by this term, the penalty is added to the objective function value of the individuals violating the constraints, strongly guiding the population to converge to the target value in the later stages of optimization. Within the feasible region where 0 = 0, the engineering safety of the final design scheme is ensured.

[0067] Finally, the algorithm outputs all constraints that are satisfied. The Pareto optimal solution set is defined by the sum of zero (=0). Decision-makers select the optimal design from the solution set using a weighted Tchebycheff metric as a pre-defined satisfaction function, based on their preference weights for cost and loss.

[0068] Example 3 like Figure 4 As shown in the figure, this embodiment three describes the scenario of applying the simulation design system constructed by this method to the multi-physics performance optimization of the spacer of a 220 kV gas-insulated transmission line.

[0069] The system's model evaluation and fusion module is activated first, constructing two performance evaluation models. The low-fidelity model uses analytical formulas or simplified circuit models to quickly calculate linear indices such as material usage (related to weight) and simplified capacitance values ​​for the spacers. The high-fidelity model employs finite element analysis to accurately calculate the three-dimensional electric field and mechanical stress distribution of the spacers under complex geometries. Subsequently, the system calculates the characteristic sensitivity of design variables (such as critical chamfer radius and stiffener thickness) to the output results of the two models and normalizes the sensitivity. Based on the sensitivity information, the system determines adaptive weighting coefficients, weights and sums the efficiency results of the low-fidelity model and the accuracy results of the high-fidelity model to obtain the fusion objective function evaluation value of the current design scheme.

[0070] Next, the evolutionary selection module begins its work. The system initializes the population based on the design variables and initiates the non-dominated sorting genetic algorithm. In the initial generations of optimization, the system primarily uses a low-fidelity model to quickly evaluate and explore the population. When the number of generations reaches a preset switching threshold, the system enters the convergence phase, at which point a high-fidelity model is prioritized to accurately evaluate a small number of individuals located on the Pareto front. In each generation of selection, the system performs a hierarchical non-dominated sorting of all individuals, identifying those that have already undergone high-fidelity evaluation, along with unevaluated individuals in their neighborhoods with small Euclidean distances in the design space, as high-priority populations. This ensures that these high-quality solutions are preferentially selected by the elite preservation strategy.

[0071] Meanwhile, the hard constraint modeling module is integrated throughout the entire evolutionary process. This module first models the key safety indicators for the spacer design, including ensuring that the maximum electric field strength does not exceed the breakdown threshold of the gas medium and that the maximum mechanical stress does not exceed the long-term allowable stress of the insulating material. The system calculates the total constraint violation degree for each design scheme. When selecting individuals, the module applies the constraint dominance principle, prioritizing design schemes with lower total constraint violation degrees. Furthermore, the module introduces a dynamic penalty function, whose penalty strength increases synchronously with the optimization algebra and constraint violation degree. This penalty term is superimposed on the objective function value of the individual violating the constraints, strongly guiding the entire population to converge towards the feasible region that satisfies all safety constraints.

[0072] Finally, the output filtering module presents the final design results. The system outputs a Pareto optimal solution set that has undergone rigorous constraint verification and satisfies all maximum electric field strength and maximum mechanical stress constraints. This set includes a series of non-dominated solutions, such as those with minimum weight and optimal insulation performance. Based on the user-preset satisfaction function (e.g., a weighted Tchebycheff metric) and combined with the design engineer's preference weights for "weight reduction" and "increased insulation strength," the system automatically filters the final optimized spacer design scheme that best meets the engineering requirements from the Pareto solution set.

[0073] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for simulation design of electrical performance of a cable based on multi-objective optimization, characterized in that, The application relates to a cable design optimization method based on low-fidelity model and high-fidelity model. The method comprises the following steps: a low-fidelity model and a high-fidelity model are constructed to evaluate the electrical performance of a cable, and the characteristic sensitivity of a cable design variable to the output of the low-fidelity model and the high-fidelity model is calculated; the evaluation characteristics of the low-fidelity model and the high-fidelity model are fused according to the characteristic sensitivity to obtain the objective function evaluation result of a current design scheme; a population of design variables is initialized, and a non-dominated sorting genetic algorithm is used; in the initial number of optimization generations, the low-fidelity model is used to evaluate the objective function; in the convergence stage of optimization, the high-fidelity model is preferentially used to evaluate the individuals located on the Pareto frontier; the hierarchical non-dominated sorting is performed on all individuals in the population, and in the convergence stage, the individuals evaluated by the high-fidelity model and the neighborhood solutions are selected as the population with higher priority; the hard constraints of the cable design are modeled; in the optimization process, the constraint dominance principle is used to process the constraint violation individuals in the population; a dynamic penalty function is introduced, and the penalty strength is dynamically adjusted according to the optimization generation number and the constraint violation degree, so that the generated Pareto solution set is located in the feasible region; 2. The method of claim 1, wherein, a Pareto optimal solution set satisfying all hard constraints is output; and according to a preset satisfaction function, an optimal design scheme is selected from the Pareto optimal solution set. The low-fidelity model and the high-fidelity model are specifically as follows:

3. The method of claim 1, wherein, the low-fidelity model adopts an analytical formula and / or a simplified circuit model and is used to evaluate the ohmic loss and the linear electrical performance index of the capacitance value of the cable; and the high-fidelity model adopts a finite element method and is used to calculate the electric field distribution, the temperature field distribution and the thermal-electric-mechanical multi-physical field coupling nonlinear coupling performance index of the cable. The calculation of the characteristic sensitivity comprises the following steps: a preset small perturbation increment is applied to any design variable in the set of cable design variables; the low-fidelity model and the high-fidelity model are used to respectively calculate the characteristic values of the model output before and after the perturbation of the design variable, and the corresponding change amount of the model output characteristic value is obtained; the characteristic sensitivity of the design variable is quantitatively obtained by calculating the ratio of the small perturbation increment of the design variable to the corresponding change amount of the model output characteristic value through the finite difference method; 4. The method of claim 1, wherein, the characteristic sensitivities of all design variables are normalized to eliminate the dimension influence. The fusion of the evaluation characteristics of the low-fidelity model and the high-fidelity model according to the characteristic sensitivity comprises the following steps: for each performance target to be evaluated of the cable design scheme, an adaptive weighting coefficient is determined based on the characteristic sensitivity; the adaptive weighting coefficient is in a positive correlation with the characteristic sensitivity of the design variable to the output of the high-fidelity model; 5. The method of claim 4, wherein, the performance characteristic values of the design scheme evaluated by the low-fidelity model and the high-fidelity model are obtained; the performance characteristic values of the low-fidelity model and the performance characteristic values of the high-fidelity model are weighted and summed to obtain the fusion characteristic value under the performance target to be evaluated; and the fusion characteristic values of all performance targets and the violation degrees of the hard constraints are collected to form the objective function evaluation result of the current design scheme. The violation degree of the hard constraint is a non-negative index for quantifying the degree of non-satisfaction of the current design scheme to the hard constraint, and the single-item violation degree is calculated for each hard constraint. For the constraint with maximum limit, the single item violation degree equals to the difference between the actual calculated value and the allowed maximum threshold; if the actual calculated value does not exceed the maximum threshold, the violation degree is zero; For the constraint with minimum limit, the single item violation degree equals to the difference between the required minimum threshold and the actual calculated value; If the actual calculated value does not fall below the minimum threshold, the violation degree is zero; For the logical and / or isolated constraint, the single item violation degree is quantified by a logical judgment; The total constraint violation degree of the design scheme is obtained by accumulating and summing the violation degrees of all single hard constraints.

6. The method of claim 5, wherein: The specific use of the non-dominated sorting genetic algorithm includes the following steps: According to the number of generations of the evolution process, the population evaluation strategy is divided into an initial number of generations exploration stage and a convergence stage; in the initial number of generations exploration stage, the non-dominated sorting genetic algorithm uses the eigenvalues of the low-fidelity model when evaluating the objective function; in the convergence stage, the non-dominated sorting genetic algorithm uses the eigenvalues of the high-fidelity model when evaluating the objective function; In each generation of the evolution process, based on the total constraint violation degree and the evaluation results of the objective function, the current population is non-dominantly sorted; in the convergence stage, the non-dominated sorting genetic algorithm processes the individuals that have been evaluated by the high-fidelity model and the individuals in the neighborhood that have not been evaluated as a high-priority population when sorting and selecting operations are performed; Based on the non-dominant sorting results, an elite reservation strategy is applied to select the next generation of parent population; the selected parent population is subjected to crossover operation and mutation operation to generate a new child population, and enters the next generation of iterative evaluation.

7. The method of claim 1, wherein, The specific way of processing the constraint violation individuals in the population includes: Before the selection operation of the population, the constraint dominance principle is applied to sort the individuals, and when the total constraint violation degrees of two individuals are not equal, the design scheme with lower total constraint violation degree is selected; a dynamic penalty function is introduced, taking the total constraint violation degree as input and combining the current optimization generation to calculate the dynamic penalty term; The dynamic penalty term is superimposed and calculated to the objective function value of the individual that violates the constraint to form a new objective function value; the objective function value corrected by the dynamic penalty and the total constraint violation degree are combined as the final evaluation basis of the individual in the selection operation.

8. A cable electrical performance simulation design system based on multi-objective optimization, characterized by, It includes: Model evaluation and fusion module: construct a low-fidelity model and a high-fidelity model for evaluating the electrical performance of the cable, and calculate the characteristic sensitivity of the cable design variables to the output results of the low-fidelity model and the high-fidelity model; According to the characteristic sensitivity, the evaluation characteristics of the low-fidelity model and the high-fidelity model are fused to obtain the objective function evaluation results of the current design scheme; Evolution selection module: initialize the design variable population and use the non-dominated sorting genetic algorithm; in the initial number of generations of optimization, the low-fidelity model is used for objective function evaluation; in the convergence stage of optimization, the individuals on the Pareto frontier are preferentially evaluated by the high-fidelity model; all individuals in the population are subjected to hierarchical non-dominant sorting, and in the convergence stage, the individuals evaluated by the high-fidelity model and the neighborhood solutions are treated as a higher priority population for selection operation; Hard constraint modeling module: model the hard constraints of the cable design; In the optimization process, the constraint violation individuals in the population are handled by the constraint dominance principle; a dynamic penalty function is introduced, and the penalty strength is dynamically adjusted according to the optimization algebra and the constraint violation degree, so as to ensure that the generated Pareto solution set is located in the feasible region. An output filtering module is configured to output a Pareto optimal solution set satisfying all hard constraints, and select an optimal design scheme from the Pareto optimal solution set according to a preset satisfaction function.

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