Intelligent optimization design method for barrel welding flanging structure
By using parametric finite element analysis and intelligent optimization algorithms, an optimized design method for cylindrical welded flange structures is constructed, which solves the problems of inaccurate design and material waste in existing technologies, and achieves efficient and safe design optimization.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-08
- Publication Date
- 2026-03-17
AI Technical Summary
In existing technologies, the design of cylindrical welded flange structures relies on experience and simplified formulas, resulting in inaccurate design, material waste, and low design efficiency. Furthermore, it lacks scientific basis and is difficult to cope with new materials and complex load conditions.
A parametric finite element analysis model combined with intelligent optimization algorithms is used to construct a comprehensive optimization objective function. The optimal curl radius is automatically searched through intelligent optimization algorithms such as genetic algorithms, and an explicit empirical formula is established by combining machine learning to achieve precise design.
This has enabled a paradigm shift from experience-based design to simulation-driven design, improving design accuracy and safety, reducing material waste, and enhancing design efficiency and economy.
Smart Images
Figure CN121683113A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of mechanical engineering structural design and optimization technology, and more specifically, to an intelligent optimization design method for a cylindrical welded flange structure. Background Technology
[0002] Cylindrical pressure vessels and storage tanks (hereinafter referred to as "cylindrical tanks") are widely used critical equipment. The connection between their bottom and the flat bottom plate is usually a welded structure. This joint bears internal pressure, external loads, and cyclic stress, making it a weak point in structural integrity. Traditional straight-edge end-to-end welding suffers from severe stress concentration, easily leading to fatigue cracks under alternating loads, resulting in sealing failure and media leakage, and causing safety accidents. To improve joint strength, engineering commonly adopts a structure where the bottom of the tank is rolled outwards before welding to the bottom plate. This rolled-out design effectively reduces stress concentration and improves the stress state by increasing the weld contact area and forming a ring-shaped reinforcing ring. However, currently, the determination of the rolled-out dimensions (especially the radius) mainly relies on engineers' experience, industry practices, or simplified empirical formulas. Designers usually select based on analogy, referring to similar products, or using rough guidelines such as "the rolled-out height is generally 2-3 times the plate thickness." This design method has significant drawbacks: First, it is highly dependent on experience and lacks universal scientific basis. For new materials, non-standard dimensions, or complex load conditions, experience may be completely ineffective. Secondly, conservative design tends to lead to material waste and poor economic efficiency. To avoid risks, designers often opt for larger flange dimensions, increasing unnecessary material and manufacturing costs. Furthermore, the design process is disconnected from performance verification. After determining the dimensions, complex finite element analysis or experiments are required to verify whether they meet strength and lifespan requirements. If not, redesign is necessary, creating an iterative cycle of "design-verification-modification," which is inefficient. Summary of the Invention
[0003] The purpose of this invention is to provide an intelligent optimization design method for a cylindrical welded flange structure, in order to solve the above-mentioned problems existing in the prior art.
[0004] The application is as follows: This invention provides an intelligent optimization design method for a cylindrical welded flange structure, comprising the following steps: S1: Determine the optimization target parameter, input parameters, and design criteria. The optimization target parameter is the curling radius R to be determined. The input parameters include geometric material parameters consisting of barrel thickness TH, diameter D, height H, material elastic modulus E, and yield strength σ_y, and a set of load parameters consisting of the load conditions acting on the barrel. The design criteria include a safety factor S for static strength assessment, a target fatigue life N for fatigue assessment, and a process-feasible value range [R_min, R_max] for the curling radius R. S2: Construct a parametric finite element analysis model. The input of the model includes the geometric material parameters, load parameters, and candidate curling radius values R_candidate. Perform calculation and analysis, and output the mechanical response index at the weld joint. The mechanical response index includes at least the maximum equivalent stress σ_max at the weld and the number of fatigue life cycles N_actual. S3: Construct a comprehensive optimization objective function F(R) to quantitatively evaluate the merits of candidate designs R_candidate. The smaller the function value, the better the design. The construction of the comprehensive optimization objective function F(R) satisfies the following: its value increases with the increase of the output index σ_max and decreases with the increase of the output index N_actual. Furthermore, when R_candidate exceeds the range of [R_min, R_max], or σ_max exceeds the allowable stress σ_y / S, or N_actual is lower than N, the function value is significantly penalized and increases. S4: Call the intelligent optimization algorithm, using the comprehensive optimization objective function F(R) as the fitness evaluation basis, and automatically search and output the curling radius that minimizes the value of F(R) during the iteration process, as the optimal curling radius R_opt.
[0005] Furthermore, in step S1, the load condition includes one or more of internal pressure P, bending moment M, axial force F, and torque T.
[0006] Furthermore, in step S3, the comprehensive optimization objective function F(R) is expressed as the sum of performance evaluation terms and constraint penalty terms, and its specific form is as follows:
[0007] in, and p(R) is a non-negative weighting coefficient set according to the design focus, and p(R) is a constraint penalty function.
[0008] Furthermore, the constraint penalty function P(R) is used to penalize designs that violate the design criteria described in step S1, and its expression includes the following penalty terms: a penalty term for violating R_min≤R≤R_max; a penalty term for violating σ_max≤σ_y / S; and a penalty term for violating N_actual≥N.
[0009] Furthermore, a specific expression for the constraint penalty function P(R) is as follows: P(R)=λ_1*max(0,σ_max-σ_y / S)^2+λ_2*max(0,N-N_actual)^2+λ_3*max(0,R_min-R)^2+λ_4*max(0,R-R_max)^2 Among them, λ_1, λ_2, λ_3, and λ_4 are extremely large positive penalty coefficients.
[0010] Furthermore, in step S4, the intelligent optimization algorithm is one of a genetic algorithm, a particle swarm optimization algorithm, or a simulated annealing algorithm.
[0011] Furthermore, step S5 is also included: based on multiple sets of different input parameter combinations obtained through S1-S4 and the corresponding optimal curl radius R_opt, a prediction model that can directly output the recommended curl radius R_rec is trained through machine learning regression analysis; wherein, when executing S5, the multiple sets of data are divided into training set and test set, the prediction model is obtained by using the training set for regression analysis, and the prediction accuracy of the model is verified by using the test set.
[0012] Furthermore, the prediction model is an explicit empirical formula, which is expressed in dimensionless form as follows:
[0013] Where C0, C1, C2, C3, C4, and C5 are constants determined through fitting. It is a dimensionless function related to the load parameter set L and the material yield strength σ_y; φ(N) is a dimensionless function constructed based on the target fatigue life N.
[0014] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the intelligent optimization design method for the cylindrical welded flange structure described in the above embodiments.
[0015] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the intelligent optimization design method for the cylindrical welded flange structure described in the above embodiments.
[0016] Compared with the prior art, the embodiments of the present invention achieve the following beneficial effects: This invention represents a paradigm shift from experience-based design to simulation-driven, globally automated optimization, balancing design accuracy, safety, and economy. It breaks away from design methods reliant on analogy and rough experience, automatically searching for the global optimum under multiple objectives (static strength, fatigue life) and constraints (process boundaries, strength and life limits). This allows design decisions to be based on precise mechanical simulation and mathematical optimization, rather than subjective experience. Thus, while ensuring structural safety, the optimization algorithm automatically avoids overly conservative designs, achieving an optimal balance between safety, durability, and material economy.
[0017] This invention transforms complex simulation optimization processes into efficient and easy-to-use engineering design knowledge, significantly improving design efficiency. It utilizes machine learning methods to extract explicit, experience-based guiding formulas from numerous optimization results for various operating conditions. When designing new products, there's no need to repeatedly run time-consuming simulation optimization processes; simply substituting basic parameters into the formula instantly yields a scientific and reliable initial design value. This shortens the design cycle from days or even weeks to minutes, enabling the effective accumulation, efficient reuse, and rapid transfer of design knowledge. Attached Figure Description
[0018] Figure 1 This is a flowchart illustrating the intelligent optimization design method for the cylindrical welding flange structure provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the cylindrical flange structure provided in an embodiment of the present invention. Detailed Implementation
[0019] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments given herein are for illustration and explanation only and are not intended to limit the present invention.
[0020] It should be noted that many specific details are set forth in the following description in order to provide a full understanding of the present invention. However, the present invention may have other embodiments, and therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.
[0021] Example 1
[0022] See attached document Figure 1-2 As shown in the figure, the intelligent optimization design method for a cylindrical welded flange structure provided in this embodiment includes the following steps: S1 Determine the optimization target parameters, input parameters, and constraints: This step aims to define clear design goals and boundaries for the entire optimization process. For a cylindrical welded structure to be designed, the core optimization target parameter is the flange radius R to be determined.
[0023] Input parameters include geometric and material parameters and load parameters. The geometric and material parameters define the structure's inherent physical properties and are intrinsic determinants of its mechanical response. These include at least the barrel diameter D, barrel height H, and wall thickness TH. Material parameters include at least the elastic modulus E for calculating elastic deformation, the yield strength σ_y for evaluating strength, and material fatigue performance curves or related parameters for fatigue life assessment. The load parameter set defines the external forces acting on the structure, serving as the external excitation for the mechanical response. Depending on the actual operating conditions, the loads may include, but are not limited to, uniform internal pressure P, bending moment M acting on the barrel, axial force F, or torque T.
[0024] Design criteria include a safety factor S for static strength assessment and a target fatigue life cycle number N for fatigue assessment. The process-feasible range of the crimp radius R is [R_min, R_max], where R_min is usually determined by the minimum bending radius of the material, and R_max is determined by structural space, material cost, or process equipment limitations.
[0025] S2 Constructing a Parametric Finite Element Analysis Model: This step aims to establish a digital simulation model capable of automatically and accurately evaluating the structural performance corresponding to any given curl radius R. The key to this model lies in its parametric nature, meaning it can automatically complete the entire modeling and analysis process based on input parameters. The model's input consists of all the input parameters determined in step S1 and a specific candidate value for the curl radius R_candidate. In the computer system, this model automatically performs the following core operations: Geometric modeling and parameter-driven: Based on the input D, H, TH and the current R_candidate, automatically generate a 3D or 2D axisymmetric geometric model of the barrel body and base plate with flange features. The geometry is automatically updated when R_candidate changes.
[0026] Material Assignment and Mesh Generation: Assign material properties to the model defined by E and σ_y, etc. Refine the mesh in and around the weld joint to ensure accurate capture of stress concentration effects at that location.
[0027] Load and boundary condition application: Based on the input load parameter set L (such as P, M, etc.), the corresponding loads are applied to the model (e.g., applying pressure P to the inner wall of the barrel). At the same time, boundary conditions that conform to the actual constraints are applied (e.g., fixing the bottom plate).
[0028] Solution and Result Extraction: Finite element statics solution is performed. After calculation, the model automatically extracts the mechanical response data of key components from the result file as output. These outputs include at least: the maximum equivalent stress σ_max at the critical point of the weld, and the estimated fatigue life cycle number N_actual calculated based on the stress spectrum and material fatigue performance data (such as SN curve) at that point. This model is equivalent to a "virtual performance testing machine," providing fast and accurate performance predictions for each design draft.
[0029] S3. Constructing the Optimization Objective Function: This step aims to define a mathematical criterion that can comprehensively and quantitatively evaluate the merits of different designs. This function needs to comprehensively reflect the degree to which the design meets the design criteria described in S1; the smaller the value F(R), the better the design. The constructed comprehensive optimization objective function F(R) is as follows:
[0030] Where: σ_max / (σ_y / S) is the stress ratio term, a value greater than 1 indicates that the static strength requirement is not met, and a smaller value indicates a higher safety margin; N / N_actual is the life ratio term, a value greater than 1 indicates that the fatigue life requirement is not met, and a smaller value indicates a more abundant life margin; ω_1 and ω_2 are weighting coefficients, satisfying ω_1+ω_2=1. Their values reflect the different emphases on static strength safety and fatigue life durability in the design. P(R) is the constraint penalty function, used to severely penalize design schemes that violate the design criteria described in step S1. Specifically, P(R) applies penalties for the following three types of criterion violations: Penalty terms for violating R_min≤R≤R_max; penalty terms for violating σ_max≤σ_y / S; penalty terms for violating N_actual≥N.
[0031] A specific expression for P(R) is: P(R)=λ_1*max(0,σ_max-σ_y / S)^2+λ_2*max(0,N-N_actual)^2+λ_3*max(0,R_min-R)^2+λ_4*max(0,R-R_max)^2 Where λ_1, λ_2, λ_3, and λ_4 are extremely large positive penalty coefficients. Any design that violates the constraints will cause F(R) to increase sharply, thus being eliminated in the optimization process.
[0032] The value F(R) comprehensively reflects the degree of deviation of the design scheme from the minimum requirements in terms of strength and lifespan. Therefore, the goal of the optimization problem is to find the design scheme that minimizes the objective function value F(R) by adjusting the design variable R, that is, to seek the best balance between safety and economy.
[0033] S4 invokes the intelligent optimization algorithm: This step performs iterative optimization, aiming to automatically and efficiently search for the optimal solution using an intelligent algorithm. The parameterized model S2 serves as the performance evaluator, and the objective function S3 is used as the evaluation criterion, driving the design variable R towards its optimal value. This embodiment uses a genetic algorithm as an example. The algorithm first randomly initializes a population consisting of multiple potential solutions (called "individuals") within the feasible design space of R. Then, it enters an iterative loop: Analysis and Evaluation: The R value represented by each individual in the current population is passed as input to the parameterized finite element model in step S2. The model calculates and returns the corresponding (σ_max, N_actual).
[0034] Fitness Calculation: Substitute the performance metrics obtained in the previous step into the objective function formula of step S3 to calculate the F(R) value for each individual. Genetic algorithms typically seek to maximize "fitness," so fitness can be defined as Fitness = 1 / (1 + F(R)), where a smaller F(R) results in a higher fitness. The introduction of the penalty function P(R) ensures that individuals violating the constraints have extremely low fitness, thus being naturally eliminated during evolution.
[0035] Evolutionary operations: Based on fitness, genetic operations such as selection, crossover, and mutation are performed. Individuals with higher fitness have a higher probability of being selected to participate in the generation of the next generation; selected individuals exchange some information through the "crossover" operation and introduce random, minute changes through the "mutation" operation. These operations together produce a new generation of the population.
[0036] Convergence check: Repeat steps 1 to 3, and the average fitness of the population will increase generation by generation. The algorithm terminates when the fitness of the best individual no longer improves significantly over several consecutive generations, or when the preset maximum number of iterations is reached.
[0037] When the algorithm terminates, the R value corresponding to the individual with the highest fitness in the current population is output as the optimal curl radius R_opt that satisfies all constraints and optimizes the objective function. This method effectively avoids getting trapped in local optima, thus finding a globally or near-globally optimal design.
[0038] In addition to genetic algorithms, those skilled in the art may also choose other intelligent optimization algorithms, such as particle swarm optimization and simulated annealing, the core of which lies in driving the parameterized model and the objective function to perform iterative optimization.
[0039] Example 2
[0040] Example 1 provides an optimization design method for a specific design. To achieve the accumulation and reuse of design knowledge, this example, based on Example 1, performs step S5 to extract a universally applicable explicit empirical formula from a large number of optimization cases through systematic data accumulation and machine learning. This formula will serve as a direct tool for rapid design.
[0041] This step aims to obtain the data foundation for analysis. Within the parameter system framework defined in step S1 of Example 1, a large number of different design conditions are systematically constructed by changing the values of key design variables. Specifically, experimental design methods such as Latin hypercube sampling are used to generate M different combinations of input parameters within the range of common engineering parameters. Each set of parameters includes a complete set of geometric material parameters, load parameters, and durability parameters. For each of these M sets of parameters, it is treated as an independent design task, and steps S1 to S4 as detailed in Example 1 are executed completely once. That is, for each set of inputs, an intelligent optimization process is run, and the corresponding optimal helix radius R_opt is finally output. Thus, we obtain a structured dataset in which each record is precisely associated with a set of design conditions {D,H,TH,E,σ_y,L,S,N} and its corresponding optimal solution R_opt.
[0042] To facilitate effective model training and validation, the generated M datasets are randomly divided into two parts, for example, 80% as the training set and 20% as the test set. The training set is used for regression fitting, and the test set is used to evaluate the predictive performance of the formula. The training set is preprocessed and features are constructed in preparation for regression analysis. Directly fitting the raw data with dimensions makes it difficult to obtain a model with clear physical meaning and strong generalization ability. Therefore, based on dimensional analysis and engineering principles, suitable dimensionless features are constructed, transforming the optimization objective R_opt and the main influencing factors into the following dimensionless parameters: Target variable: Input features: diameter-to-thickness ratio D / TH, height-to-diameter ratio H / D, safety factor S (which is itself a dimensionless number).
[0043] Dimensionless functions related to load and material strength The specific form of this function term depends on the principal components of the load parameter set L. In the most common case, when the load is dominated by internal pressure P, this term can be taken as (P / σ_y). For other load types (such as bending moment M, axial force F, torque T, or combinations thereof), corresponding dimensionless combinations can be constructed based on the mechanical effects of the load. For example, for bending moment, it can be constructed as (M / (σ_y*TH*D²)); for combined loads, it can be constructed as a dimensionless term based on equivalent stress (σ_eq / σ_y), where σ_eq is the stress level calculated from L.
[0044] Since the target fatigue life N is a dimensional quantity, a dimensionless function φ(N) needs to be constructed to characterize its influence. Its construction is based on the fundamental principles of fatigue mechanics, namely, the power-law relationship (SN curve) between stress level and the number of failure cycles. This can be expressed as:
[0045] Wherein, N_ref is a preset reference life value, and k is a constant related to the fatigue performance of the material, which can be determined based on the negative slope of the standard SN curve of the material in a double logarithmic coordinate system.
[0046] Subsequently, the specific mathematical form of the mapping function is determined and fitted. Based on engineering experience, a preferred model form is the power model. This model is directly expressed in the dimensionless form described in the claims, i.e., it seeks the following relationship:
[0047] To determine these coefficients from the training set data, a multiple linear regression method based on logarithmic transformation is used. Taking the natural logarithm of both sides of the above model equation linearizes it: =
[0048] Let Y=ln(R_opt / TH), X1=ln(D / TH), X2=ln(H / D), X3=ln( X4=ln(S), X5=ln(φ(N)), β0=ln(C0), then the above formula is transformed into a standard multiple linear regression model:
[0049] The algorithm's input is the entire dataset {X1,X2,X3,X4,X5,Y} after the aforementioned transformation. The core process involves applying the least squares method to fit the optimal linear hyperplane, thus obtaining the best estimates for all coefficients β0, C1, C2, C3, C4, and C5 in one step. Then, the coefficients of the original model are obtained through the inverse transformation C0 = exp(β0). Finally, a definite empirical formula is output. Substituting the fitted coefficients back into the original power model yields a completely definite explicit empirical guiding formula:
[0050] To verify the accuracy and generalization ability of the formula, a reserved test set was used for evaluation. The design parameters {TH,D,H,L,σ_y,S,N} of each data set in the test set were substituted into the empirical formula to calculate the predicted recommended radius R. This predicted radius R was then compared with the actual optimized value R_opt corresponding to the test set, and indices such as mean relative error and root mean square error were calculated. Typically, within a reasonable parameter range, the mean relative error of this empirical formula can be controlled within an engineering-acceptable range (e.g., within ±5%), thus verifying its effectiveness. Therefore, when facing new design tasks, there is no need to repeat the complex optimization process; simply substituting the design parameters TH,D,H,L,σ_y,S,N into this empirical formula directly yields a scientifically reliable initial recommended value R for the curl radius.
[0051] Numerous specific details are set forth in the specification provided herein. However, it will be understood that embodiments of the invention 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.
[0052] Furthermore, those skilled in the art will understand that although some embodiments herein include certain features included in other embodiments but not others, combinations of features from different embodiments are intended to be within the scope of the invention and form different embodiments. Any of the claimed embodiments can be used in any combination.
Claims
1. An intelligent optimization design method for a barrel welded flange structure, characterized in that, The method comprises the following steps: S1: determining optimization target parameters, input parameters and design criteria, the optimization target parameters being a to-be-solved hemming radius R, the input parameters including geometric material parameters composed of a barrel body thickness TH, a diameter D, a height H, a material elastic modulus E and a yield strength σ_y, a load parameter set L composed of load working conditions acting on the barrel body, and the design criteria including a safety factor S for static strength evaluation, a target fatigue life N for fatigue evaluation, and a process feasible value range [R_min, R_max] of the hemming radius R; S2: constructing a parameterized finite element analysis model, the input of the model including the geometric material parameters, the load parameters and a candidate hemming radius value R_candidate, performing calculation and analysis, and outputting mechanical response indexes at the welded joint, the mechanical response indexes at least including a maximum equivalent stress σ_max at the welded joint and a fatigue life cycle number N_actual; S3: constructing a comprehensive optimization objective function F(R) for quantitatively evaluating the pros and cons of the candidate design R_candidate, and the smaller the function value is, the better the design is; the construction of the comprehensive optimization objective function F(R) satisfies that the value thereof increases with the increase of the output index σ_max and decreases with the increase of the output index N_actual, and when R_candidate exceeds the range [R_min, R_max], or σ_max exceeds the allowable stress σ_y / S, or N_actual is lower than N, the function value is significantly punished and increases; S4: calling an intelligent optimization algorithm, taking the comprehensive optimization objective function F(R) as the fitness evaluation basis, automatically searching and outputting the hemming radius making the value of F(R) minimum in the iteration process as the optimal hemming radius R_opt.
2. The method for intelligent optimization design of cylindrical shell welded flange structure according to claim 1, characterized in that, In the step S1, the load working conditions include one or more of an internal pressure P, a bending moment M, an axial force F and a torque T.
3. The method of intelligent optimization design of cylindrical shell welded flange structure according to claim 1, characterized in that, In the step S3, the comprehensive optimization objective function F(R) is expressed as the sum of a performance evaluation term and a constraint penalty term, and the specific form is: wherein, and are non-negative weight coefficients set according to the design focus, and P(R) is a constraint penalty function.
4. The method of intelligent optimization design of cylindrical shell welded flange structure according to claim 3, characterized in that, The constraint penalty function P(R) is used for punishing the design that violates the design criteria in the step S1, and the expression thereof contains the following penalty terms: a penalty term for violating R_min≤R≤R_max; a penalty term for violating σ_max≤σ_y / S; and a penalty term for violating N_actual≥N.
5. The method of intelligent optimization design of cylindrical shell welded flange joint according to claim 4, characterized in that, A specific expression of the constraint penalty function P(R) is: P(R)=λ_1*max(0,σ_max-σ_y / S)^2+λ_2*max(0,N-N_actual)^2+λ_3*max(0,R_min-R)^2+λ_4*max(0,R-R_max)^2 Wherein, λ_1, λ_2, λ_3 and λ_4 are extremely large positive penalty coefficients.
6. The method of intelligent optimization design of cylindrical shell welded flange joint according to claim 1, characterized in that, In the step S4, the intelligent optimization algorithm is one of a genetic algorithm, a particle swarm optimization algorithm or a simulated annealing algorithm.
7. The method of intelligent optimization design of cylindrical shell welded flange joint according to claim 1, characterized in that, Further comprising a step S5: based on the multiple sets of different input parameter combinations and the corresponding optimal bead radii R_opt obtained by any of the methods of claims 1-6, a prediction model capable of directly outputting a recommended bead radius R_rec is trained through machine learning regression analysis; wherein when performing S5, the multiple sets of data are divided into a training set and a test set, the training set is used to perform regression analysis to obtain the prediction model, and the test set is used to verify the prediction accuracy of the model.
8. The method of intelligent optimization design of cylindrical shell welded flange structure according to claim 7, characterized in that, The prediction model is an explicit empirical formula, which is expressed in dimensionless form as: where Co, Ci, C2, C3, C4, C5 are constants determined by fitting, is a dimensionless function related to the set of load parameters L and the material yield strength σ_y; φ(N) is a dimensionless function constructed based on the target fatigue life N.
9. A computer readable storage medium having stored thereon a computer program, characterized in that, The computer program, when executed by a processor, implements the method of any of claims 1-8.
10. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor, when executing the program, implements the method of any of claims 1-8.