Electromagnetic induction ethylene cracking furnace heating section parameter multi-objective optimization method

Abstract

A multi-objective optimization method for heating section parameters of an electromagnetic induction ethylene cracking furnace belongs to the field of ethylene cracking furnace optimization technology. It includes: determining key structural and electrical parameters of the heating section as optimization variables and setting their value ranges to construct a multi-dimensional design variable space; generating an initial sample set and initializing the particle swarm optimization using Latin hypercube sampling; establishing an electromagnetic field-heat conduction coupled simulation model to calculate the Joule heat distribution and furnace tube temperature field under different parameter combinations; constructing a multi-objective evaluation function based on temperature uniformity, electromagnetic heat transfer efficiency, and coil loss; using a multi-objective particle swarm optimization algorithm combined with non-dominated sorting and external archive mechanisms for iterative search to form a Pareto optimal solution set; and selecting the final heating section design parameter scheme according to engineering requirements. This invention can achieve multi-parameter collaborative optimization, significantly improving heating uniformity and energy utilization efficiency.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic induction heating and process industrial optimization technology, and in particular to a method for optimizing the parameters of the heating section of an electromagnetic induction ethylene cracking furnace based on Latin hypercube sampling and multi-objective particle swarm optimization. This method is applicable to the synergistic optimization of the structural and operational parameters of the heating section of an electromagnetic induction ethylene cracking furnace. Background Technology

[0002] Ethylene cracking furnaces are core equipment in petrochemical plants, with their heating sections providing high-temperature heat energy for the cracking feedstock. Traditional ethylene cracking furnaces typically use gas or oil combustion for heating, which suffers from limited thermal efficiency, high carbon emissions, insufficient temperature control precision, and localized overheating of the furnace tubes. With the development of electrification technology and the utilization of green energy, electromagnetic induction heating has gradually been applied to the heating sections of cracking furnaces to achieve efficient, clean, and controllable heating.

[0003] In electromagnetic induction ethylene cracking furnaces, the heating effect is influenced by both coil structural parameters and electrical operating parameters. These parameters are significantly coupled, and their changes simultaneously affect the electromagnetic field distribution, eddy current losses within the furnace tube, and the temperature field distribution, thereby impacting heating uniformity, electromagnetic heat transfer efficiency, and the coil's own loss level. Therefore, rationally determining the heating section parameters is crucial for improving system operating efficiency and ensuring furnace tube safety.

[0004] In existing technologies, heating section parameters are typically selected based on experience or adjusted locally using single-objective optimization methods, making it difficult to simultaneously address multiple requirements such as temperature uniformity, energy utilization efficiency, and equipment operational safety. Furthermore, because the electromagnetic induction heating process involves multi-physics coupling behavior between the electromagnetic field and the temperature field, the parameter space has a high dimension and computational complexity. Traditional stochastic initialization optimization methods are prone to problems such as uneven sample distribution, slow convergence speed, or getting trapped in local optima.

[0005] Therefore, how to improve the efficiency of multi-objective optimization and obtain the optimal design scheme that takes into account multiple performance indicators while ensuring the uniformity of parameter space coverage has become an urgent technical problem to be solved in the design of the heating section of the electromagnetic induction ethylene cracking furnace. Summary of the Invention

[0006] The summary section introduces a series of simplified concepts, which will be further explained in detail in the detailed description section. The summary section of this invention is not intended to limit the key features and essential technical features of the claimed technical solution, nor is it intended to determine the scope of protection of the claimed technical solution.

[0007] To address the issue that existing electromagnetic induction ethylene cracking furnace heating section parameter design mainly relies on empirical selection or single-objective optimization methods, which make it difficult to simultaneously consider multiple performance indicators such as temperature uniformity, electromagnetic heat transfer efficiency, and coil losses, and also suffer from uneven sample distribution, low optimization efficiency, and susceptibility to local optima in high-dimensional parameter spaces, this invention, for the first time, combines Latin hypercube sampling with electromagnetic-thermal coupling simulation and multi-objective particle swarm optimization algorithm to construct a unified design framework suitable for the collaborative optimization of the heating section structure and operating parameters of electromagnetic induction ethylene cracking furnaces.

[0008] In view of the above-mentioned technical problems, the present invention adopts the following technical solution:

[0009] A multi-objective optimization method for the heating section parameters of an electromagnetic induction ethylene cracking furnace includes the following steps.

[0010] S1. Determine the structural and electrical parameters of the heating section of the electromagnetic induction ethylene cracking furnace as optimization variables, and set the value range of each optimization variable to construct a multi-dimensional design variable space; S2, an initial sample set is generated in the multidimensional design variable space using the Latin hypercube sampling method, and the particle swarm is initialized based on the initial sample set; S3. Establish a coupled simulation model of electromagnetic field and heat conduction, and calculate the Joule heat distribution and furnace tube temperature field corresponding to each combination of sample parameters. S4. Based on the furnace tube temperature distribution, electromagnetic heat transfer efficiency, and coil loss, a multi-objective function is constructed. S5, construct a multi-objective optimization model, update particle velocity and position based on non-dominated sorting and external archive mechanism, and perform iterative search; S6. Update the external archive based on the iteration results to obtain the Pareto optimal solution set; S7. Select the target heating section parameter scheme from the Pareto optimal solution set according to the engineering constraints.

[0011] Preferably, the design variables in step S1 include coil structure parameters and electrical operating parameters, forming a multi-dimensional design variable vector: ; Where N is the number of coil turns, d is the turn spacing, R is the coil winding radius, and D o D is the outer diameter of the furnace tube. i Let I be the inner diameter of the furnace tube, I be the amplitude of the excitation current, and f be the operating frequency. Each variable is set within a reasonable range based on engineering constraints, forming a multi-dimensional parameter design space.

[0012] Preferably, the Latin hypercube sampling in step S2 includes: dividing each design variable interval into m equally probable sub-intervals; randomly generating a normalized sample value in each sub-interval; randomly arranging and combining the sample values ​​of each dimension to form a unique parameter combination; and converting the normalized sample value into an actual physical parameter value through linear mapping.

[0013] Preferably, the multiphysics simulation model in step S3 is an electromagnetic field and heat conduction coupling model established based on the finite element method, used to calculate the Joule heat generated by electromagnetic induction and the temperature field distribution of the furnace tube. The simulation model can reflect the coupling relationship between the electromagnetic field and the temperature field, wherein the Joule loss obtained from the electromagnetic field calculation is loaded as a heat source term into the temperature field control equation to realize electromagnetic-thermal coupling calculation.

[0014] Preferably, in step S3, the temperature field distribution is achieved by uniformly arranging temperature sampling points along the axial and circumferential directions on the outer wall of the furnace tube to obtain furnace tube temperature data. Let the length of the furnace tube heating section be... The number of axial sampling points is The number of circumferential sampling points is The location of the temperature sampling point is

[0015] Axial position: ; Radial position: ;

[0016] Preferably, the temperature uniformity index, electromagnetic heat transfer efficiency index, and coil loss index mentioned in step S4 are all obtained by statistical analysis or extraction based on the calculation results of the coupled simulation model. A multi-objective function system is constructed based on the simulation results, and a multi-objective optimization model is built, including:

[0017] (1) Temperature uniformity index

[0018] The standard deviation of furnace tube surface temperature is used to express the following: ; Where Tᵢ is the temperature at the sampling point, and T̄ is the average temperature.

[0019] (2) Electromagnetic heat transfer efficiency index: ; Among them, P tube For the power absorbed by the furnace tube, P input This refers to the input electrical power.

[0020] (3) Coil loss index: ; (4) Construct a multi-objective optimization model: ; Where, x i To design the variable vector, x min As the lower bound of the design variable, x max The upper limit of the design variables is set. Since the temperature uniformity index and the coil loss index are expected to be minimized, while the electromagnetic heat transfer efficiency is expected to be maximized, in order to unify the optimization direction, the efficiency index is incorporated into the multi-objective minimization model after symbol transformation.

[0021] Preferably, the multi-objective optimization algorithm in step S5 is a multi-objective particle swarm optimization algorithm, and its particle velocity and position update process includes: ; Where ω is the inertia weight, c1 and c2 are learning factors, r1 and r2 are random factors, pbestᵢ is the particle's historical best position, and gbest is the guiding particle selected in the current non-dominated solution set.

[0022] Preferably, the termination condition in step S5 includes the number of iterations reaching a preset upper limit, or the external file changing less than a preset threshold within several consecutive generations.

[0023] Preferably, the non-dominated sorting in step S5 is as follows: when a solution is not inferior to another solution in all objective functions and is superior to the other solution in at least one objective function, the solution is determined to dominate the other solution; the solutions not dominated by any solution constitute the non-dominated solution set of the current generation.

[0024] Preferably, the external archive mechanism in step S5 is as follows: during the optimization process, an external storage structure independent of the particle swarm is set up to store the non-dominated solutions obtained in each iteration; after each generation of particles is updated, the non-dominated solutions in the current particle swarm are merged with the solutions in the external archive, and the merged solution set is filtered by non-dominated sorting to remove dominated solutions, thereby updating the non-dominated solution set in the external archive; when the capacity of the external archive exceeds a preset upper limit, the non-dominated solutions are filtered to maintain the size and distribution characteristics of the solution set.

[0025] Preferably, the step S6 of updating the external archive based on the iteration results means that after each iteration, the non-dominated solutions generated by the current particle swarm are merged with the historical non-dominated solutions in the external archive, and the merged solution set is filtered based on the non-dominated sorting to remove dominated solutions, thereby obtaining the updated external non-dominated solution archive; during multiple iterations, the non-dominated solutions in the external archive gradually accumulate and tend to stabilize, eventually forming the Pareto optimal solution set.

[0026] In summary, this invention establishes a mapping relationship between design variables and performance indicators by constructing an electromagnetic-thermal coupling simulation model, and obtains a Pareto solution set for the coordinated optimization of multiple performance indicators by combining a multi-objective optimization method, thereby achieving systematic optimization of the heating section parameters of an electromagnetic induction ethylene cracking furnace.

[0027] Compared with the prior art, the beneficial effects of this invention are:

[0028] This invention introduces the Latin hypercube sampling method to perform hierarchical random sampling of the multidimensional design variable space, so that the initial samples are uniformly distributed in the high-dimensional space. This overcomes the problems of sample aggregation and insufficient coverage in traditional random initialization methods, thereby improving the diversity of the initial population and enhancing the global search capability and convergence stability of the multi-objective optimization process.

[0029] This invention establishes a coupled simulation model of electromagnetic field and heat conduction, which quantitatively characterizes the influence of structural and electrical parameters on heating performance in the form of Joule heat distribution and temperature field. It realizes an accurate mapping between design parameters and performance indicators such as temperature uniformity, electromagnetic heat transfer efficiency and coil loss, thereby improving the physical reliability and engineering applicability of the optimization results.

[0030] This invention is based on a multi-objective particle swarm optimization method using non-dominated sorting and external archive mechanisms. It performs synergistic optimization of temperature uniformity, electromagnetic heat transfer efficiency, and coil loss, and can obtain the Pareto optimal solution set among multiple objectives. This achieves a reasonable trade-off between multiple performance indicators, thereby improving energy utilization efficiency and reducing coil loss while ensuring heating uniformity, and enhancing the overall operating performance of the system. Attached Figure Description

[0031] The following figures are included as part of this application for understanding the application. The figures illustrate embodiments of the application and their descriptions, serving to explain the apparatus and principles of the application. In the figures,

[0032] Figure 1 This is a schematic diagram of the overall process structure of the multi-objective optimization method for the heating section parameters of the electromagnetic induction ethylene cracking furnace described in this invention; Detailed Implementation

[0033] The following description provides numerous specific details to offer a more thorough understanding of this application. However, it will be apparent to those skilled in the art that this application can be practiced without one or more of these details. In other instances, certain technical features well-known in the art have not been described to avoid confusion with this application.

[0034] It should be understood that this application can be implemented in various forms and should not be construed as being limited to the embodiments set forth herein. Rather, providing these embodiments will make the disclosure thorough and complete, and will fully convey the scope of this application to those skilled in the art. In the drawings, for clarity, the dimensions and relative dimensions of layers and regions may be exaggerated. The same reference numerals denote the same elements throughout.

[0035] It should be understood that although the terms first, second, third, etc., may be used to describe various elements, components, areas, layers, and / or parts, these elements, components, areas, layers, and / or parts should not be limited by these terms. These terms are only used to distinguish one element, component, area, layer, or part from another element, component, area, layer, or part. Therefore, without departing from the teachings of this application, the first element, component, area, layer, or part discussed below may be referred to as the second element, component, area, layer, or part.

[0036] Spatial relation terms such as "below," "under," "below," "under," "above," and "above" are used here for convenience to describe the relationship between one element or feature shown in the figure and other elements or features. It should be understood that, in addition to the orientation shown in the figure, spatial relation terms are intended to also include different orientations of devices in use and operation.

[0037] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of this application. When used herein, the singular forms “a,” “an,” and “the” are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the terms “comprising” and / or “including,” when used in this specification, identify the presence of the stated features, integers, steps, operations, elements, and / or components, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups. When used herein, the term “and / or” includes any and all combinations of the associated listed items.

[0038] Embodiments of the invention are described herein with reference to cross-sectional views that serve as schematic diagrams of preferred embodiments (and intermediate structures) of this application. Thus, variations in the shown shape are contemplated due to, for example, manufacturing techniques and / or tolerances. Therefore, embodiments of this application should not be limited to the specific shapes shown herein, but include shape deviations due to, for example, manufacturing processes. Consequently, the figures are substantially schematic, and their shapes are not intended to show the actual shape of the device and are not intended to limit the scope of this application.

[0039] The present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Equivalent substitutions or modifications made by those skilled in the art without departing from the spirit of the present invention are all within the protection scope of the present invention.

[0040] The embodiments are described in detail below with reference to the accompanying drawings, such as... Figure 1 As shown, this application provides a multi-objective optimization method for the heating section parameters of an electromagnetic induction ethylene cracking furnace, wherein the method includes:

[0041] S1: Determine the structural and electrical parameters of the heating section of the electromagnetic induction ethylene cracking furnace as optimization variables, set the value range of each optimization variable, and construct a multi-dimensional design variable space.

[0042] Specifically, optimization variables refer to parameters that can be adjusted to improve system performance while ensuring the structural integrity and safe operation of the equipment. The variables involved in this invention include both electromagnetic excitation parameters such as current amplitude and frequency, and geometric structural parameters such as coil size and furnace tube size, which together determine the electromagnetic field distribution, induced current density, and heat generation and transfer processes. By synergistically optimizing these variables, an overall improvement in multiple performance indicators can be achieved.

[0043] Specifically, forming a multidimensional design variable space refers to selecting structural and operational parameters that significantly influence heating performance based on the electromagnetic-thermal coupling mechanism of the heating section of an electromagnetic induction ethylene cracking furnace. Under the premise of meeting equipment structural constraints, power supply capacity, and safe operating conditions, the upper and lower limits of each parameter's value are determined. When each variable has a definite value range, the combination of these ranges constitutes a multidimensional continuous design space, where any point corresponds to a complete combination of structural and operational parameters. Furthermore, this multidimensional design variable space provides the parameter distribution range for subsequent Latin hypercube sampling, provides the input variable set for electromagnetic-thermal coupling simulation, and serves as the search boundary and feasible region basis for the multi-objective particle swarm optimization algorithm, ensuring that the optimization process is carried out within the physically realizable range.

[0044] Execution Steps: This embodiment takes the heating section of an industrial-scale electromagnetic induction ethylene cracking furnace as the research object. By analyzing the electromagnetic induction heating mechanism and the operating requirements of the cracking furnace, structural parameters and operating parameters that significantly affect the heating performance are selected as optimization variables, and a seven-dimensional design variable vector is determined, including: the number of coil turns N, the turn spacing d, the coil winding radius R, and the furnace tube outer diameter D. o Furnace tube inner diameter D i Excitation current amplitude I, operating frequency f.

[0045] By combining the structural dimensions, power capacity, and material temperature resistance requirements of actual engineering equipment, reasonable value ranges are given for each optimization variable. The operating frequency is set to 5–50 kHz, the excitation current to 50–300 A, the coil winding radius to 80–150 mm, the turn spacing to 10–20 mm, the number of coil turns to 3000–4000, the furnace tube outer diameter to 40–50 mm, and the furnace tube inner diameter to 5–10 mm. The above variables and their upper and lower limits are further constructed into a seven-dimensional parameter space to establish a basic design domain for subsequent sampling and optimization calculations.

[0046] S2: An initial sample set is generated in the multidimensional design variable space using the Latin hypercube sampling method, and the particle swarm is initialized based on the initial sample set.

[0047] Specifically, Latin hypercube sampling is a stratified random sampling method. Its core idea is to perform equal-probability stratification within each dimension of the variable interval and ensure that each layer is sampled only once, thereby avoiding the clustering of samples in high-dimensional space and improving the uniformity and representativeness of the sample distribution.

[0048] Specifically, Latin hypercube sampling is employed before performing multi-objective particle swarm optimization on the induction heating parameters to obtain a uniformly distributed and representative initial sample set within the high-dimensional design variable space. Because the optimization variables involved in this invention have a high dimension and are coupled with each parameter, directly using random initialization of the particle swarm can easily lead to sample clustering in local regions or insufficient coverage of certain variable intervals, thereby reducing the algorithm's global search capability and increasing the risk of getting trapped in local optima. Latin hypercube sampling, while ensuring a limited number of samples, ensures uniform coverage of each variable interval, improving the diversity and spatial dispersion of the initial population. This provides a good initial distribution foundation for subsequent multi-objective particle swarm optimization, thereby enhancing the stability of the optimization process and the global optimization effect.

[0049] Execution steps: Divide the value range of each design variable into m sub-intervals (m=120 in this embodiment); randomly generate a sampling point in each sub-interval; randomly arrange and combine the m sampling points generated in each dimension to form a unique combination among the sampling points in each dimension; map the generated normalized samples to the actual value range of each design variable to obtain actual physical parameter samples; use the obtained sample matrix as the initial population of the multi-objective optimization algorithm.

[0050] In this embodiment, the specific application process of Latin hypercube sampling is illustrated using the operating frequency variable as an example. First, the actual operating frequency range of 5–50 kHz is normalized and mapped to the [0,1] interval. This normalized interval is then divided into 120 equal sub-intervals, each with a width of 1 / 120. For the k-th sub-interval, its range is [(k−1) / 120, k / 120]. Subsequently, a uniformly distributed random number u (0≤u≤1) is generated within this sub-interval, and a normalized sampled value is constructed. This ensures that only one random sample point is generated within each sub-interval, while maintaining the uniform distribution of samples within the interval. After random sampling of 120 sub-intervals, the resulting 120 normalized sample values ​​are randomly arranged to break the sequence correspondence between different variables. Finally, the normalized sample values ​​are converted into actual operating frequency values ​​through a linear mapping relationship. This yields 120 actual operating frequency samples that are evenly distributed and cover the entire frequency range. This method ensures that the operating frequencies achieve hierarchical and uniform coverage within the engineering feasible range, while maintaining randomness and sample independence. Furthermore, the remaining design variables are processed using the same hierarchical random generation and linear mapping method. Cross-dimensional combinations are achieved through independent random permutations of the sampling sequences of each variable, thus forming a parameter sample matrix covering the complete seven-dimensional design variable space, which is used for subsequent electromagnetic-thermal coupling simulation calculations and multi-objective particle swarm optimization search.

[0051] S3. Establish a coupled simulation model of electromagnetic field and heat conduction, and calculate the Joule heat distribution and furnace tube temperature field corresponding to each combination of sample parameters.

[0052] Specifically, the electromagnetic-thermal coupling simulation model is used to describe the energy transfer relationship between the electromagnetic field and the temperature field during electromagnetic induction heating. Under the action of an alternating magnetic field, an induced current is generated inside the furnace tube material. This current generates Joule heat due to the material's resistance, and this Joule heat acts as a heat source to drive changes in the temperature field. Therefore, by transforming the electromagnetic field solution into a heat source term and coupling it to the heat conduction control equation, a physical mapping relationship between design variables and heating performance indicators can be established, thereby achieving a quantitative characterization of the impact of parameter changes on temperature uniformity and energy utilization efficiency.

[0053] Specifically, the electromagnetic-thermal coupling simulation model is used not only to describe the energy conversion mechanism between the electromagnetic field and the temperature field, but also to establish a quantitative mapping relationship between design variables and performance indicators. This allows multidimensional parameter changes to be transformed into evaluable indicators such as temperature uniformity, electromagnetic heat transfer efficiency, and coil losses through numerical calculations. This mapping process achieves the transformation from "parameter space" to "performance space," providing a data foundation and evaluation basis for subsequent multi-objective function construction and particle swarm optimization search. It is a key supporting link in the entire optimization process.

[0054] Execution steps: By establishing a geometric model of the electromagnetic induction heating system, a three-dimensional or axisymmetric calculation structure is constructed, including the induction coil region, the furnace tube region, and the external air calculation domain. The corresponding structural dimension parameters are input, and corresponding material property parameters are assigned to each region. The coil region is assigned conductive material parameters, the furnace tube region is assigned conductive and thermal property parameters, and the air domain is assigned electrical insulation and low thermal conductivity parameters, thereby forming a complete electromagnetic-thermal coupling physical model.

[0055] By applying high-frequency alternating current excitation boundary conditions to the coil region and setting reasonable electromagnetic open or insulating boundary conditions, the distribution of alternating electromagnetic field is solved to obtain the magnetic induction intensity, current density, and Joule heat power density distribution. Then, the Joule heat power density generated in the furnace tube region is used as a volume heat source and applied to the heat conduction control equation. At the same time, convection and radiation heat transfer boundary conditions are set on the outer surface of the furnace tube, and fluid temperature or heat transfer boundary conditions are set inside the furnace tube to complete the coupled solution of the electromagnetic field and temperature field.

[0056] By performing steady-state or transient calculations, the overall temperature field distribution and power deposition of the furnace tube are obtained. Temperature data is extracted and the temperature standard deviation is calculated by equidistant sampling points on the outer surface of the furnace tube. At the same time, the Joule loss power of the coil and the input electrical power data are statistically analyzed to calculate the electromagnetic heat transfer efficiency, thereby obtaining the performance indicators required for multi-objective optimization.

[0057] S4. Based on the furnace tube temperature distribution, electromagnetic heat transfer efficiency, and coil loss, a multi-objective function is constructed.

[0058] Specifically, the multi-objective evaluation system is used to quantitatively characterize the comprehensive performance of the heating section of the electromagnetic induction ethylene cracking furnace. Its core lies in the coordinated evaluation of the system's operating status from three dimensions: heating uniformity, energy utilization efficiency, and system energy consumption level. Specifically, the standard deviation of the furnace tube's outer surface temperature reflects the temperature uniformity during the heating process; smaller temperature fluctuations indicate more uniform heating distribution, which is beneficial for the stable progress of the cracking reaction. The Joule loss power of the coil reflects the system's electrical energy loss level; a smaller value indicates more efficient energy utilization. The electromagnetic heat transfer efficiency characterizes the proportion of input electrical energy converted into effective thermal energy in the furnace tube, and is an important indicator for measuring energy utilization performance.

[0059] Because there are coupling and constraint relationships among the above indicators, for example, increasing the excitation current or frequency may improve the temperature distribution, but at the same time increase coil losses or reduce overall efficiency. Optimizing a single indicator often leads to the deterioration of other performance. Therefore, it is necessary to construct a multi-objective collaborative optimization model. By uniformly evaluating and weighing multiple performance indicators, a non-dominated solution set is formed, thereby achieving a reasonable balance between heating uniformity, efficiency and losses, and ensuring that the optimization results have engineering feasibility and comprehensive performance advantages.

[0060] Execution steps: Electromagnetic-thermal coupling simulation calculations were performed on each of the 120 sets of sample parameters obtained in step S2, extracting data on the temperature distribution of the furnace tube's outer surface, the power input, and the Joule loss power in the coil region. Statistical analysis was conducted on 30 uniformly distributed sampling points along the axial and circumferential directions of the furnace tube's outer surface to calculate the temperature uniformity index, with a standard deviation ranging from 8.6℃ to 19.4℃. Simultaneously, the effective heat absorption power and input power of the furnace tube under various operating conditions were statistically analyzed, calculating the electromagnetic heat transfer efficiency to be between 72.5% and 88.2%; the Joule loss power of the coil ranged from 12.8kW to 26.5kW. The above statistical results show that the three performance indicators fluctuate significantly under different parameter combinations. While some operating conditions exhibit high heat transfer efficiency, they also show poor temperature uniformity or high coil losses, indicating that the system performance exhibits multi-objective conflict characteristics, requiring comprehensive adjustment and balance through multi-objective optimization methods.

[0061] S5 constructs a multi-objective optimization model, updates particle velocity and position based on non-dominated sorting and external archive mechanism, and performs iterative search.

[0062] Specifically, the multi-objective particle swarm optimization model uses the initial sample set generated in step S2 as the initial position of the particle swarm. Each particle corresponds to a set of heating section structure and electrical parameter combinations, and its fitness value is determined by the multi-objective evaluation system constructed in step S4. The particles fly in a multi-dimensional design variable space, achieving a global search of the parameter space through the combined effect of their individual historical best position and the global guiding position. The model uses parameters such as population size, maximum number of iterations, and inertia weight as control variables, and continues to iterate and search until the termination condition is met.

[0063] Furthermore, a termination check structure is set up during the optimization process. After each generation of particles completes the velocity and position update and recalculates the fitness value, the current iteration number or the change in the objective function is checked. If the maximum number of iterations has not been reached or the solution set has not converged, the process returns to the update step to continue the iterative search. If the termination condition is met, the iteration stops, and the non-dominated solution set in the current external archive is output. Through this iterative loop mechanism, a gradual approximation search process of the parameter space is achieved.

[0064] The non-dominated ranking refers to classifying particles in a population according to the dominance relationships among multiple objectives. A particle is considered to dominate another particle if it is not inferior to it in all objective metrics and is superior to it in at least one objective. By comparing the dominance relationships among all particles, individuals not dominated by any particle are classified into the first tier, and the remaining particles form the second and subsequent tiers. Non-dominated ranking is used to identify high-quality solutions in the current population and provides a basis for updating external archives.

[0065] The external archive mechanism is used to store the set of non-dominated solutions generated during each iteration. After each iteration, the non-dominated solutions in the current population are merged with the historical solutions in the archive, and the dominance relationship is screened again to remove dominated solutions. The size of the archive is controlled according to the uniformity of solution distribution to prevent the solution set from becoming overly concentrated or growing indefinitely. Through continuous updates to the external archive, it is ensured that excellent solutions obtained during optimization are not lost due to population updates, while improving the stability and diversity of the Pareto solution set.

[0066] Execution steps: Using the sample parameters generated in step S2 as the initial positions of the particle swarm, the particle swarm size is set to 60, the maximum number of iterations to 120, the external archive capacity to 40, the initial inertia weight to 0.9 which gradually decreases with iteration, and both the individual learning factor and the global learning factor to 1.8. The velocity vectors and individual historical best positions of each particle are initialized. In each iteration, based on the multi-objective evaluation index values ​​calculated in S4, the current particle swarm is non-dominated and sorted to determine the dominance level of each particle, and the individual historical best solutions and the global guiding particles in the external archive are updated.

[0067] By updating the particle velocity and position based on the current optimal position of the individual and the guiding particles selected from the external archive, and performing boundary correction processing on particles that exceed the range of variable values, it is ensured that all parameters are always within the preset engineering design domain. After the update is completed, electromagnetic-thermal coupling simulation calculation and objective function evaluation are performed again to obtain the fitness value of the new generation of particle swarm.

[0068] After each iteration, it is determined whether the current iteration count has reached the set upper limit, or whether the change in the non-dominated solution set in the external archive is less than the preset threshold within several consecutive iterations. If the termination condition is not met, the process returns to the particle update step to continue iterative search; if the termination condition is met, the iteration process stops, the non-dominated solution set saved in the external archive is output, and the process proceeds to the next step for Pareto solution set analysis.

[0069] S6. Update the external archive based on the iteration results to obtain the Pareto optimal solution set.

[0070] Specifically, the Pareto optimal solution set refers to the set of non-dominated solutions formed during multi-objective optimization. Any set of parameter solutions in this set is superior to other solutions in at least one objective index, and is not inferior to the corresponding solutions in the remaining objectives, thus avoiding a situation where it is comprehensively superior to other solutions. The Pareto optimal solution set reflects the trade-off between temperature uniformity, electromagnetic heat transfer efficiency, and coil losses, and is the optimal compromise solution set for the multi-objective optimization problem within the current design space.

[0071] During the iteration process in step S5, the external archive continuously stores the non-dominated solutions generated in each iteration. When the termination condition is met, a final dominance relationship screening and duplicate solution removal are performed on the solutions in the external archive. The solutions are then organized according to their distribution in the target space to form a stable Pareto optimal solution set. Each parameter combination in this solution set corresponds to a different performance emphasis; for example, some solutions are biased towards improving temperature uniformity, while others are biased towards reducing coil losses, or a relatively balanced state is achieved among the three indicators. By forming the Pareto optimal solution set, the search for a single optimal solution is transformed into a multi-scheme compromise optimization, providing multiple optional design schemes for engineering applications.

[0072] Execution steps: After the iteration terminates in step five, all non-dominated solutions saved in the external archive are read, uniformly organized and statistically analyzed, and duplicate or boundary outliers are removed to obtain the final Pareto optimal solution set. In this embodiment, under the conditions of a particle swarm size of 60 and a maximum number of iterations of 120, 32 sets of non-dominated parameter combinations are finally obtained; the corresponding temperature standard deviation distribution range is 6.3℃~9.8℃, the electromagnetic heat transfer efficiency distribution range is 84.1%~91.6%, and the coil Joule loss power distribution range is 14.2kW~19.7kW.

[0073] Comparative analysis of the performance indicators in the Pareto solution set reveals that when the temperature standard deviation decreases to around 6.3℃, the coil loss increases slightly; and when the heat transfer efficiency increases to over 84%, the temperature uniformity index fluctuates slightly, indicating a clear trade-off between the various performance objectives. By forming this optimal Pareto solution set, coordinated optimization among multiple performance objectives is achieved, providing a variety of feasible design parameter combinations for subsequent engineering scheme selection.

[0074] S7. Select the target heating section parameter scheme from the Pareto optimal solution set according to the engineering constraints.

[0075] Specifically, since the various parameter sets in the Pareto solution set represent different trade-offs among multiple objectives, the final selection must be made in conjunction with the engineering priorities. For example, when temperature uniformity is a priority, the parameter combination with the smallest temperature standard deviation can be selected; when energy-saving operation is a priority, a combination with higher heat transfer efficiency and lower coil loss can be selected; alternatively, a weighted scoring method can be used to comprehensively rank the multiple objective indicators to determine the final design scheme.

[0076] Execution steps: Based on the actual operating requirements of the pyrolysis furnace, this embodiment selects a combination of parameters with a temperature standard deviation of 7.4℃, a heat transfer efficiency of 89.2%, and a coil loss of 16.8kW as the final heating section design parameters. The corresponding operating frequency is 32kHz, the excitation current is 210A, and the number of coil turns is 3600. Other structural parameters are determined simultaneously for subsequent engineering implementation.

[0077] In summary, the beneficial effects of the embodiments of this application are:

[0078] By constructing a multidimensional design variable space and introducing the Latin hypercube sampling method, uniform coverage and efficient initialization of key structural and electrical parameters of the heating section of an electromagnetic induction ethylene cracking furnace are achieved. An electromagnetic-thermal coupling simulation model is established to achieve quantitative mapping between design parameters and performance indicators such as temperature uniformity, electromagnetic heat transfer efficiency, and coil losses. Furthermore, a multi-objective particle swarm optimization algorithm combining non-dominated sorting and external archive mechanisms is used to enhance global search capabilities while ensuring solution set diversity, forming a stable Pareto optimal solution set, and selecting the optimal compromise solution based on engineering requirements. This method can effectively improve heating uniformity and energy utilization efficiency, reduce coil losses, and enhance the systematicness and controllability of the design process, demonstrating significant engineering application value and promotion potential.

[0079] Although exemplary embodiments have been described herein with reference to the accompanying drawings, it should be understood that the above exemplary embodiments are merely illustrative and are not intended to limit the scope of this application. Various changes and modifications can be made therein by those skilled in the art without departing from the scope and spirit of this application. All such changes and modifications are intended to be included within the scope of this application as claimed in the appended claims.

[0080] Numerous specific details are set forth in the specification provided herein. However, it will be understood that embodiments of this application may be practiced without these specific details. In some instances, well-known methods, structures, and techniques have not been shown in detail so as not to obscure the understanding of this specification.

[0081] Similarly, it should be understood that, in order to streamline this application and aid in understanding one or more of the various inventive aspects, features of this application may sometimes be grouped together in a single embodiment, figure, or description thereof in the description of exemplary embodiments of this application. However, this approach should not be construed as reflecting an intention that the claimed application requires more features than are expressly recited in each claim. Rather, as reflected in the corresponding claims, its inventive point lies in solving the corresponding technical problem with features fewer than all features of a single disclosed embodiment. Therefore, the claims following the detailed description are hereby expressly incorporated into that detailed description, wherein each claim itself is a separate embodiment of this application.

[0082] Those skilled in the art will understand that, apart from the mutual exclusion of features, all features disclosed in this specification (including the accompanying claims, abstract, and drawings) and all processes or units of any method or apparatus so disclosed can be combined in any combination. Unless otherwise expressly stated, each feature disclosed in this specification (including the accompanying claims, abstract, and drawings) may be replaced by an alternative feature serving the same, equivalent, or similar purpose.

[0083] Furthermore, those skilled in the art will understand that although some embodiments described herein include certain features but not others included in other embodiments, combinations of features from different embodiments are intended to be within the scope of this application and form different embodiments. For example, in the claims, any one of the claimed embodiments can be used in any combination.

[0084] It should be noted that the above embodiments are illustrative of this application and not restrictive of this application, and that those skilled in the art can devise alternative embodiments without departing from the scope of the appended claims.

Claims

1. A multi-objective optimization method for heating section parameters of an electromagnetic induction ethylene cracking furnace, characterized in that, Includes the following steps: S1. Determine the structural and electrical parameters of the heating section of the electromagnetic induction ethylene cracking furnace as optimization variables, and set the value range of each optimization variable to construct a multi-dimensional design variable space; S2, an initial sample set is generated in the multidimensional design variable space using the Latin hypercube sampling method, and the particle swarm is initialized based on the initial sample set; S3. Establish a coupled simulation model of electromagnetic field and heat conduction, and calculate the Joule heat distribution and furnace tube temperature field corresponding to each combination of sample parameters. S4. Based on the furnace tube temperature distribution, electromagnetic heat transfer efficiency, and coil loss, a multi-objective function is constructed. S5, construct a multi-objective optimization model, update particle velocity and position based on non-dominated sorting and external archive mechanism, and perform iterative search; S6. Update the external archive based on the iteration results to obtain the Pareto optimal solution set; S7. Select the target heating section parameter scheme from the Pareto optimal solution set according to the engineering constraints.

2. The method according to claim 1, characterized in that, The design variables mentioned in step S1 include: operating frequency, excitation current, coil winding radius, turn spacing, number of coil turns, furnace tube outer diameter, and furnace tube inner diameter.

3. The method according to claim 1, characterized in that, The multiphysics simulation model mentioned in step S3 is an electromagnetic field and heat conduction coupled model established based on the finite element method, which is used to calculate the Joule heat generated by electromagnetic induction and the temperature field distribution of the furnace tube.

4. The method according to claim 4, characterized in that, Temperature sampling points are evenly arranged along the axial and circumferential directions on the outer wall of the furnace tube to obtain furnace tube temperature data; assuming the length of the furnace tube heating section is... The number of axial sampling points is The number of circumferential sampling points is The location of the temperature sampling point is Axial position: ； Radial position:

5. The method according to claim 1, characterized in that, The multi-objective function mentioned in step S4 includes: (1) Temperature uniformity index: Calculated using the standard deviation of temperature at sampling points on the outer surface of the furnace tube: ； Where Tᵢ is the temperature at the sampling point, and T̄ is the average temperature; (2) Electromagnetic heat transfer efficiency index: ； where P tube is the absorbed power by the furnace tubes, P input is the input electric power; (3) Coil loss index 。 6. The method according to claim 1, characterized in that, The multi-objective evaluation system mentioned in step S4 includes: ； Where, x i To design the variable vector, x min As the lower bound of the design variable, x max The upper limit of the design variables is defined as follows: the temperature uniformity index and the coil loss index are minimized, and the electromagnetic heat transfer efficiency is maximized. These are transformed into minimized objectives through symbol conversion.

7. The method according to claim 1, characterized in that, The multi-objective optimization algorithm mentioned in step S5 is a multi-objective particle swarm optimization algorithm, and the termination conditions include: reaching a preset maximum number of iterations or the Pareto solution set change rate being less than a preset threshold.

8. The method according to claim 1, characterized in that, The method is used for optimizing the structural parameters and power matching of the heating section of an electromagnetic induction ethylene cracking furnace.

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