Degradable coronary stent with negative Poisson's ratio structure and optimization design method thereof

Abstract

The invention relates to a degradable coronary stent with a negative Poisson's ratio structure and an optimization design method of the degradable coronary stent, aims to make up for the defects of comprehensive mechanical properties of an existing stent, and belongs to the field of interventional medical instruments. The stent structure is formed by arranging concave hexagons serving as representative structural units in the axial direction and the circumferential direction, and the stent structure is made of degradable polymers. According to the optimization design method, on the basis that finite element simulation analysis is conducted on key mechanical properties of the support, an optimization problem is defined, design parameters are used for representing the geometrical shape of the support, a design space is established, a Kriging agent model and finite element simulation are combined to determine the approximate relation between an optimization target and the design parameters, and the optimization problem is solved. And multi-objective optimization is carried out through the NSGA-II. And when the optimal solution meets a convergence condition, outputting a final optimization design result of the stent. By adopting the optimization design method of the proxy model, the precision is ensured while the design efficiency is improved, and the optimized degradable coronary stent with the negative Poisson's ratio structure shows excellent comprehensive mechanical properties.

Description

Technical Field

[0001] The present invention belongs to the technical field of interventional medical devices, and in particular relates to a degradable coronary stent with a negative Poisson's ratio structure and an optimization design method thereof. Background Art

[0002] Coronary artery disease is one of the most common and dangerous cardiovascular diseases. It is caused by the accumulation of atherosclerotic plaques in the arteries. At present, percutaneous coronary intervention (PCI) has become the most common and effective treatment method in clinical practice due to its high efficiency and minimally invasive characteristics. Degradable stents can avoid problems such as restenosis and late thrombosis caused by permanent retention in the body. Commonly used degradable coronary stent materials are divided into degradable polymers and degradable metals. Among them, polymer stents have attracted widespread attention from scholars due to their good biocompatibility, renewability and processability.

[0003] However, the insufficient mechanical properties of some degradable polymer coronary stents have hindered their application in clinical treatment. During the deployment of the stent, due to the insufficient radial stiffness of the degradable polymer stent, the stent rebounds significantly after balloon unloading, resulting in a higher radial recoil rate, which easily leads to a higher probability of in-stent restenosis (ISR). Increasing the thickness of the stent can reduce the radial recoil rate, but the arterial stress will also increase, thereby damaging the blood vessel. Another prominent problem is the axial shortening phenomenon. The study by Schiavone et al. pointed out that commercial stents such as Palmaz-Schatz, Cypher, Xience and Endeavor all have axial shortening during expansion. This will not only lead to incomplete coverage of the lesion, but also affect the positioning accuracy of the stent. In the service stage of the stent, due to the lack of sufficient radial stiffness of the polymer stent, its radial support performance is often much smaller than that of the metal stent. For this reason, the strut thickness and width of the polymer stent are currently thicker and wider than those of the metal stent. However, this makes the surface area of ​​the stent larger and the lumen area reduced, affecting the normal flow of blood. When in service, the stent is also required to have good bending compliance to better adapt to the morphology of the diseased blood vessels, but the improvement of the radial stiffness of the stent often restricts the improvement of the bending compliance.

[0004] Therefore, how to reduce the thickness and width of the stent while improving the comprehensive mechanical properties of the stent through appropriate structural design and ensuring its long-term safety and effectiveness is a key issue facing the development of polymer coronary stents. The invention patent application number 201910233257.4 of Fan Yubo et al. discloses "a negative Poisson's ratio degradable vascular stent structure". Although the proposed structure enables the stent to match the negative Poisson's ratio effect of the vascular endothelial tissue after implantation, thereby reducing vascular tissue damage, it does not consider the optimization design method of the stent size parameters, nor does it perform numerical simulation analysis on the key mechanical properties of the stent. The improvement effect remains to be verified. The invention patent application number 201911084942.1 of Li Hongxia et al. discloses a "polymer vascular stent structure optimization design method considering scale effect". This method improves the structural design of the stent through finite element simulation and proxy model optimization methods based on the influence of scale effect on the mechanical behavior of the stent. However, due to its structural limitations, the axial shortening phenomenon of the stent always exists, and the bending compliance performance of the stent is not considered. In order to solve the above problems, the present invention proposes a degradable coronary stent with a negative Poisson's ratio structure and an optimization design method thereof. Summary of the invention

[0005] The purpose of the present invention is to propose a degradable coronary stent with a negative Poisson's ratio structure and an optimization design method thereof to solve the problems raised in the background technology. The degradable coronary stent with a negative Poisson's ratio structure proposed in the present invention can prevent the stent from axial shortening after expansion due to its unique deformation characteristics. The optimization method adopts a combination of finite element method and proxy model to reduce R&D costs and time, and ultimately improve the comprehensive mechanical properties of the stent.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] A degradable coronary stent with a negative Poisson's ratio structure, the coronary stent is a tubular object composed of concave hexagons as representative structural units, and thus has a negative Poisson's ratio effect; each of the concave hexagons includes two straight sides that are parallel to each other and equal in length, and two groups of oblique sides that extend inward from the same-side endpoints of the straight sides with the same angle and length; the coronary stent is made of a degradable material.

[0008] Preferably, in the concave hexagonal representative structural unit, the straight sides and the axial direction of the coronary stent are parallel to each other, and the oblique sides are folded inwards.

[0009] Preferably, two axially adjacent inward-concave hexagonal representative structural units are connected by a straight line at the intersection of their respective hypotenuses, and the straight line and the straight sides in the inward-concave hexagonal representative structural unit maintain the same length; and two circumferentially adjacent inward-concave hexagonal representative structural units share a straight side.

[0010] Preferably, the number of the concave hexagonal representative structural units arranged circumferentially of the coronary stent is 5 to 7, and the number of the axially arranged units is greater than 2. The specific number shall depend on the clinical application and the length of the coronary stent required by the patient.

[0011] Preferably, the sharp corners of the inwardly concave hexagonal representative structural unit are subjected to arc transition treatment, which can effectively avoid stress concentration occurring when the stent is expanded.

[0012] Preferably, the degradable coronary stent with a negative Poisson's ratio structure is made of a degradable polymer material, which can be a single material or a composite of multiple degradable polymer materials. Therefore, the preparation method can be 3D printing or laser engraving.

[0013] Furthermore, the present invention can achieve the optimal design of the degradable coronary stent and improve the comprehensive mechanical properties of the stent by adjusting the geometric parameters in the representative structural unit of the concave hexagon. The optimization design method is based on the finite element simulation analysis of the key mechanical properties of the stent, defines the optimization problem and characterizes the geometric shape of the stent with design parameters, establishes the design space, uses the Kriging proxy model and finite element simulation to determine the approximate relationship between the optimization target and the design parameters, and performs multi-objective optimization through NSGA-Ⅱ. When the optimal solution meets the convergence condition, the final optimization design result of the stent is output.

[0014] The optimization design method of the degradable coronary stent with a negative Poisson's ratio structure comprises the following steps:

[0015] Step 1: Define the structural optimization problem of degradable coronary stent:

[0016] The initial structural form of the stent is selected, and the key mechanical properties are analyzed by finite element simulation; the optimization problem is defined, including optimization objectives, constraints, optimization parameters and design space; in order to avoid the risk of intrinsic stenosis of the degradable polymer stent due to excessive width and thickness of the struts, the optimization design method improves the mechanical properties of the stent by adjusting the geometric parameters of the stent structure without changing the stent thickness and strut width. The degradable coronary stent with a negative Poisson's ratio structure no longer has axial shortening. In order to ensure the radial stiffness and bending flexibility of the stent, the length H, angle θ, circumferential number N and arc radius R of the concave hexagonal structural unit cell are used as design variables to ensure that the radial support force P(x) is closest to the baseline design while minimizing the bending stiffness k(x); the upper and lower limits of the design variables are set by considering the self-contact limit of the stent; in this process, the diameter, thickness and number of axial arrays of representative structural units of the stent remain unchanged; the optimization problem is expressed as:

[0017]

[0018] Among them, P(x) and k(x) are optimization objectives, x is the design variable, and DS is the design space;

[0019] Step 2: Generate the initial data set using Optimal LHS:

[0020] Sampling by Optimal LHS first requires determining the variable dimension (m) and sample size (Q), dividing the distribution interval of each variable into Q equally probable intervals, and randomly selecting a point from a single interval of each variable to complete sampling; then obtaining the response value of each sample point through finite element simulation; modeling the bracket structure based on the information of each sample point in the sample set, assigning material properties to the bracket and dividing the mesh in Abaqus, and then conducting plane compression tests and bending stiffness measurements respectively;

[0021] Step 3: Build the proxy model:

[0022] Based on the sample set in step 2, a Kriging surrogate model of P(x) and k(x) is constructed in MATLAB to fit the approximate relationship between the optimization objective and the design variables. The Kriging surrogate model is a semi-parametric method consisting of a regression part and a non-parametric part. The model expression is as follows:

[0023]

[0024] where the vector represents the i-th sample point containing p variables, is the best approximate function to fit the existing sample points, β is the regression coefficient, and f T (x i ) is the regression polynomial describing the global approximation of the simulation, z(x i ) is a randomly distributed error that provides an approximate simulation of the local deviation and has the following statistical characteristics:

[0025] E[z(x i )]=0 (3)

[0026]

[0027] Where E[], Var[], and Con[] represent the expected function, variance function, and spatial correlation function, respectively. i ,x j ) is the Gaussian correlation function with θ, which characterizes the spatial correlation between the two samples. According to the known sample points and their corresponding responses, the following formula can be used to estimate the sample points by maximum likelihood to obtain the unknown parameters θ, β and σ 2 .

[0028]

[0029] Where y represents the set of response values ​​obtained from the sample: y = {y 1 ,y 2 ,…,y n}, n is the number of sample points.

[0030] Using the above key parameters, the Kriging proxy model can be preliminarily established, and the response of new sample points can be predicted using the following formula:

[0031]

[0032] r(x new )=[R(θ,x 1 ,x new ),R(θ,x 2 ,x new ),…,R(θ,x n ,x new )] (10)

[0033]

[0034] Where Y is the corresponding response of the known sample point, and r is the correlation function between the new point and the known point.

[0035] Step 4: Multi-objective optimization of the support structure:

[0036] Based on the Kriging proxy model established in step 3, the non-dominated sorting genetic algorithm (NSGA-II) is used in MATLAB to solve the Pareto solution set, and the optimal sample points are selected from them. The prediction results are corrected by comparing with the finite element simulation results.

[0037] The optimization stopping criteria are as follows:

[0038]

[0039] Among them, q is the number of iterations, y q is the actual response obtained by the finite element method, is the predicted value of the Kriging proxy model, and the inequality represents the relative error between the predicted value and the finite element response value; ε is the given convergence accuracy, which is set to 0.05; when the optimal solution meets the stopping criterion, the final optimization design result of the bracket is output, otherwise the optimal solution will be added to the sample set based on the minimization prediction criterion and steps 3 to 4 will be repeated.

[0040] Beneficial Effects

[0041] The present invention adopts the above technical solution, which has the following advantages:

[0042] (1) The degradable coronary stent with a negative Poisson's ratio structure provided by the present invention can completely eliminate the axial shortening phenomenon existing in the traditional stent structure, and provides a new idea for the design and development of future stents.

[0043] (2) The present invention adopts an optimization design method that combines the Kriging proxy model and the NSGA-Ⅱ optimization algorithm, which overcomes the high cost of traditional clinical trials and the limitations of experimental verification. It completes the preliminary verification of the stent design in computer simulation, optimizes the design parameters and performance indicators through simulation, and provides an accurate and efficient stent geometry optimization method to meet multiple design goals.

[0044] (3) The optimization design method provided by the present invention improves the stability and flexibility of the optimized stent in clinical applications, thereby reducing postoperative complications of patients and improving the effect of minimally invasive interventional treatment. It is expected to provide a design solution that meets clinical needs in the field of vascular interventional treatment through superior mechanical properties.

[0045] (4) The multi-objective optimization design method adopted in the present invention can provide a Pareto candidate solution set corresponding to different parameters after optimization. When manufacturing or selecting coronary stents, the mechanical properties of the stent, the patient's vascular morphology, equipment conditions and other factors can be comprehensively considered, and a suitable stent can be selected according to the specific situation to achieve the best treatment effect.

[0046] (5) The negative Poisson's ratio structure and multi-objective optimization method proposed in the present invention are not only applicable to the design of degradable polymer coronary stents, but also provide a reference for the development of other new stents. This design concept has promotion value in the development of future stents and other medical implants. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 Schematic diagram of a representative structural unit of the degradable coronary stent with a negative Poisson's ratio structure mentioned in Example 1 of the present invention;

[0048] Figure 2 A three-dimensional model diagram of the degradable coronary stent with a negative Poisson's ratio structure mentioned in Example 1 of the present invention;

[0049] Figure 3 This is a flow chart of the optimization design method of the degradable coronary stent with a negative Poisson's ratio structure mentioned in Example 1 of the present invention;

[0050] Figure 4 This is a schematic diagram of the finite element experiment mentioned in Example 1 of the present invention, wherein: Figure 4 a is the balloon dilation test, Figure 4 b is the plane compression test, Figure 4c is the bending stiffness measurement experiment. DETAILED DESCRIPTION

[0051] The present invention will be further described below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms fall within the scope limited by the appended claims of the application equally.

[0052] Embodiment 1:

[0053] The present invention provides a degradable coronary stent with a negative Poisson's ratio structure, and a schematic diagram of a representative structural unit thereof is shown as follows: Figure 1 As shown. Side 1 is the straight side of the representative structural unit of the concave hexagon, and side 2 is the hypotenuse of the representative structural unit of the concave hexagon. The two straight sides are parallel to each other and of equal length. The two sets of hypotenuses are folded inward to form a concave hexagon. The sharp corners of the concave hexagon are processed with arc transition, which can effectively avoid the stress concentration phenomenon when the stent is expanded.

[0054] The three-dimensional model of the biodegradable coronary stent is composed of concave hexagons as representative structural units arranged along the axial and circumferential directions of the stent. Figure 2 As shown in the figure, two axially adjacent concave hexagons are connected by a straight line at the intersection of their respective hypotenuses, and the straight line and the straight edge in the representative structural unit of the concave hexagon maintain the same length; two circumferentially adjacent concave hexagons share a straight edge. When the stent expands, the side 2 that was originally in a folded state will gradually unfold, and the distance between the two axially adjacent concave hexagons will increase, thus forming a negative Poisson's ratio effect.

[0055] The number of concave hexagonal representative structural units arranged circumferentially in the coronary stent is selected as 6, and the number of axially arranged units is selected as 5. The numbers of circumferential and axial arrangements here are only for illustration, and the specific number of circumferential arrangements will be determined after optimization, while the number of axial arrangements should be determined according to clinical applications and the length of the coronary stent required by the patient.

[0056] The degradable coronary stent with negative Poisson's ratio structure provided by the present invention is suitable for degradable polymer materials, which can be a single material or a composite of multiple degradable polymer materials. 3D printing or laser engraving can be selected to complete the preparation of the stent. PLA is selected as the stent material here for illustration only.

[0057] The flow chart of the optimization design method of biodegradable coronary stent with negative Poisson's ratio is as follows Figure 3 As shown, the following steps are included:

[0058] Step 1: Define the structural optimization problem of degradable coronary stent:

[0059] The initial structural form of the stent was selected, and the key mechanical properties were analyzed through finite element simulation. The outer diameter, thickness, length and strut width of the stent are 2.4mm, 0.1mm, 5.9mm and 0.12mm, respectively. The length H, angle θ, circumferential number N and arc radius R of the concave hexagon are 1.712mm, 50°, 6 and 0.12mm, respectively. The radial shrinkage rate of the stent in its initial form is 4.5%, the axial shortening rate is -22.9%, the radial support force is 85.145N / m, and the bending stiffness is 18.870N·mm 2 .

[0060] In order to avoid the risk of intrinsic stenosis of the degradable polymer stent due to the excessive width and thickness of the struts, the optimization design method is to improve the mechanical properties of the stent by adjusting the geometric parameters of the stent structure without changing the stent thickness and strut width. The degradable coronary stent with a negative Poisson's ratio structure no longer has axial shortening. In order to ensure the radial stiffness and bending flexibility of the stent, the length H, angle θ, circumferential number N and arc radius R of the concave hexagonal structural unit cell are used as design variables to minimize the bending stiffness k(x) while ensuring that the radial support force P(x) is closest to the baseline design; the upper and lower limits of the design variables are set by considering the self-contact limit of the stent; in this process, the diameter, thickness and number of axial arrays of representative structural units of the stent remain unchanged; the optimization problem is expressed in the following formula:

[0061]

[0062] Among them, P(x) and k(x) are optimization objectives, x is the design variable, and DS is the design space.

[0063] Step 2: Generate the initial data set using Optimal LHS:

[0064] First, the variable dimension is determined to be 4 and the sample size is 15. The distribution interval of each variable is divided into 15 intervals of equal probability. A point is randomly selected from a single interval of each variable to complete the sampling. Then, the response value of each sample point is obtained through finite element simulation. The stent structure is modeled according to the information of each sample point in the sample set. The material properties of the stent are assigned and the grid is divided in Abaqus. Then, balloon expansion test, plane compression test and bending stiffness test are carried out respectively. The experimental schematic diagrams are shown in Figure 2. Figure 4 The specific simulation results are shown in Table 1.

[0065] Table 1 Sample point information and corresponding responses

[0066]

[0067] Step 3: Build the proxy model:

[0068] Based on the sample set, the Kriging surrogate model of P(x) and k(x) is constructed in MATLAB to fit the approximate relationship between the optimization objective and the design variables. The detailed process is shown in formulas (2)-(11).

[0069] Step 4: Multi-objective optimization of the support structure:

[0070] Based on the established Kriging agent model, the non-dominated sorting genetic algorithm (NSGA-II) was used in MATLAB to solve the Pareto solution set, and the optimal sample points were selected from them. The prediction results were corrected by comparing with the finite element simulation results. When the optimal solution meets the stopping criterion, the final optimization design result of the bracket is output, otherwise the optimal solution will be added to the sample set based on the minimization prediction criterion and steps 3 to 4 will be repeated.

[0071] The final optimization results are shown in Table 2.

[0072] Table 2 Comparison of key mechanical properties between optimized scaffold and initial scaffold

[0073]

[0074] The results of finite element numerical simulation show that the radial support force of the stent is 82.800N / m, which is only 2.75% different from the baseline design. The bending stiffness of the stent is 7.525N·mm, which is 60.12% lower than the baseline design. Therefore, the optimization program effectively improves the problem of high bending stiffness of the PLA-RH stent while ensuring radial support performance. At the same time, the radial shrinkage rate of the optimized stent was measured to be 1.26%, which is 62.34% lower than the baseline design.

[0075] In summary, the degradable coronary stent with a negative Poisson's ratio structure constructed in the present invention completely eliminates the axial shortening phenomenon and has better expansion performance. The optimized design method further improves the stability and flexibility of the stent in clinical applications, improves the comprehensive mechanical properties of the stent, and enhances the effect of minimally invasive interventional treatment.

[0076] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. For ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles described in the present invention, and these improvements and modifications should also be regarded as the protection scope of the present invention.

Claims

1. A degradable coronary stent with a negative Poisson's ratio structure, characterized in that: The coronary stent is made of a degradable material, specifically a tubular object composed of concave hexagons as representative structural units, and has a negative Poisson's ratio effect; Each of the concave hexagons includes two straight sides that are parallel to each other and of equal length, and two groups of oblique sides that extend inwardly from the same-side endpoints of the straight sides and have the same angle and length.

2. The degradable coronary stent with a negative Poisson's ratio structure according to claim 1, characterized in that: In the representative concave hexagonal structural unit, the straight sides are parallel to the axial direction of the coronary stent, and the oblique sides are folded inwards.

3. The degradable coronary stent with a negative Poisson's ratio structure according to claim 1, characterized in that: Two axially adjacent inward-concave hexagonal representative structural units are connected by a straight line at the intersection of their respective oblique sides, and the straight line and the straight sides in the inward-concave hexagonal representative structural unit maintain the same length; Two circumferentially adjacent inwardly concave hexagonal representative structural units share a straight side.

4. The degradable coronary stent with a negative Poisson's ratio structure according to claim 1, characterized in that: The number of the inwardly concave hexagonal representative structural units arranged in the circumferential direction of the coronary stent is 5 to 7, and the number of the inwardly concave hexagonal representative structural units arranged in the axial direction depends on the clinical application and the length of the coronary stent required by the patient.

5. The degradable coronary stent with a negative Poisson's ratio structure according to claim 1, characterized in that: The sharp corners of the concave hexagonal representative structural unit are processed with arc transition.

6. The degradable coronary stent with a negative Poisson's ratio structure according to claim 1, characterized in that: The coronary stent is made of a single degradable material or a plurality of degradable polymer materials, and is prepared by 3D printing or laser engraving.

7. The optimization design method of the degradable coronary stent with a negative Poisson's ratio structure according to any one of claims 1 to 6, characterized in that: The following steps are involved: Step 1: Define the structural optimization problem of degradable coronary stent: The initial structural form of the stent was selected, and the key mechanical properties were analyzed by finite element simulation. The optimization problem was defined, including optimization objectives, constraints, optimization parameters and design space. Without changing the thickness of the stent and the width of the struts, the mechanical properties of the stent were improved by adjusting the geometric parameters of the stent structure to avoid the risk of intrinsic stenosis of the degradable polymer stent due to excessive width and thickness of the struts. The length H, angle θ, circumferential number N and arc radius R of the concave hexagonal structural unit cell were used as design variables to minimize the bending stiffness k(x) while ensuring that the radial support force P(x) was closest to the baseline design. The upper and lower limits of the design variables were set by considering the self-contact limit of the stent. In this process, the diameter, thickness and axial array number of representative structural units of the stent remained unchanged. The optimization problem is stated as: Among them, P(x) and k(x) are optimization objectives, x is the design variable, and DS is the design space; Step 2: Generate the initial data set using Optimal LHS: Determine the variable dimension m and sample size Q, divide the distribution interval of each variable into Q intervals of equal probability, randomly select a point from a single interval of each variable, and finally complete the sampling; The response value of each sample point is obtained through finite element simulation; The bracket structure is modeled based on the information of each sample point in the sample set, the material properties of the bracket are assigned and the mesh is divided in Abaqus, and then the plane compression test and bending stiffness measurement are carried out respectively; Step 3: Build the proxy model: Based on the sample set in step 2, a Kriging surrogate model of P(x) and k(x) is constructed in MATLAB to fit the approximate relationship between the optimization objective and the design variables. The Kriging surrogate model is a semi-parametric method consisting of a regression part and a non-parametric part. The model expression is as follows: Among them, the vector represents the i-th sample point containing p variables, is the best approximate function to fit the existing sample points, β is the regression coefficient, f T (x i ) is the regression polynomial describing the global approximation of the simulation, z(x i ) is a random distribution error that provides an approximate simulation of the local deviation and has the following statistical characteristics: E[z(x i )]=0 (3) Where E[], Var[], and Con[] represent the expected function, variance function, and spatial correlation function, respectively; R(θ,x i ,x j ) is the Gaussian correlation function with θ, characterizing the spatial correlation between the two samples; According to the known sample points and their corresponding responses, the following formula is used to perform maximum likelihood estimation on the sample points to obtain the unknown parameters θ, β and σ 2 , the specific function is expressed as: Where y represents the set of response values ​​obtained from the sample: y = {y1, y2, ..., y n }, n is the number of sample points; Using the above key parameters, the Kriging proxy model is initially established, and the response of the new sample point is predicted using the following formula: r(x new )=[R(θ,x 1 ,x new ),R(θ,x 2 ,x new ),…,R(θ,x n ,x new )] (10) Among them, Y is the corresponding response of the known sample point, and r is the correlation function between the new point and the known point; Step 4: Multi-objective optimization of the support structure: Based on the Kriging proxy model established in step 3, the non-dominated sorting genetic algorithm is used in MATLAB to solve the Pareto solution set, and the optimal sample points are selected from them. The prediction results are corrected by comparing with the finite element simulation results; The optimization stopping criteria are as follows: Among them, q is the number of iterations, y q is the actual response obtained by the finite element method, is the predicted value of the Kriging proxy model, and the inequality represents the relative error between the predicted value and the finite element response value; ε is the given convergence accuracy, which is set to 0.05; when the optimal solution meets the stopping criterion, the final optimization design result of the bracket is output, otherwise the optimal solution will be added to the sample set based on the minimization prediction criterion and steps 3 to 4 will be repeated.

Images