Optimization method for parameters of multi-corner-angle conformal PDC tooth structure

Abstract

According to the optimization method for the structural parameters of the multi-corner-angle shape-following PDC tooth, the structural parameters of the multi-corner-angle shape-following PDC tooth, such as a ridge angle, a round angle, a corner angle height, a corner angle and a side face included angle, are taken as design factors, crushing specific energy, average cutting force, an impact force peak value and an energy absorption peak value are taken as responses, PBD test design is utilized, and a significance analysis method is combined, so that the structural parameters of the multi-corner-angle shape-following PDC tooth are optimized. The method comprises the following steps: determining structure parameters with obvious influence as a ridge angle, a fillet, a corner angle and a side surface included angle, then constructing an agent model, firstly utilizing optimal Latin hypercube sampling to obtain a sampling table, performing simulation according to data of the sampling table to obtain a corresponding simulation result, perfecting a corresponding column of the data of the sampling table, and on the basis, constructing an agent model; establishing a CPO-SVR model taking the four structural parameters as design factors and four responses to complete training and prediction of sample data; and after the model is available, carrying out iterative solution through a Hemma optimization algorithm to obtain a parameter combination when each response is optimal. Through the optimization method, a group of comprehensive optimization schemes of the PDC teeth with high cutting efficiency and strong impact resistance can be finally obtained.

Description

Technical Field

[0001] The invention relates to the field of optimization of structural parameters of multi-angular conformal PDC teeth on a shield machine disc cutter, and specifically to an optimization method for structural parameters of multi-angular conformal PDC teeth based on agent model prediction and intelligent optimization algorithm optimization. Background Art

[0002] PDC teeth are polycrystalline diamond composite teeth, which are mainly composed of two parts: the upper part is a polycrystalline diamond layer, which has extremely high hardness and wear resistance and can effectively cut hard formations such as rocks; the lower part is a cemented carbide matrix, which can provide good support for the polycrystalline diamond layer and ensure the overall strength and stability. In terms of shield machine tools, tools with PDC teeth can adapt to a variety of formation conditions, have excellent cutting and rock breaking performance in soft rock and some hard rock formations, and often have more advantages in service life and rock breaking effect than traditional tools.

[0003] As one of the key components of the shield machine, the shield cutter is equivalent to the "teeth" and is the main component for the shield machine to achieve excavation. However, with the large-scale equipment and the increase in construction difficulty, the forces on the shield cutter are becoming more and more complex. The common forms of damage to the shield cutter are cutter ring wear, cutter ring edge breakage and cutter body deformation. The traditional reinforced cutter can no longer meet the long-distance excavation requirements under extreme working conditions. For high-strength hard strata and complex soft-hard strata with frequent force changes, multi-angular conformal PDC teeth are designed. The multi-angular design is intended to improve its rock breaking efficiency. The structural diagram is shown in the figure below. Figure 2 as shown; Figure 6 As shown in the figure, during cutting, the "edges" first contact the rock surface, forming concentrated stress at the edges, making it easier to cut into the rock. After cutting into the rock, the three edges form a "V" shape to break the rock; the follow-up shape means that the radius of the side arc of the PDC tooth is 254mm, which is the same as the radius of the embedded single-edged disc cutter. This design helps to maintain the stability of the cutter during the cutting process. During the cutting process, the cutter is subjected to complex cutting forces. If the radius of the PDC tooth arc is different from the radius of the cutter, additional radial force may be generated, causing the cutter to vibrate. Figure 3 As shown in the figure, the PDC teeth are reasonably embedded in the cutter body as the cutter head, which is expected to increase the life of the single-edged disc cutter and thus improve the tunneling efficiency. In order to improve the service life and rock breaking efficiency of the multi-angular conformal PDC teeth, the rock breaking process of the PDC teeth was simulated using Abaqus software, as shown in the figure. Figure 5As shown in the figure, during the rock breaking process, the movement of the disc cutter is the rotational movement around the central axis of the cutter disc and the linear movement of the cutter disc in the forward direction, so the PDC cutting teeth on the disc cutter make a spiral movement in the forward direction. However, the cutting depth of the disc cutter is small, that is, the cutting depth of a single PDC cutting tooth is small, and the spiral angle of one rotation is very small. Therefore, the rotational movement of a single PDC cutting tooth is simplified to a linear movement of a fixed cutting depth. The calculation efficiency and accuracy are comprehensively considered to establish a simulation model of a single PDC tooth cutting rock. During the rotation of the shield machine cutter disc, the disc cutter makes a circular motion at a certain speed. When the cutter disc contacts the rock, the kinetic energy it carries will be released instantly, forming impact energy and generating a large impact force, causing the PDC cutting teeth on the cutter disc to crack and break. Therefore, it is very necessary to analyze the influence of impact energy on the PDC teeth. The calculation efficiency and accuracy are comprehensively considered to establish an impact simulation model of the impact block impacting a single PDC tooth. The structural parameters of the multi-angular conformal PDC teeth are optimized. Therefore, it is of great significance to study the structural parameters of the designed multi-angular conformal PDC teeth. Summary of the invention

[0004] In order to solve the problems in the prior art, the present invention proposes a method for optimizing the structural parameters of a multi-angular conformal PDC tooth, which comprises the following steps:

[0005] S1: Preliminarily determine the structural parameters that need to be optimized for the multi-angular conformal PDC teeth, and implement parametric modeling in the 3D design software based on the structural parameters;

[0006] S2: Based on the value range of the structural parameters, the PBD test design is performed in the Design-Expert software to establish the test table A, M groups of test data combinations are obtained, several performance parameters of the tooth are determined as responses, and several response columns are reserved in the test table A;

[0007] S3: According to several groups of test data combinations in the experimental table, three-dimensional models of different PDC teeth are established in the three-dimensional design software, imported into the simulation software for simulation, and several response data corresponding to each test data combination are obtained, and filled in the response column in the test table A.

[0008] Improve the experimental table A;

[0009] S4: Take the structural parameters in the improved experimental table A as design factors and the response as the optimization target, perform significance analysis in the Design-Expert software, and obtain some key structural parameters that have significant impact on the response; significance analysis plays an important role in parameter optimization, screening key parameters: it can help determine which of the many parameters have a significant impact on the target performance, thereby screening out key parameters that need to be optimized, and avoiding wasting too much energy on unimportant parameters; parameter optimization refers to the process of adjusting and improving relevant parameters through a series of methods in a specific system, model or process to achieve better performance, effect or meet specific goals.

[0010] S5: Perform optimal Latin hypercube sampling on the key structural parameters in step S4 to obtain N groups of test data, and form experimental table B, reserving several response columns;

[0011] S6: Import the N groups of test data in S5 into the simulation software for simulation, obtain the response corresponding to each group of test data and complete the experimental table B.

[0012] S7: Import the data of the improved experimental table B in S6 into Matlab, complete the training and prediction of the sample data through the CPO-SVR proxy model, train an effective proxy model and determine it; the proxy model is a commonly used tool in complex system analysis and optimization. It constructs a relatively simple model by sampling or training the original complex system. This proxy model can approximately reflect the input-output relationship of the original system to a certain extent.

[0013] S8: The CPO-SVR proxy model determined in S7 is used as the fitness function in the Hippo optimization algorithm. The Hippo optimization algorithm program is written through Matlab to optimize the fitness function. In the feasible domain, the corresponding value combination of each structural parameter under the optimal response is found respectively, and the analysis results of the CPO-SVR proxy model are verified and optimized, and finally the optimal structural parameter combination is obtained. The optimization algorithm finds the optimal solution of the objective function through continuous iterative search, which mainly includes determining the objective function, setting the initial solution, iterative search, etc. By combining the proxy model with the optimization algorithm to find the best solution, it not only overcomes the difficulty of directly processing complex systems, but also can efficiently find solutions that meet the optimization goals.

[0014] Preferably, step S1 specifically comprises:

[0015] The method designs a multi-angle conformal PDC tooth, and determines five structural parameters, namely, the angle between the main inclined surfaces on both sides of the transverse ridge of the designed tooth top is the ridge angle, the radius of the arc of the transverse ridge is the fillet, the distance between the lower end of the side edge and the tooth bottom surface is the edge angle height, the angle between the side inclined surfaces on both sides of the side edge is the edge angle, and the angle between the side edge and the tooth bottom surface plane is the side angle. The value range of each of the above structural parameters is determined, and then modeling is performed in the three-dimensional design software Solidworks, and each parameter is named in the form of "=DS_" to realize parametric modeling. Then, the completed three-dimensional model is converted into XT format in Solidworks; other three-dimensional modeling software with equivalent functions can also be used.

[0016] The ridge angle, fillet, edge height, edge angle and side angle of the PDC tooth are used as dimensional parameters. They are named in the form of "=DS_" in the Solidworks sketch interface. The equation can be found in the tool above. Different PDC tooth models can be generated by entering different parameters in the equation, thereby realizing parametric modeling and improving modeling efficiency. According to the use scenarios and current problems of the single-edged disc cutter of the shield machine, its design goal is to improve the service life and cutting efficiency of the cutter. The PDC tooth is designed and reasonably embedded in the cutter to improve the service life and cutting efficiency of the cutter. The PDC tooth is designed by consulting the data and factory experience. The multi-angle conformal PDC tooth with extended service life and improved cutting efficiency is designed, and the size range of the PDC tooth is determined;

[0017] Preferably, step S2 specifically comprises:

[0018] The five structural parameters of the multi-angular conformal PDC tooth structure are taken as five factors, namely ridge angle A, fillet B, edge height C, edge D and side angle E. In order to investigate the influence of ridge angle, fillet, edge height, edge and side angle on crushing specific energy, average cutting force, impact force peak and energy absorption peak, the five factors of ridge angle, fillet, edge height, edge and side angle in the multi-angular conformal PDC tooth structure are taken, and the upper and lower limits of their value range are determined by referring to papers and according to factory experience. PBD test design is carried out in Design-Expert software to establish test table A, and M=12 groups of test data are obtained, and four response columns are set in test table A; the four performance parameters of the multi-angular conformal PDC tooth, namely crushing specific energy, average cutting force, impact force peak and energy absorption peak, are determined as responses.

[0019] Preferably, step S3 specifically comprises: according to the test data combination of test table A of S2, modifying each structural parameter in Solidworks according to the requirements of each data combination, generating different PDC teeth, converting the PDC tooth three-dimensional model into XT format, importing it into ABAQUS software for cutting simulation and impact simulation, and obtaining the crushing specific energy, average cutting force, impact force peak value and energy absorption peak value under each data combination; its sub-steps are as follows:

[0020] S3.0 generates different 3D models of PDC teeth in Solidworks according to the result parameters of experimental table A, and converts the 3D models of PDC teeth into XT format;

[0021] S3.1 Establish a cutting simulation model, import the XT format files of each PDC tooth three-dimensional model, and obtain the crushing specific energy and average cutting force under each data combination;

[0022] In the rock breaking process, the disc cutter moves in rotation around the center axis of the cutter disc and in linear motion in the forward direction of the cutter disc, so the PDC cutting teeth on the disc cutter make a spiral motion in the forward direction; however, the cutting depth of the disc cutter is small, that is, the cutting depth of a single PDC cutting tooth is small, and the helical angle of one rotation is very small, so the rotational motion of a single PDC cutting tooth is simplified to a linear motion of a fixed cutting depth;

[0023] The crushing specific energy (MSE) is used to characterize the energy required to crush a unit volume of rock. The smaller the MSE, the less energy is required to crush a unit volume of rock, and the higher the efficiency of the PDC cutter in crushing rocks. Therefore, the crushing specific energy in the stable cutting stage is taken as the response. The crushing specific energy can be calculated according to the following formula:

[0024]

[0025] In formula (1), V is the total rock crushing volume, F is the cutting force, ds is the length of the cutting stage, v is the cutting speed, and dt is the time of the cutting stage;

[0026] Cutting force is used to characterize the difficulty of PDC cutting teeth in breaking rocks. The smaller the cutting force required to break rocks, the easier it is to break them. Since the cutting force fluctuates during the cutting process, the average cutting force in the stable cutting stage is taken as the response.

[0027] In summary, a simulation of limestone cutting by a single multi-angular conformal PDC tooth is established to obtain its crushing specific energy and average cutting force, so as to judge the cutting performance of PDC teeth with different parameters.

[0028] S3.1.1 Input model

[0029] The XT format of the PDC tooth model generated by S3 parametric modeling was imported into ABAQUS. Considering the model size and calculation efficiency, a finite element model of a single multi-angular conformal PDC tooth cutting limestone was established. The size of the limestone model was 50mm×50mm×20mm.

[0030] S3.1.2 Setting properties

[0031] The material of the PDC layer is polycrystalline diamond, and its density is 3520kg / m 3 , elastic modulus 8.9E+5Mpa, Poisson's ratio 0.07; rock material is limestone, density 2500kg / m 3 , elastic modulus 40000Mpa, Poisson's ratio 0.4;

[0032] S3.1.3 Create an assembly and set up analysis steps

[0033] After the material properties are set, the model needs to be assembled and the cutting depth of the multi-angular conformal PDC teeth is set to 2 mm;

[0034] Set the analysis step to dynamic explicit general, set the whole cutting process to 0.16s to improve the analysis efficiency, and keep the rest as default settings;

[0035] S3.1.4 Setting up interactions and loads

[0036] Set the interaction properties, set the friction formula in the tangential behavior to penalty, the friction coefficient to 0.3, and the rest to default settings; select the pressure interference in the normal behavior as hard contact, and the rest to default settings; set the multi-angle conformal PDC tooth to rigid body, and the contact type to general contact;

[0037] Set the load, completely fix the limestone base layer, convert the shield machine cutter head rotation speed into linear speed, and set the cutting speed of the multi-angle conformal PDC teeth;

[0038] S3.1.5 Grid division

[0039] The overall mesh size of the limestone is set to 5 mm, and the cutting part further refines the mesh to 0.5 mm. The PDC teeth are set as rigid bodies and will not deform, so the mesh size is set to 1.5 mm to speed up the analysis process;

[0040] After completing the above pre-processing, simulation is performed, and after completing the simulation, post-processing is performed, and the data is imported into the origin software for curve drawing to obtain the cutting force-time curve. The crushing specific energy and average cutting force are calculated in the stable cutting stage;

[0041] S3.2 Establish an impact simulation model, import the XT format files of each PDC tooth three-dimensional model, and obtain the impact force peak value and energy absorption peak value under each data combination;

[0042] When the cutterhead of the shield machine rotates, the disc cutter moves in a circular motion at a certain speed. When the cutter contacts the rock, the kinetic energy it carries will be released instantly, forming impact energy and generating a large impact force, which will cause the PDC cutting teeth on the cutter to crack and break. Therefore, the analysis of the impact force is particularly important. Energy absorption usually refers to the ability of a material to absorb and dissipate energy when it is impacted or pressed. For PDC teeth, its energy absorption characteristics are mainly reflected in its impact resistance and wear resistance. The energy absorption characteristics of PDC teeth are a key factor in its design and application, which directly affects the efficiency and life of PDC teeth. In summary, the simulation of the impact block impacting a single multi-angular conformal PDC tooth is established to obtain the impact force peak value and energy absorption peak value, so as to judge the advantages and disadvantages of the impact resistance of PDC teeth with different parameters.

[0043] S3.2.1 Input model

[0044] After the three-dimensional models of the PDC layer and carbide substrate of the PDC tooth generated by S3 parametric modeling were assembled in SoildWorks, they were converted into XT format and imported into ABAQUS;

[0045] S3.2.2 Setting properties

[0046] The material of the PDC layer is polycrystalline diamond, and its density is 3520kg / m 3 , elastic modulus 8.9E+5Mpa, Poisson's ratio 0.07, compressive strength 7600Mpa. Since the strain of polycrystalline diamond before fracture is very small, in order to make the simulation results more obvious, the plastic strain is set to 1 after reaching the compressive strength limit; the impact block material used in the simulation analysis is steel with a density of 7850kg / m 3 , elastic modulus 200Gpa, Poisson's ratio 0.3;

[0047] S3.2.3 Create an assembly and set up analysis steps

[0048] After the material properties are set, the model needs to be assembled. To ensure the analysis efficiency, the distance between the impact block and the multi-angular conformal PDC tooth is set to 0, that is, the distance between the two when the impact is about to occur;

[0049] Set the analysis step to general dynamic display. The impact force reaches the maximum value in a very short time. Therefore, set the whole process of the test collision to 5E-04s to improve the analysis efficiency. The rest are set to default.

[0050] S3.2.4 Setting up interactions and loads

[0051] Set the interaction properties. In the tangential behavior, the friction formula is set to penalty, the friction coefficient is 0.3, and the rest are set by default. In the normal behavior, the pressure interference is selected as hard contact, and the rest are set by default. Set the impact block to rigid body, and the contact type is general contact.

[0052] Set the load, completely fix the hard base part of the multi-angle conformal PDC tooth, and then set the impact block speed according to the impact work of 750J;

[0053] S3.2.5 Grid division

[0054] The PDC layer is the main impact part, and the mesh size is set to 1.2mm. The fillet and corner parts are further refined and set to 0.5-0.8mm. The mesh size of the hard matrix part is reduced to speed up the analysis process; the impact block is set as a rigid body and will not deform, so the mesh size is set to 5mm to speed up the analysis process;

[0055] After completing the above pre-processing, simulation is performed, and after completing the simulation, post-processing is performed, and the data is imported into the origin software for curve drawing. The impact force-time curve and energy-time curve are obtained, and the impact force peak value and energy absorption peak value are calculated.

[0056] Preferably, step S4 is specifically:

[0057] The five factors of ridge angle, fillet, edge height, edge and side angle in the multi-angle conformal PDC tooth structure are taken as design factors, and the crushing specific energy, average cutting force, impact force peak and energy absorption peak are taken as optimization targets. The 12 groups of data obtained in S3 are imported into the Plackett-Burmans module in the Design-Expert software, and the test data are analyzed for significance to obtain the significance test results. The significance results are measured by the size of the p value. The p value of the first and second terms of the variable is observed. If the p value is less than 0.05, it means that the factor represented by this variable has a significant effect on the test results. Otherwise, the factor has no obvious effect on the response target. After the analysis is completed, the design factors that have significant influence on the crushing specific energy, average cutting force, impact force peak and energy absorption peak among the five factors are ridge angle, fillet, edge and side angle, which are determined as key structural parameters.

[0058] Preferably, step S5 is specifically:

[0059] Obtain sample data, and obtain the structural parameters with significant influence, such as ridge angle, fillet, edge angle and side angle, according to the significance analysis in S4. On this basis, perform optimal Latin hypercube sampling. Select the DOE module and EXCEL module in the Isight software and connect the two together. Add the four columns A, B, D, and E in EXCEL to DOE, and select optimal Latin hypercube sampling in DOE. According to the empirical formula, determine the sampling number as 60, and then click Generate to obtain the sampling table, and obtain N=60 groups of test data to form Experimental Table B.

[0060] Preferably, step S6 is specifically as follows: in ABAQUS software, the scheme combinations in the sampling table of S5 are subjected to cutting simulation and impact simulation according to step S3 to obtain four response data of each group, which are filled into the corresponding columns in the table to improve the test table B, so as to prepare for the subsequent construction of the CPO-SVR proxy model.

[0061] Preferably, step S7 specifically includes:

[0062] The simulation data obtained in S6 are subjected to grey correlation analysis to construct the CPO-SVR proxy model. The 60 groups of data are divided into 50 training sets and 10 test sets. The CPO-SVR proxy model is used to complete the training and prediction of the data. The root mean square error (RMSE) and the determination coefficient (R) are used to calculate the predicted value. 2 Verify the model validity and proceed to the next step if the model is valid;

[0063] S7.1 Grey correlation analysis

[0064] Grey relational analysis is to judge whether the connection is close according to the similarity of the geometric shapes of sequence curves. The closer the curves are, the greater the grey relational degree between the corresponding sequences. This method can be used for correlation analysis between factors and responses in the system, and can also be used for comprehensive evaluation. Considering the complexity of solving multi-objective response problems, grey relational analysis is introduced to convert multi-response problems into corresponding grey relational degrees, and the size of the grey relational degree can be used as the model output to judge the quality of the response.

[0065] S7.1.1 Normalize the raw data

[0066] Since the responses are not of the same type, the test response values ​​need to be normalized to between [0,1]; the smaller the crushing specific energy and average cutting force, the better, while the larger the impact force and energy absorption, the better. The peak impact force and energy absorption peak can be turned into negative numbers, so they can be normalized using formula (1);

[0067]

[0068] In formula (2), B ikIt represents the normalized response value of the i-th group test when the index is k, where k=1 means the index is the crushing specific energy, k=2 means the index is the average cutting force, k=3 means the index is the impact force peak, k=4 means the index is the energy absorption peak, L k represents all test response values ​​with index k, L ik It indicates the test response value of group i when the index is k;

[0069] S7.1.2 Determine the reference sequence

[0070] Use B 0k It represents the reference sequence, which means the optimal value obtained when the indicator k is sampled. The first two indicators in this paper are as small as possible, so the reference sequence is the minimum response value corresponding to each indicator. After normalization, B is obtained. 0k ={1,1}, the latter two indicators are as large as possible, so the reference sequence is the maximum response value corresponding to each indicator, and B is obtained after normalization. 0k ={0,0};

[0071] S7.1.3 Calculation of grey correlation coefficient

[0072] The specific steps are as follows:

[0073] Δ ik =|B 0k -B ik | (3)

[0074]

[0075] In formulas (3)-(6), Δ ik Indicates the deviation sequence of the index k, the i-th group of experiments; Δ min It means to search for the deviation sequence by k, where k = 1, 2, 3, 4, and then search by i, where i = 1, 2, 3...n1, n1 is the optimal Latin hypercube sampling number, which is 60, and get the minimum value Δ of the deviation sequence min ; Δ max It means that the deviation sequence is first searched by k, and then searched by i to obtain the maximum value Δ of the deviation sequence max ;μ ik It indicates the grey correlation coefficient of the i-th group of data when the index is k, ξ indicates the resolution coefficient, which is usually taken as 0.5;

[0076] S7.1.4 Determine the weight of each response using the entropy weight method

[0077] The entropy weight method determines the objective weight of each indicator based on the variability of the indicator. The smaller the information of the indicator, the greater the degree of variability, the greater the role it can play in the comprehensive evaluation, and the greater its weight.

[0078] The specific calculation process is as follows:

[0079]

[0080] D k =1-e k (9)

[0081]

[0082] In formulas (7)-(10), the k-th index represents the proportion of the i-th group of tests, which is the normalized data calculated by formula (2); k is the information entropy of indicator k. The smaller the information entropy, the greater the discrete degree of the indicator, and the greater the objective weight of the indicator. In addition, because we need to calculate lnp ik , if B ik is 0, then P ik The computer cannot calculate it because it is 0. Therefore, the translation method is used. For the indicator column that appears 0 during the normalization process, a translation amount is added to the column data at the same time. The translation amount is the absolute value of the minimum value of the column data plus 0.01, and the new B is obtained. ik , which can solve this problem; D k is the information redundancy of index k; m2 is the number of indicators, which is 4; w k is the weight of indicator k;

[0083] S7.1.5 Calculation of grey relational degree

[0084] Convert each group of response values ​​into the corresponding grey correlation degree. The higher the grey correlation degree, the more it meets the requirements. The calculation process is as follows:

[0085]

[0086] In formula (11), h ik Indicates that the index is k, the grey relational degree corresponding to the i-th group of experiments, m2 is the number of indicators, which is 4; W k represents the objective weight of indicator k, U ik The index is k, and the grey correlation coefficient corresponding to the i-th group of experiments;

[0087] S7.2 Construction of CPO-SVR surrogate model

[0088] The crested porcupine optimizer (CPO) is similar to most metaheuristic swarm algorithms.

[0089] The initial population search process of CPO is:

[0090]

[0091] In formula (12): X iis the i-th solution to be selected in the search space; L, U are the lower and upper limits of the search range; r is a random number between 0 and 1; N is the population size;

[0092] The CPO algorithm uses a cyclic population reduction technique (CPR). In order to speed up the convergence speed while ensuring the diversity of the population, the CPO algorithm uses a cyclic population reduction technique (CPR). This strategy borrows a concept: not all crested porcupines (CP) in the population will actively activate defense mechanisms, and these mechanisms will only be activated when they feel threatened. Based on this, the CPR strategy selects some CPs from the population during the optimization process to speed up the convergence speed, and puts these CPs back into the population to enhance diversity and prevent falling into a local optimal solution.

[0093] The mathematical model of cycle reduction is as follows:

[0094]

[0095] In formula (13): N min is the minimum number of newly generated populations, t is the current function evaluation, T is the number of cycles, and T max is the maximum number of function evaluation loops, % is the remainder or modulus operator;

[0096] The CPO algorithm is inspired by the various defensive behaviors of crested porcupines in nature, which include four different protection mechanisms: vision, hearing, smell and physical attack, to identify the aggressiveness of alien species; among them, vision and hearing are also called the first and second defense strategies, and they also reflect the exploration behavior in the CPO algorithm; smell and physical attack are also called the third and fourth defense strategies, reflecting the utilization behavior in the CPO algorithm; the entire CPO algorithm uses the above four defense strategies to work together in practical applications to ensure the optimality of the final result.

[0097] The entire optimization process of the four defense strategies in the CPO algorithm is as follows:

[0098] (1) When the crested porcupine first realizes the existence of alien species, it activates the first defense strategy. At this time, for the crested porcupine, the alien species has two possibilities: continue to approach or stay away. If mathematical methods are used to simulate these two situations, the normal distribution can be used to generate random values ​​and judge the size. If the absolute value is less than 1, the crested porcupine will continue to approach, otherwise it will stay away. The mathematical model is as follows:

[0099]

[0100] In formula (14): are the positions of the i-th individual at iteration t and t+1 respectively; τ 1 , τ 2They are normally distributed random numbers and random values ​​in the interval [0, 1] respectively; is the best solution obtained; Represents the vector generated between the current individual and the random individual;

[0101] (2) When the alien species approach to a certain extent, the second defense strategy is launched. The crested porcupine starts to make noise to warn the alien species, and the sound will increase as the distance shortens. The mathematical model is as follows:

[0102]

[0103] In formula (15): r 1 、r 2 are two random positive integers in [1, N]; U 1 are the three possible situations in the simulation strategy; τ 3 It is a randomly generated value between 0 and 1;

[0104] (3) In order to prevent alien species from approaching further, the crested porcupine will launch a third defense strategy, secreting a foul odor in the surrounding area to warn alien species; the mathematical model is as follows:

[0105]

[0106] In formula (16), δ is the parameter for controlling the direction; γ t It is a defense factor; is the odor diffusion factor;

[0107] (4) If the above three defense strategies fail to prevent the alien species from approaching, the crested porcupine will launch the fourth defense strategy and launch a physical attack on the alien species. The mathematical model is as follows:

[0108]

[0109] In formula (17): α is the convergence factor; F is the average force of CP on the i-th alien species;

[0110] Support Vector Machine Regression Model (SVR)

[0111] The SVR model is based on structural risk minimization and solves nonlinear problems with high dimensions and few samples. Compared with other models, the SVR model has faster convergence efficiency and is more effective in handling multivariate function estimation problems.

[0112] The principle of the SVR model is as follows: The decision function expression of the SVR regression model is:

[0113] μ k (t) = A k (t)cos(φ k(t)) (18)

[0114]

[0115] In formula (19), D(f) is the optimal linear regression plane; C is the penalty factor; R ε is the ε control error function; the optimization problem can be simplified as:

[0116]

[0117] In formula (20): is a regularization term used to control the complexity of the model; C is a regularization parameter used to balance the complexity of the model and the training error; ξ j , is the relaxation factor; W T is the hyperplane coefficient vector; is the nonlinear mapping function; b is the bias;

[0118] The Lagrange equation and duality theory are used to transform equation (20) into the following formula:

[0119]

[0120] The optimal solution can be expressed as:

[0121]

[0122] In formula (22), x is the input feature vector; x j is the support vector in the training set; a r , is the Lagrange multiplier used to control the influence of the support vector; K(x r , x j ) is the kernel function, which is used to map the input data into a high-dimensional space;

[0123] S7.3 Construction of CPO-SVR surrogate model

[0124] The specific steps are as follows:

[0125] S7.3.1 Select 60 sets of sample data obtained by optimal Latin hypercube sampling, randomly select 50 sets of samples as training sets, and the remaining 10 sets of samples as test sets. Use the mapminmax program in Matlab to normalize the inputs of the training set and the test set, and name the normalization method inputs. Similarly, normalize the outputs of the training set and the test set, and name the normalization method outputs.

[0126] S7.3.2 Set the parameters of the CPO optimization algorithm, including the number of CPs, the number of iterations, the number of parameters to be optimized, the upper and lower limits of the parameters to be optimized, and the fitness function. Define the fitness function fitSVM: use 5-fold cross validation, use radial basis function (RBF) as the kernel function of SVM, set the penalty parameter C of SVM, the parameter gamma of the RBF kernel, and specify the type of SVM as epsilon-SVR (regression type);

[0127] S7.3.3 Use the libsvmtrain function to train the SVR model and perform cross-validation. The regularization parameter C of the SVM and the parameter gamma of the RBF kernel are determined by the best position obtained by the CPO algorithm.

[0128] S7.3.4 Use the trained SVR model to predict the training set and the test set, and use the mapminmax function to denormalize the prediction results from the normalized state to obtain the predicted values ​​of the original data;

[0129] S7.3.5 Utilization of the coefficient of determination R 2 The root mean square error (RMSE) is used to test the model training accuracy. If the accuracy meets the requirements, continue training. If not, retrain the network.

[0130] S7.3.6 When the accuracy of the training set model meets the requirements, the model parameters are imported in the same way as in S7.3.4, combined with the test set data to obtain the model output, and the model output is denormalized to obtain the predicted value of the test set;

[0131] S7.3.7 is the same as S7.3.5. Check the model. If the accuracy requirement is met, the training ends. Otherwise, return to S7.3.1 to retrain the network.

[0132] S7.4CPO-SVR model accuracy test

[0133] The root mean square error (RMSE) and the coefficient of determination (R 2 ) to test the accuracy of the neural network, and the specific implementation is as follows:

[0134]

[0135] In formulas (23)-(24), RMSE represents the root mean square error, m3 represents the number of samples tested, and y i and Represent the true value and predicted value of the i-th group of samples, R 2 represents the coefficient of determination, Represents the average value of the samples in group m3; RMSE is required to be less than 0.2, R 2If it is greater than 0.8, it means that the accuracy of model training meets the requirements and is determined to be an available model.

[0136] The combination of the crested porcupine optimization algorithm (CPO) and the support vector machine (SVR) can effectively improve the performance of SVR. The crested porcupine optimization algorithm can help optimize the key parameters of SVR. There are some important parameters in SVR, such as penalty parameters and kernel function parameters. These parameters have a great influence on the regression accuracy of SVR. The crested porcupine optimization algorithm is used to find the optimal combination of these parameters. The specific combination process is as follows: First, the parameters of SVR are used as the search object of the crested porcupine optimization algorithm. Initialize a group of porcupine individuals, each of which represents a set of SVR parameters. Then use the iterative mechanism of the crested porcupine optimization algorithm to move and update these individuals in the parameter space. In each iteration, the parameters represented by the current individual are used to build the SVR model, and the performance of the model is evaluated based on the given data set (such as evaluating the mean square error through cross-validation, etc.). The individuals are ranked according to their performance, and individuals with good performance are more likely to guide the search direction. After multiple iterations, the parameter combination that optimizes the SVR performance is finally found, thereby constructing a more efficient combination model for data regression analysis. The basic flow chart of the CPO-SVR agent model is shown below. Fig.11 shown.

[0137] Preferably, step S8 is as follows: on the premise that the accuracy of the CPO-SVR model constructed in S7 meets the requirements, combine it with the Hippo optimization algorithm to seek the optimal response and the optimal values ​​of its corresponding structural parameters within the feasible domain;

[0138] The algorithm of the Hippopotamus optimization algorithm simulates the position updates, defense strategies against predators, and avoidance methods of hippos in rivers or ponds;

[0139] (1) In the initialization phase, the hippopotamus are candidate solutions to the optimization problem, which means that the position of each hippopotamus in the search space is updated to represent the value of the decision variable; the vector formula for generating the decision variable is:

[0140] X(:,i)=X min (i)+r 1 ×(X max (i)-X min (i)) (25)

[0141] In formula (25), X(:,i) represents the position of the i-th candidate solution; r 1 represents a random number in the interval [0,1]; X min (i) X max (i) represents the lower and upper limits of the i-th decision variable;

[0142] (2) Exploration phase In the optimization process of this study, the exploration is divided into two phases; Exploration phase 1: The position of hippos in the river or pond is updated: hippos tend to gather close to each other, and the dominant hippo is determined iteratively based on the objective function value; the position formula of male hippos in the group is:

[0143] X_P 1 (i,:)=X(i,:)+r 2 ×(D hippo -I 1 X(i,:)) (26)

[0144] In formula (26): X_P 1 (i,:) indicates the position of the male hippopotamus; D hippo Indicates the position of the dominant male hippopotamus; r 2 is a random number in the interval [0, 1]; I 1 Represents a random number in the interval [1, 2];

[0145] When the juvenile hippopotamus is far away from the mother hippopotamus, the position update formula of male and female or juvenile hippopotamus in the group is:

[0146]

[0147] In formula (27): X_P 2 (i,:) indicates the position of female or juvenile hippopotamus in the group; r 5 represents a random vector; MG i represents the average value of randomly selecting some hippos; T represents the selection probability; I 2 Represents a random number in the interval [1, 2];

[0148] Exploration Stage 2 Hippopotamus defending against predators: When a hippopotamus is attacked by a predator or other creatures invading its territory, it triggers a defensive response, using their terrifying jaws to make sounds to deter and repel the attacker; the location of the predator or other creature invading the hippopotamus' territory is:

[0149]

[0150] In formula (28): X_P 3 (i,:) indicates the location of a predator or other organism invading the hippopotamus’ territory; represents a random vector with Levy distribution, which is used to describe the mutation of the predator position when attacking hippopotamus; predator j Represents the position of the predator in the search space; represents the distance from the i-th hippopotamus to the predator; b, c, d, and g all represent uniformly distributed random numbers, but their value ranges are different. The value range of b is [2, 4], the value range of c is [1, 1.5], the value range of d is [2, 3], and the value range of g is [2, 4]; r 9 is a random variable in the interval [-1,1]; Factors that cause hippos to adopt defensive behaviors to protect themselves from predators; F i is the objective function value;

[0151] (3) Hippos escape from predators during the development phase: Warnings are ineffective. Lone, sick, and immature hippos are easily attacked by predators. Hippos seek to stay away from predators. The safe locations that hippos search for in order to find the nearest safe place are:

[0152]

[0153] In formula (29): X_P 4 (i,:) indicates searching for the hippopotamus's location to find the nearest safe place; r 10 Represents a random number in the interval [0, 1]; r 11 Represents a random number that conforms to the normal distribution; t is the current iteration number;

[0154] The specific steps for seeking the optimal response and the optimal values ​​of its corresponding structural parameters are as follows:

[0155] S8.11 Set the total number of hippo populations, the maximum number of iterations, the problem dimension, and the upper and lower bounds of the parameters;

[0156] S8.12 Use formula (25) to initialize the initial position of each hippopotamus. The position is usually randomly initialized within the constraints of the problem.

[0157] S8.13 uses the CPO-SVR agent model as the objective function to minimize and evaluates the fitness of each hippopotamus according to its position;

[0158] S8.14 updates the position of the hippopotamus, determines the dominant hippopotamus according to the fitness value of the objective function, that is, finds the current optimal solution, and uses formula (26) to update the position of male hippopotamus and tend to move closer to the dominant male hippopotamus. Use formula (27) to update the position of female and juvenile hippopotamus, which depends on the average position of some randomly selected hippopotamus in the group, and is simulated in the algorithm by moving towards the local optimal solution;

[0159] S8.15 When a predator or other creature invades the hippopotamus's territory, the hippopotamus will trigger a defensive response and use formula (28) to update its position; S8.16 If the warning is ineffective, the hippopotamus will look for the nearest safe place to escape the predator and use formula (29) to update its position. In the algorithm, this can be achieved by randomly moving to other areas of the search space to avoid local optimality;

[0160] S8.17 The algorithm repeats the above steps until the maximum number of iterations or other termination conditions are reached;

[0161] At the end of S8.18 algorithm, the position of the hippopotamus with the highest fitness and the current value of each factor are output as the optimal solution to the problem.

[0162] Compared with the prior art, the advantages of the optimization method in this patent are: first, the PBD test table is designed through Design-Expert and the significance analysis module of the software is used. The structural parameters of the multi-angular PDC teeth are used as design variables, and the crushing specific energy, average cutting force, impact force peak and energy absorption peak are used as optimization targets. The structural parameters that have a significant impact on the PDC tooth structure are obtained through significance analysis. The significance analysis can simplify the model, reasonably allocate resources, improve prediction accuracy, and clarify the key points. On this basis, the proxy model is further fitted, the structural parameters with significant influence are used as design variables, and the crushing specific energy, average cutting force, impact force peak and energy absorption peak are used as optimization targets. The CPO-SVR model is used for training and prediction. Under the premise that the accuracy meets the requirements, the Hippo optimization algorithm is combined with the constructed CPO-SVR model to find the structural parameter combination under the optimal response. After optimizing the structural parameters of the multi-angular PDC teeth, a set of comprehensive optimization solutions with high cutting efficiency and strong impact resistance can be finally obtained. This patent combines software and algorithms to perform numerical simulation and optimization on the designed multi-angular conformal PDC tooth structural parameters, which has a guiding role in the PDC tooth structure optimization process.

[0163] The present invention proposes a new idea for optimizing the structure of multi-angular conformal PDC teeth.

[0164] The invention is based on the optimization targets of the crushing specific work, average cutting force, impact force peak and energy absorption peak of the PDC tooth in the process of single-edged disc cutter rock breaking of the shield machine, selects the designed 5 structural parameters as design variables, establishes a PBD test table, and uses Abaqus software to simulate the sample data to obtain the response value, and then uses Design-Expert software to obtain the influence of each design factor on the four responses. After determining the design factors with significant influence, the sample data required by the CPO-SVR model is obtained, and the sample data is obtained by the optimal Latin hypercube sampling method, and the Abaqus software is used to simulate it to obtain the response value. In view of the complexity of the multi-response problem, the gray correlation analysis combined with the entropy weight method is used to convert the multi-response into the corresponding gray correlation degree. The CPO-SVR model is constructed in Matlab, and the "black box" model between the input structural parameters and the corresponding gray correlation degree is constructed by training the model. Under the premise that the model accuracy meets the requirements, the optimal structural parameters in the feasible domain are obtained by using the Hippo optimization algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0165] Figure 1 This is the overall flow chart of this method;

[0166] Figure 2 This is a three-dimensional model diagram of a multi-angular conformal PDC tooth;

[0167] Figure 3 It is a schematic diagram of the combination of multi-angle conformal PDC teeth and single-edge disc cutter;

[0168] Figure 4 This is the PBD test table A;

[0169] Figure 5 This is a schematic diagram of the motion trajectory of the disc cutter breaking rock;

[0170] Figure 6 It is a cutting simulation model;

[0171] Figure 7 is the cutting force-time curve;

[0172] Figure 8 It is an impact simulation model;

[0173] Fig. 9 It is the impact force curve and energy absorption curve;

[0174] Fig.10 is the experimental table B formed after optimal Latin hypercube sampling;

[0175] Fig.11 This is the flow chart of the CPO-SVR model;

[0176] Fig.12 Flowchart of the Hippo optimization algorithm. DETAILED DESCRIPTION

[0177] The optimization method of the multi-angular conformal PDC tooth structural parameters is described in detail below with reference to the accompanying drawings.

[0178] Example 1: See Figure 1 , an optimization method for the structural parameters of multi-angular conformal PDC teeth, Figure 1 The method is a simplified flow chart, which includes the following steps:

[0179] S1: Preliminarily determine the structural parameters that need to be optimized for the multi-angular conformal PDC teeth, and implement parametric modeling in the 3D design software based on the structural parameters;

[0180] S2: Based on the value range of the structural parameters, the PBD test design is performed in the Design-Expert software to establish the test table A, M groups of test data combinations are obtained, several performance parameters of the tooth are determined as responses, and several response columns are reserved in the test table A;

[0181] S3: According to several groups of test data combinations in the experimental table, three-dimensional models of different PDC teeth are established in the three-dimensional design software, and imported into the simulation software for simulation, so as to obtain several response data corresponding to each test data combination, fill in the response column in the test table A, and improve the test table A;

[0182] S4: The structural parameters in the improved experimental table A are used as design factors, and the response is used as the optimization target. A significance analysis is performed in the Design-Expert software to obtain some key structural parameters that have a significant impact on the response.

[0183] S5: Perform optimal Latin hypercube sampling on the key structural parameters in step S4 to obtain N groups of test data, and form experimental table B, reserving several response columns;

[0184] S6: Import the N groups of test data in S5 into the simulation software for simulation, obtain the response corresponding to each group of test data and complete the experimental table B.

[0185] S7: Import the data of experimental table B improved in S6 into Matlab, complete the training and prediction of sample data through the CPO-SVR proxy model, train an effective proxy model and determine it;

[0186] The surrogate model is a commonly used tool in complex system analysis and optimization. It constructs a relatively simple model by sampling or training the original complex system. This surrogate model can approximately reflect the input-output relationship of the original system to a certain extent.

[0187] S8: The CPO-SVR proxy model determined in S7 is used as the fitness function in the Hippo optimization algorithm. The Hippo optimization algorithm program is written by Matlab to optimize and solve the fitness function. In the feasible domain, the corresponding value combinations of each structural parameter under the optimal response are found respectively, and the analysis results of the CPO-SVR proxy model are verified and optimized, and finally the optimal structural parameter combination is obtained.

[0188] The optimization algorithm is to find the optimal solution of the objective function through continuous iterative search, which mainly includes determining the objective function, setting the initial solution, iterative search, etc. By combining the proxy model with the optimization algorithm, it not only overcomes the difficulty of directly dealing with complex systems, but also can efficiently find solutions that meet the optimization goals.

[0189] Example 2, see Figure 1-12 Embodiment 2 is a further refinement of Embodiment 1. Embodiment 2 is a method for optimizing the structural parameters of a multi-angular conformal PDC tooth. Figure 1 The overall flow chart of the method is as follows:

[0190] S1: Preliminarily determine the required optimized structural parameters of the multi-angular conformal PDC teeth, and implement parametric modeling in the 3D design software based on the structural parameters;

[0191] This method designs multi-angle conformal PDC teeth, see Figure 2 , and determine the angle between the main bevels on both sides of the designed tooth top transverse ridge as the ridge angle, the radius of the arc of the transverse ridge as the fillet, the distance between the lower end of the side edge and the tooth bottom surface as the edge angle height, the angle between the side bevels on both sides of the side edge as the edge angle, and the angle between the side edge and the tooth bottom surface plane as the side angle as five structural parameters, determine the value range of each of the above structural parameters, and then model in the 3D design software Solidworks, and name each parameter in the form of "=DS_" to achieve parametric modeling, then convert the completed 3D model into XT format in Solidworks. In the process of modeling and format conversion, other 3D modeling software with the same function can also be used.

[0192] According to the use scenarios and current problems of single-edged disc cutters of shield machines, the design goal is to improve the service life and cutting efficiency of the cutters, design PDC teeth and reasonably embed them on the cutters, see Figure 3, improve the service life and cutting efficiency of the hob, design the PDC teeth by consulting the data and factory experience, design the multi-angle conformal PDC teeth with extended service life and improved cutting efficiency, and determine the size range of the PDC teeth; in this embodiment, the ridge angle, fillet, edge height, edge and side angle of the PDC teeth are used as size parameters, and they are named in the form of "=DS_" in the Solidworks sketch interface, and the equation is found in the tool above. Different PDC tooth models can be generated by entering different parameters in the equation, thereby realizing parametric modeling and improving modeling efficiency.

[0193] S2: Based on the value range of the structural parameters, the PBD test design is performed in the Design-Expert software to establish the test table A, and M groups of test data combinations are obtained. Several performance parameters of the teeth are determined as responses, and several response columns are reserved in the test table A, see Figure 4 ;

[0194] In order to investigate the influence of ridge angle, fillet, edge height, edge and side angle on crushing specific energy, average cutting force, impact force peak and energy absorption peak, the five factors of ridge angle, fillet, edge height, edge and side angle in the multi-angular conformal PDC tooth structure were taken, and the upper and lower limits of their value range were determined by consulting papers and based on factory experience.

[0195] The five structural parameters of the multi-angular conformal PDC tooth structure are taken as five factors, namely ridge angle A, fillet B, edge height C, edge angle D and side angle E, and the upper and lower limits of their value range are determined. PBD test design is carried out in the Design-Expert software to establish test table A, and M=12 groups of test data are obtained. Four response columns are set in test table A; the four performance parameters of the multi-angular conformal PDC tooth, namely crushing specific energy, average cutting force, impact force peak and energy absorption peak, are determined as responses.

[0196] S3: According to several groups of test data combinations in the experimental table, three-dimensional models of different PDC teeth are established in the three-dimensional design software, and imported into the simulation software for simulation, so as to obtain several response data corresponding to each test data combination, fill in the response column in the test table A, and improve the test table A;

[0197] According to the test data combination of S2 test table A, various structural parameters are modified in Solidworks according to the requirements of each data combination to generate different PDC teeth, and the PDC tooth three-dimensional model is converted into XT format and imported into ABAQUS software for cutting simulation and impact simulation to obtain the crushing specific energy, average cutting force, impact force peak value and energy absorption peak value under each data combination; its sub-steps are as follows:

[0198] S3.0 generates different 3D models of PDC teeth in Solidworks according to the result parameters of experimental table A, and converts the 3D models of PDC teeth into XT format;

[0199] S3.1 Establish a cutting simulation model, import the XT format files of each PDC tooth 3D model, and obtain the crushing specific energy and average cutting force under each data combination, see Figure 6 ;

[0200] In the rock breaking process, the disc cutter moves in rotation around the center axis of the cutter disc and in linear motion in the forward direction. The PDC cutting teeth on the disc cutter make a spiral motion in the forward direction. However, the cutting depth of the disc cutter is small, that is, the cutting depth of a single PDC cutting tooth is small, and the helix angle of one rotation is very small. Therefore, the rotational motion of a single PDC cutting tooth is simplified to a linear motion of a fixed cutting depth. Figure 5 ;

[0201] The crushing specific energy (MSE) is used to characterize the energy required to crush a unit volume of rock. The smaller the MSE, the less energy is required to crush a unit volume of rock, and the higher the efficiency of the PDC cutter in crushing rocks. Therefore, the crushing specific energy in the stable cutting stage is taken as the response. The crushing specific energy can be calculated according to the following formula:

[0202]

[0203] In formula (1), V is the total rock crushing volume, F is the cutting force, ds is the length of the cutting stage, v is the cutting speed, and dt is the time of the cutting stage;

[0204] Cutting force is used to characterize the difficulty of PDC cutting teeth in breaking rocks. The smaller the cutting force required to break rocks, the easier it is to break them. Since the cutting force fluctuates during the cutting process, the average cutting force in the stable cutting stage is taken as the response.

[0205] In summary, a simulation of limestone cutting by a single multi-angular conformal PDC tooth is established to obtain its crushing specific energy and average cutting force, so as to judge the cutting performance of PDC teeth with different parameters.

[0206] S3.1.1 Input model

[0207] The XT format of the PDC tooth model generated by S3 parametric modeling was imported into ABAQUS. Considering the model size and calculation efficiency, a finite element model of a single multi-angular conformal PDC tooth cutting limestone was established. The size of the limestone model was 50mm×50mm×20mm.

[0208] S3.1.2 Setting properties

[0209] The material of the PDC layer is polycrystalline diamond, and its density is 3520kg / m 3 , elastic modulus 8.9E+5Mpa, Poisson's ratio 0.07; rock material is limestone, density 2500kg / m 3 , elastic modulus 40000Mpa, Poisson's ratio 0.4;

[0210] S3.1.3 Create an assembly and set up analysis steps

[0211] After the material properties are set, the model needs to be assembled and the cutting depth of the multi-angular conformal PDC teeth is set to 2 mm;

[0212] Set the analysis step to dynamic explicit general, set the whole cutting process to 0.16s to improve the analysis efficiency, and keep the rest as default settings;

[0213] S3.1.4 Setting up interactions and loads

[0214] Set the interaction properties, set the friction formula in the tangential behavior to penalty, the friction coefficient to 0.3, and the rest to default settings; select the pressure interference in the normal behavior as hard contact, and the rest to default settings; set the multi-angle conformal PDC tooth to rigid body, and the contact type to general contact;

[0215] Set the load, completely fix the limestone base layer, convert the shield machine cutter head rotation speed into linear speed, and set the cutting speed of the multi-angle conformal PDC teeth;

[0216] S3.1.5 Grid division

[0217] The overall mesh size of the limestone is set to 5 mm, and the cutting part further refines the mesh to 0.5 mm. The PDC teeth are set as rigid bodies and will not deform, so the mesh size is set to 1.5 mm to speed up the analysis process;

[0218] After completing the above pre-processing, simulation is performed. After completing the simulation, post-processing is performed and the data is imported into the origin software for curve drawing to obtain the cutting force-time curve. Figure 7 , the crushing specific energy and average cutting force are calculated in the stable cutting stage;

[0219] S3.2 Establish an impact simulation model, import the XT format files of each PDC tooth three-dimensional model, and obtain the impact force peak value and energy absorption peak value under each data combination. Figure 8; As the shield machine cutterhead rotates, the disc cutter moves in a circular motion at a certain speed; when the cutter contacts the rock, the kinetic energy it carries will be released instantly, forming impact energy and generating a large impact force, causing the PDC cutting teeth on the cutter to crack and break, so the analysis of the impact force is particularly important; Energy absorption usually refers to the ability of a material to absorb and dissipate energy when it is impacted or pressurized; for PDC teeth, their energy absorption characteristics are mainly reflected in impact resistance and wear resistance. The energy absorption characteristics of PDC teeth are a key factor in their design and application, and directly affect the efficiency and life of PDC teeth; In summary, a simulation of an impact block impacting a single multi-angular conformal PDC tooth is established to obtain the impact force peak value and energy absorption peak value, so as to judge the advantages and disadvantages of the impact resistance of PDC teeth with different parameters;

[0220] S3.2.1 Input model

[0221] After the three-dimensional models of the PDC layer and cemented carbide substrate of the PDC tooth generated by S3 parametric modeling were assembled in SoildWorks, they were converted into XT format and imported into ABAQUS;

[0222] S3.2.2 Setting properties

[0223] The material of the PDC layer is polycrystalline diamond, and its density is 3520kg / m 3 , elastic modulus 8.9E+5Mpa, Poisson's ratio 0.07, compressive strength 7600Mpa. Since the strain of polycrystalline diamond before fracture is very small, in order to make the simulation results more obvious, the plastic strain is set to 1 after reaching the compressive strength limit; the impact block material used in the simulation analysis is steel with a density of 7850kg / m 3 , elastic modulus 200Gpa, Poisson's ratio 0.3;

[0224] S3.2.3 Create an assembly and set up analysis steps

[0225] After the material properties are set, the model needs to be assembled. To ensure the analysis efficiency, the distance between the impact block and the multi-angular conformal PDC tooth is set to 0, that is, the distance between the two when the impact is about to occur;

[0226] Set the analysis step to Dynamic Explicit General. The impact force reaches the maximum value in a very short time. Therefore, set the entire test collision process to 5E-04s to improve the analysis efficiency. The rest are set to default.

[0227] S3.2.4 Setting up interactions and loads

[0228] Set the interaction properties. In the tangential behavior, the friction formula is set to penalty, the friction coefficient is 0.3, and the rest are set by default. In the normal behavior, the pressure interference is selected as hard contact, and the rest are set by default. Set the impact block to rigid body, and the contact type is general contact.

[0229] Set the load, completely fix the hard base part of the multi-angle conformal PDC tooth, and then set the impact block speed according to the impact work of 750J;

[0230] S3.2.5 Grid division

[0231] The PDC layer is the main impact part, and the mesh size is set to 1.2mm. The fillet and corner parts are further refined and set to 0.5-0.8mm. The mesh size of the hard matrix part is reduced to speed up the analysis process; the impact block is set as a rigid body and will not deform, so the mesh size is set to 5mm to speed up the analysis process;

[0232] After completing the above pre-processing, simulation is performed. After completing the simulation, post-processing is performed and the data is imported into the origin software for curve drawing. The obtained impact force curve and energy absorption curve are shown in Figure 2. Fig. 9 , the peak impact force and peak energy absorption are calculated.

[0233] S4: The structural parameters in the improved experimental table A are used as design factors, and the response is used as the optimization target. A significance analysis is performed in the Design-Expert software to obtain some key structural parameters that have a significant impact on the response.

[0234] The five factors of ridge angle, fillet, edge height, edge and side angle in the multi-angle conformal PDC tooth structure are taken as design factors, and the crushing specific energy, average cutting force, impact force peak and energy absorption peak are taken as optimization targets. The 12 groups of data obtained in S3 are imported into the Plackett-Burmans module in the Design-Expert software, and the test data are analyzed for significance to obtain the significance test results. The significance results are measured by the size of the p value. The p value of the first and second terms of the variable is observed. If the p value is less than 0.05, it means that the factor represented by this variable has a significant effect on the test results. Otherwise, the factor has no obvious effect on the response target. After the analysis is completed, the design factors that have significant influence on the crushing specific energy, average cutting force, impact force peak and energy absorption peak among the five factors are ridge angle, fillet, edge and side angle, which are determined as key structural parameters.

[0235] In parameter optimization, significance analysis plays an important role in screening key parameters: it can help determine which of the many parameters have a significant impact on the target performance, thereby screening out the key parameters that need to be optimized and avoiding wasting too much energy on unimportant parameters; parameter optimization refers to the process of adjusting and improving relevant parameters through a series of methods in a specific system, model or process to achieve better performance, effects or meet specific goals.

[0236] S5: The key structural parameters in step S4 are subjected to optimal Latin hypercube sampling to obtain N groups of test data, and form experimental table B, reserving several response columns, see Fig.10 ;

[0237] Obtain sample data, and obtain the structural parameters with significant influence, such as ridge angle, fillet, edge angle and side angle, according to the significance analysis in S4. On this basis, perform optimal Latin hypercube sampling, select DOE module and EXCEL module in Isight software, and connect the two together, add the four columns A, B, D, and E in EXCEL to DOE, and select optimal Latin hypercube sampling in DOE. According to the empirical formula, determine the sampling number as 60, and then click Generate to obtain the sampling table, and obtain N=60 groups of test data; form experimental table B.

[0238] S6: Import the N groups of test data in S5 into the simulation software for simulation, obtain the response corresponding to each group of test data and complete the experimental table B.

[0239] In ABAQUS software, the scheme combinations in the S5 sampling table are subjected to cutting simulation and impact simulation according to step S3 to obtain the four response data of each group, which are filled into the corresponding columns in the table to complete the test table B and prepare for the subsequent construction of the CPO-SVR proxy model.

[0240] S7: Import the data of experimental table B improved in S6 into Matlab, complete the training and prediction of sample data through CPO-SVR proxy model, train an effective proxy model and determine it, see Fig.11 ;

[0241] Specifically, the simulation data obtained in S6 are subjected to grey correlation analysis to construct the CPO-SVR proxy model. The 60 data sets are divided into 50 training sets and 10 test sets. The CPO-SVR proxy model is used to complete the training and prediction of the data. The root mean square error (RMSE) and the determination coefficient (R) are used to calculate the predicted value. 2 Verify the model validity and proceed to the next step if the model is valid;

[0242] S7.1 Grey correlation analysis

[0243] Grey relational analysis is to judge whether the connection is close according to the similarity of the geometric shapes of sequence curves. The closer the curves are, the greater the grey relational degree between the corresponding sequences. This method can be used for correlation analysis between factors and responses in the system, and can also be used for comprehensive evaluation. Considering the complexity of solving multi-objective response problems, grey relational analysis is introduced to convert multi-response problems into corresponding grey relational degrees, and the size of the grey relational degree can be used as the model output to judge the quality of the response.

[0244] S7.1.1 Normalize the raw data

[0245] Since the responses are not of the same type, the test response values ​​need to be normalized to between [0,1]; the smaller the crushing specific energy and average cutting force, the better, while the larger the impact force and energy absorption, the better. The peak impact force and energy absorption peak can be turned into negative numbers, so they can be normalized using formula (1);

[0246]

[0247] In formula (2), B ik It represents the normalized response value of the i-th group test when the index is k, where k=1 means the index is the crushing specific energy, k=2 means the index is the average cutting force, k=3 means the index is the impact force peak, k=4 means the index is the energy absorption peak, L k represents all test response values ​​with index k, L ik It indicates the test response value of group i when the index is k;

[0248] S7.1.2 Determine the reference sequence

[0249] Use B 0k It represents the reference sequence, which means the optimal value obtained when the indicator k is sampled. The first two indicators in this paper are as small as possible, so the reference sequence is the minimum response value corresponding to each indicator. After normalization, B is obtained. 0k ={1,1}, the latter two indicators are as large as possible, so the reference sequence is the maximum response value corresponding to each indicator, and B is obtained after normalization. 0k ={0,0};

[0250] S7.1.3 Calculation of grey correlation coefficient

[0251] The specific steps are as follows:

[0252] Δ ik =|B 0k -B ik | (3)

[0253]

[0254]

[0255] In formulas (3)-(6), Δ ik Indicates the deviation sequence of the index k, the i-th group of experiments; Δ min It means to search for the deviation sequence by k, where k = 1, 2, 3, 4, and then search by i, where i = 1, 2, 3...n1, n1 is the optimal Latin hypercube sampling number, which is 60, and get the minimum value Δ of the deviation sequence min ; Δ max It means that the deviation sequence is first searched by k, and then searched by i to obtain the maximum value Δ of the deviation sequence max ;μ ik It indicates the grey correlation coefficient of the i-th group of data when the index is k, ξ indicates the resolution coefficient, which is usually taken as 0.5;

[0256] S7.1.4 Determine the weight of each response using the entropy weight method

[0257] The entropy weight method determines the objective weight of each indicator based on the variability of the indicator. The smaller the information of the indicator, the greater the degree of variability, the greater the role it can play in the comprehensive evaluation, and the greater its weight.

[0258] The specific calculation process is as follows:

[0259]

[0260] D k =1-e k (9)

[0261]

[0262] In formulas (7)-(10), the k-th index represents the proportion of the i-th group of tests, which is the normalized data calculated by formula (2); k is the information entropy of indicator k. The smaller the information entropy, the greater the discrete degree of the indicator, and the greater the objective weight of the indicator. In addition, because we need to calculate lnp ik , if B ik is 0, then P ik The computer cannot calculate it because it is 0. Therefore, the translation method is used. For the indicator column that appears 0 during the normalization process, a translation amount is added to the column data at the same time. The translation amount is the absolute value of the minimum value of the column data plus 0.01, and the new B is obtained. ik , which can solve this problem; D k is the information redundancy of index k; m2 is the number of indicators, which is 4; w k is the weight of indicator k;

[0263] S7.1.5 Calculation of grey relational degree

[0264] Convert each group of response values ​​into the corresponding grey correlation degree. The higher the grey correlation degree, the more it meets the requirements. The calculation process is as follows:

[0265]

[0266] In formula (11), h ik Indicates that the index is k, the grey relational degree corresponding to the i-th group of experiments, m2 is the number of indicators, which is 4; W k represents the objective weight of indicator k, U ik The index is k, and the grey correlation coefficient corresponding to the i-th group of experiments;

[0267] S7.2 Construction of CPO-SVR surrogate model

[0268] The crown porcupine optimization algorithm (CPO), similar to most meta-heuristic swarm algorithms, has an initial population search process as follows:

[0269]

[0270] In formula (12): X i is the i-th solution to be selected in the search space; L, U are the lower and upper limits of the search range; r is a random number between 0 and 1; N is the population size;

[0271] The CPO algorithm uses the cyclic population reduction technique (CPR). The mathematical model of cyclic reduction is as follows:

[0272]

[0273] In formula (13): N min is the minimum number of newly generated populations, t is the current function evaluation, T is the number of cycles, and T max is the maximum number of function evaluation loops, % is the remainder or modulus operator;

[0274] In order to ensure the diversity of the population while accelerating the convergence speed, the CPO algorithm adopts the cyclic population reduction technology (CPR); this strategy borrows a concept: not all crested porcupines (CP) in the population will actively activate the defense mechanism, and these mechanisms will be activated only when they feel threatened; based on this, the CPR strategy selects some CPs from the population during the optimization process to accelerate the convergence speed, and puts these CPs back into the population to enhance diversity and prevent falling into the local optimal solution.

[0275] The CPO algorithm is inspired by the various defensive behaviors of crested porcupines in nature, which include four different protection mechanisms: vision, hearing, smell and physical attack, to identify the aggressiveness of alien species; among them, vision and hearing are also called the first and second defense strategies, and they also reflect the exploration behavior in the CPO algorithm; smell and physical attack are also called the third and fourth defense strategies, reflecting the utilization behavior in the CPO algorithm; the entire CPO algorithm uses the above four defense strategies to work together in practical applications to ensure the optimality of the final result.

[0276] The entire optimization process of the four defense strategies in the CPO algorithm is as follows:

[0277] (1) When the crested porcupine first realizes the existence of alien species, it activates the first defense strategy. At this time, for the crested porcupine, the alien species has two possibilities: continue to approach or stay away. If mathematical methods are used to simulate these two situations, the normal distribution can be used to generate random values ​​and judge the size. If the absolute value is less than 1, the crested porcupine will continue to approach, otherwise it will stay away. The mathematical model is as follows:

[0278]

[0279] In formula (14): are the positions of the i-th individual at iteration t and t+1 respectively; τ 1 , τ 2 They are normally distributed random numbers and random values ​​in the interval [0, 1] respectively; is the best solution obtained; Represents the vector generated between the current individual and the random individual;

[0280] (2) When the alien species approach to a certain extent, the second defense strategy is launched. The crested porcupine starts to make noise to warn the alien species, and the sound will increase as the distance shortens. The mathematical model is as follows:

[0281]

[0282] In formula (15): r 1 、r 2 are two random positive integers in [1, N]; U 1 are the three possible situations in the simulation strategy; τ 3 It is a randomly generated value between 0 and 1;

[0283] (3) In order to prevent alien species from approaching further, the crested porcupine will launch a third defense strategy, secreting a foul odor in the surrounding area to warn alien species; the mathematical model is as follows:

[0284]

[0285] In formula (16), δ is the parameter for controlling the direction; γ t It is a defense factor; is the odor diffusion factor;

[0286] (4) If the above three defense strategies fail to prevent the alien species from approaching, the crested porcupine will launch the fourth defense strategy and launch a physical attack on the alien species. The mathematical model is as follows:

[0287]

[0288] In formula (17): α is the convergence factor; is the average force of CP on the i-th alien species;

[0289] Support Vector Machine Regression Model (SVR)

[0290] The SVR model is based on structural risk minimization and solves nonlinear problems with high dimensions and few samples. Compared with other models, the SVR model has faster convergence efficiency and is more effective in handling multivariate function estimation problems.

[0291] The principle of the SVR model is as follows: The decision function expression of the SVR regression model is:

[0292] μ k (t) = A k (t)cos(φ k (t)) (18)

[0293]

[0294] In formula (19), D(f) is the optimal linear regression plane; C is the penalty factor; R ε is the ε control error function; the optimization problem can be simplified as:

[0295]

[0296] In formula (20): is a regularization term used to control the complexity of the model; C is a regularization parameter used to balance the complexity of the model and the training error; ξ j , is the relaxation factor; W T is the hyperplane coefficient vector; is the nonlinear mapping function; b is the bias.

[0297] The Lagrange equation and duality theory are used to transform equation (20) into the following formula:

[0298]

[0299] The optimal solution can be expressed as:

[0300]

[0301] In formula (22), x is the input feature vector; x j is the support vector in the training set; a r , is the Lagrange multiplier used to control the influence of the support vector; K(x r , x j ) is the kernel function, which is used to map the input data into a high-dimensional space.

[0302] The combination of the crested porcupine optimization algorithm (CPO) and the support vector machine (SVR) can effectively improve the performance of SVR. The crested porcupine optimization algorithm can help optimize the key parameters of SVR. There are some important parameters in SVR, such as penalty parameters and kernel function parameters. These parameters have a great influence on the regression accuracy of SVR. The crested porcupine optimization algorithm is used to find the optimal combination of these parameters. The specific combination process is as follows: First, the parameters of SVR are used as the search object of the crested porcupine optimization algorithm. Initialize a group of porcupine individuals, each of which represents a set of SVR parameters. Then use the iterative mechanism of the crested porcupine optimization algorithm to move and update these individuals in the parameter space. In each iteration, the parameters represented by the current individual are used to build the SVR model, and the performance of the model is evaluated based on the given data set (such as evaluating the mean square error through cross-validation, etc.). The individuals are ranked according to their performance, and individuals with good performance are more likely to guide the search direction. After multiple iterations, the parameter combination that optimizes the SVR performance is finally found, thereby constructing a more efficient combination model for data regression analysis. The basic flow chart of the CPO-SVR agent model is shown below. Fig.11 shown.

[0303] S7.3 Construction of CPO-SVR surrogate model

[0304] The specific steps are as follows:

[0305] S7.3.1 Select 60 sets of sample data obtained by optimal Latin hypercube sampling, randomly select 50 sets of samples as training sets, and the remaining 10 sets of samples as test sets. Use the mapminmax program in Matlab to normalize the inputs of the training set and the test set, and name the normalization method inputs. Similarly, normalize the outputs of the training set and the test set, and name the normalization method outputs.

[0306] S7.3.2 Set the parameters of the CPO optimization algorithm, including the number of CPs, the number of iterations, the number of parameters to be optimized, the upper and lower limits of the parameters to be optimized, and the fitness function. Define the fitness function fitSVM: use 5-fold cross validation, use radial basis function (RBF) as the kernel function of SVM, set the penalty parameter C of SVM, the parameter gamma of the RBF kernel, and specify the type of SVM as epsilon-SVR (regression type);

[0307] S7.3.3 Use the libsvmtrain function to train the SVR model and perform cross-validation. The regularization parameter C of the SVM and the parameter gamma of the RBF kernel are determined by the best position obtained by the CPO algorithm.

[0308] S7.3.4 Use the trained SVR model to predict the training set and the test set, and use the mapminmax function to denormalize the prediction results from the normalized state to obtain the predicted values ​​of the original data;

[0309] S7.3.5 Utilization of the coefficient of determination R 2 The root mean square error (RMSE) is used to test the model training accuracy. If the accuracy meets the requirements, continue training. If not, retrain the network.

[0310] S7.3.6 When the accuracy of the training set model meets the requirements, the model parameters are imported in the same way as in S7.3.4, combined with the test set data to obtain the model output, and the model output is denormalized to obtain the predicted value of the test set;

[0311] S7.3.7 is the same as S7.3.5. Check the model. If the accuracy requirement is met, the training ends. Otherwise, return to S7.3.1 to retrain the network.

[0312] S7.4CPO-SVR model accuracy test

[0313] The root mean square error (RMSE) and the coefficient of determination (R 2 ) to test the accuracy of the neural network, and the specific implementation is as follows:

[0314]

[0315] In formulas (23)-(24), RMSE represents the root mean square error, m3 represents the number of samples tested, and y i and Represent the true value and predicted value of the i-th group of samples, R 2 represents the coefficient of determination, Represents the average value of the samples in group m3; RMSE is required to be less than 0.2, R 2If it is greater than 0.8, it means that the accuracy of model training meets the requirements and is determined to be an available model.

[0316] S8: The CPO-SVR proxy model determined in S7 is used as the fitness function in the Hippo optimization algorithm. The Hippo optimization algorithm program is written in Matlab to optimize the fitness function. In the feasible domain, the corresponding value combination of each structural parameter under the optimal response is found respectively. The analysis results of the CPO-SVR proxy model are verified and optimized, and finally the optimal structural parameter combination is obtained. See Fig.12 .

[0317] On the premise that the accuracy of the CPO-SVR model constructed by S7 meets the requirements, it is combined with the Hippo optimization algorithm to seek the optimal response and the optimal values ​​of its corresponding structural parameters in the feasible domain;

[0318] The algorithm of the Hippopotamus optimization algorithm simulates the position updates, defense strategies against predators, and avoidance methods of hippos in rivers or ponds;

[0319] (1) In the initialization phase, the hippopotamus are candidate solutions to the optimization problem, which means that the position of each hippopotamus in the search space is updated to represent the value of the decision variable; the vector formula for generating the decision variable is:

[0320] X(:,i)=X min (i)+r 1 ×(X max (i)-X min (i)) (25)

[0321] In formula (25), X(:,i) represents the position of the i-th candidate solution; r 1 represents a random number in the interval [0,1]; X min (i) X max (i) represents the lower and upper limits of the i-th decision variable;

[0322] (2) Exploration phase In the optimization process of this study, the exploration is divided into two phases; Exploration phase 1: The position of hippos in the river or pond is updated: hippos tend to gather close to each other, and the dominant hippo is determined iteratively based on the objective function value; the position formula of male hippos in the group is:

[0323] X_P 1 (i,:)=X(i,:)+r 2 ×(D hippo -I 1 X(i,:)) (26)

[0324] In formula (26): X_P 1 (i,:) indicates the position of the male hippopotamus; D hippoIndicates the position of the dominant male hippopotamus; r 2 is a random number in the interval [0, 1]; I 1 Represents a random number in the interval [1, 2];

[0325] When the juvenile hippopotamus is far away from the mother hippopotamus, the position update formula of male and female or juvenile hippopotamus in the group is:

[0326]

[0327] In formula (27): X_P 2 (i,:) indicates the position of female or juvenile hippopotamus in the group; r 5 represents a random vector; MG i represents the average value of randomly selecting some hippos; T represents the selection probability; I 2 Represents a random number in the interval [1, 2];

[0328] Exploration Stage 2 Hippopotamus defending against predators: When a hippopotamus is attacked by a predator or other creatures invading its territory, it triggers a defensive response, using their terrifying jaws to make sounds to deter and repel the attacker; the location of the predator or other creature invading the hippopotamus' territory is:

[0329]

[0330] In formula (28): X_P 3 (i,:) indicates the location of a predator or other organism invading the hippopotamus’ territory; represents a random vector with Levy distribution, which is used to describe the mutation of the predator position when attacking hippopotamus; predator j Represents the position of the predator in the search space; represents the distance from the i-th hippopotamus to the predator; b, c, d, and g all represent uniformly distributed random numbers, but their value ranges are different. The value range of b is [2, 4], the value range of c is [1, 1.5], the value range of d is [2, 3], and the value range of g is [2, 4]; r 9 is a random variable in the interval [-1,1]; Factors that cause hippos to adopt defensive behaviors to protect themselves from predators; F i is the objective function value;

[0331] (3) Hippos escape from predators during the development phase: Warnings are ineffective. Lone, sick, and immature hippos are easily attacked by predators. Hippos seek to stay away from predators. The safe locations that hippos search for in order to find the nearest safe place are:

[0332]

[0333] In formula (29): X_P 4 (i,:) indicates searching for the hippopotamus's location to find the nearest safe place; r 10 Represents a random number in the interval [0, 1]; r 11 Represents a random number that conforms to the normal distribution; t is the current iteration number;

[0334] The specific steps for seeking the optimal response and the optimal values ​​of its corresponding structural parameters are as follows:

[0335] S8.11 Set the total number of hippo populations, the maximum number of iterations, the problem dimension, and the upper and lower bounds of the parameters;

[0336] S8.12 Use formula (25) to initialize the initial position of each hippopotamus. The position is usually randomly initialized within the constraints of the problem.

[0337] S8.13 uses the CPO-SVR agent model as the objective function to minimize and evaluates the fitness of each hippopotamus according to its position;

[0338] S8.14 updates the position of the hippopotamus, determines the dominant hippopotamus according to the fitness value of the objective function, that is, finds the current optimal solution, and uses formula (26) to update the position of male hippopotamus and tend to move closer to the dominant male hippopotamus. Use formula (27) to update the position of female and juvenile hippopotamus, which depends on the average position of some randomly selected hippopotamus in the group, and is simulated in the algorithm by moving towards the local optimal solution;

[0339] S8.15 When a predator or other creature invades the hippopotamus's territory, the hippopotamus will trigger a defensive response and use formula (28) to update its position; S8.16 If the warning is ineffective, the hippopotamus will look for the nearest safe place to escape the predator and use formula (29) to update its position. In the algorithm, this can be achieved by randomly moving to other areas of the search space to avoid local optimality;

[0340] S8.17 The algorithm repeats the above steps until the maximum number of iterations or other termination conditions are reached;

[0341] At the end of the S8.18 algorithm, the position of the hippopotamus with the highest fitness and the current value of each factor are output as the optimal solution to the problem.

[0342] This patent proposes a method for optimizing the structural parameters of multi-angular conformal PDC teeth and provides detailed operating steps. For ordinary technicians in this field, other implementation cases obtained without creative work are all within the scope of protection of the present invention.

Claims

1. A method for optimizing the structural parameters of a multi-angular conformal PDC tooth, the method comprising the following steps: S1: Preliminarily determine the structural parameters that need to be optimized for multi-angular conformal PDC teeth, and implement parametric modeling in 3D design software based on the structural parameters; S2: Based on the value range of the structural parameters, the PBD test design is performed in the Design-Expert software to establish the test table A, M groups of test data combinations are obtained, several performance parameters of the tooth are determined as responses, and several response columns are reserved in the test table A; S3: According to several groups of test data combinations in the experimental table, three-dimensional models of different PDC teeth are established in the three-dimensional design software, and imported into the simulation software for simulation, so as to obtain several response data corresponding to each test data combination, fill in the response column in the test table A, and improve the test table A; S4: The structural parameters in the improved experimental table A are used as design factors, and the response is used as the optimization target. A significance analysis is performed in the Design-Expert software to obtain some key structural parameters that have a significant impact on the response. S5: Perform optimal Latin hypercube sampling on the key structural parameters in step S4 to obtain N groups of test data, and form experimental table B, reserving several response columns; S6: Import the N groups of test data in S5 into the simulation software for simulation, obtain the response corresponding to each group of test data and complete the experimental table B. S7: Import the data of experimental table B improved in S6 into Matlab, complete the training and prediction of sample data through the CPO-SVR proxy model, train an effective proxy model and determine it; S8: The CPO-SVR proxy model determined in S7 is used as the fitness function in the Hippo optimization algorithm. The Hippo optimization algorithm program is written by Matlab to optimize and solve the fitness function. In the feasible domain, the corresponding value combinations of each structural parameter under the optimal response are found respectively, and the analysis results of the CPO-SVR proxy model are verified and optimized, and finally the optimal structural parameter combination is obtained.

2. The method for optimizing the structural parameters of a multi-angular conformal PDC tooth according to claim 1, characterized in that: Step S1 is specifically as follows: The method designs a multi-angle conformal PDC tooth, and determines five structural parameters, namely, the angle between the main inclined surfaces on both sides of the transverse ridge of the designed tooth top is the ridge angle, the radius of the arc of the transverse ridge is the fillet, the distance between the lower end of the side edge and the tooth bottom surface is the edge angle height, the angle between the side inclined surfaces on both sides of the side edge is the edge angle, and the angle between the side edge and the tooth bottom surface plane is the side angle. The value range of each of the above structural parameters is determined, and then modeling is performed in the three-dimensional design software Solidworks, and each parameter is named in the form of "=DS_" to realize parametric modeling. Then, the completed three-dimensional model is converted into XT format in Solidworks. The ridge angle, fillet, edge height, edge angle and side angle of the PDC tooth are used as dimensional parameters, and they are named in the form of "=DS_" in the Solidworks sketch interface. The equation can be found in the tool above. Different PDC tooth models can be generated by entering different parameters in the equation, thereby realizing parametric modeling and improving modeling efficiency.

3. The method for optimizing the structural parameters of a multi-angular conformal PDC tooth according to claim 1, characterized in that: Step S2 is specifically as follows: The five structural parameters of the multi-angular conformal PDC tooth structure are taken as five factors, namely ridge angle A, fillet B, edge height C, edge angle D and side angle E, and the upper and lower limits of their value range are determined. PBD test design is carried out in the Design-Expert software to establish test table A, and M=12 groups of test data are obtained. Four response columns are set in test table A; the four performance parameters of the multi-angular conformal PDC tooth, namely crushing specific energy, average cutting force, impact force peak and energy absorption peak, are determined as responses.

4. The method for optimizing the structural parameters of a multi-angular conformal PDC tooth according to claim 1, characterized in that: Step S3 is specifically as follows: according to the test data combination of S2 test table A, modify each structural parameter in Solidworks according to the requirements of each data combination, generate different PDC teeth, convert the PDC tooth three-dimensional model into XT format, import it into ABAQUS software for cutting simulation and impact simulation, and obtain the crushing specific energy, average cutting force, impact force peak value and energy absorption peak value under each data combination; its sub-steps are as follows: S3.0 generates different 3D models of PDC teeth in Solidworks according to the result parameters of experimental table A, and converts the 3D models of PDC teeth into XT format; S3.1 Establish a cutting simulation model, import the XT format files of each PDC tooth three-dimensional model, and obtain the crushing specific energy and average cutting force under each data combination; In the rock breaking process, the disc cutter moves in rotation around the center axis of the cutter disc and in linear motion in the forward direction of the cutter disc, so the PDC cutting teeth on the disc cutter make a spiral motion in the forward direction; however, the cutting depth of the disc cutter is small, that is, the cutting depth of a single PDC cutting tooth is small, and the helical angle of one rotation is very small, so the rotational motion of a single PDC cutting tooth is simplified to a linear motion of a fixed cutting depth; The crushing specific energy (MSE) is used to characterize the energy required to crush a unit volume of rock. The smaller the MSE, the less energy is required to crush a unit volume of rock, and the higher the efficiency of the PDC cutter in crushing rocks. Therefore, the crushing specific energy in the stable cutting stage is taken as the response. The crushing specific energy can be calculated according to the following formula: In formula (1), V is the total rock crushing volume, F is the cutting force, ds is the length of the cutting stage, v is the cutting speed, and dt is the time of the cutting stage; Cutting force is used to characterize the difficulty of PDC cutting teeth in breaking rocks. The smaller the cutting force required to break rocks, the easier it is to break them. Since the cutting force fluctuates during the cutting process, the average cutting force in the stable cutting stage is taken as the response. In summary, a simulation of limestone cutting by a single multi-angular conformal PDC tooth is established to obtain its crushing specific energy and average cutting force, so as to judge the cutting performance of PDC teeth with different parameters. S3.1.1 Input model The XT format of the PDC tooth model generated by S3 parametric modeling was imported into ABAQUS. Considering the model size and calculation efficiency, a finite element model of a single multi-angular conformal PDC tooth cutting limestone was established. The size of the limestone model was 50mm×50mm×20mm. S3.1.2 Setting properties The material of the PDC layer is polycrystalline diamond, and its density is 3520kg / m 3 , elastic modulus 8.9E+5Mpa, Poisson's ratio 0.07; rock material is limestone, density 2500kg / m 3 , elastic modulus 40000Mpa, Poisson's ratio 0.4; S3.1.3 Create an assembly and set up analysis steps After the material properties are set, the model needs to be assembled, and the cutting depth of the multi-angular conformal PDC tooth is set to 2mm; the analysis step is set to dynamic explicit general, and the entire cutting process is set to 0.16s to improve the analysis efficiency. The rest are set to default; S3.1.4 Setting up interactions and loads Set the interaction properties, set the friction formula in the tangential behavior to penalty, the friction coefficient to 0.3, and the rest to default settings; select the pressure interference in the normal behavior as hard contact, and the rest to default settings; set the multi-angle conformal PDC tooth to rigid body, and the contact type to general contact; Set the load, completely fix the limestone base layer, convert the shield machine cutter head rotation speed into linear speed, and set the cutting speed of the multi-angle conformal PDC teeth; S3.1.5 Grid division The overall mesh size of the limestone is set to 5 mm, and the cutting part further refines the mesh to 0.5 mm. The PDC teeth are set as rigid bodies and will not deform, so the mesh size is set to 1.5 mm to speed up the analysis process; After completing the above pre-processing, simulation is performed, and after completing the simulation, post-processing is performed, and the data is imported into the origin software for curve drawing to obtain the cutting force-time curve. The crushing specific energy and average cutting force are calculated in the stable cutting stage; S3.2 Establish an impact simulation model, import the XT format files of each PDC tooth three-dimensional model, and obtain the impact force peak value and energy absorption peak value under each data combination; S3.2.1 Input model After the three-dimensional models of the PDC layer and cemented carbide substrate of the PDC tooth generated by S3 parametric modeling were assembled in SoildWorks, they were converted into XT format and imported into ABAQUS; S3.2.2 Setting properties The material of the PDC layer is polycrystalline diamond, and its density is 3520kg / m 3 , elastic modulus 8.9E+5Mpa, Poisson's ratio 0.07, compressive strength 7600Mpa. Since the strain of polycrystalline diamond before fracture is very small, in order to make the simulation results more obvious, the plastic strain is set to 1 after reaching the compressive strength limit; the impact block material used in the simulation analysis is steel with a density of 7850kg / m 3 , elastic modulus 200Gpa, Poisson's ratio 0.3; S3.2.3 Create an assembly and set up analysis steps After the material properties are set, the model needs to be assembled. To ensure the analysis efficiency, the distance between the impact block and the multi-angular conformal PDC tooth is set to 0, that is, the distance between the two when the impact is about to occur; Set the analysis step to general dynamic display. The impact force reaches the maximum value in a very short time. Therefore, set the whole process of the test collision to 5E-04s to improve the analysis efficiency. The rest are set to default. S3.2.4 Setting up interactions and loads Set the interaction properties. In the tangential behavior, the friction formula is set to penalty, the friction coefficient is 0.3, and the rest are set by default. In the normal behavior, the pressure interference is selected as hard contact, and the rest are set by default. Set the impact block to rigid body, and the contact type is general contact. Set the load, completely fix the hard base part of the multi-angle conformal PDC tooth, and then set the impact block speed according to the impact work of 750J; S3.2.5 Grid division The PDC layer is the main impact part, and the mesh size is set to 1.2mm. The fillet and corner parts are further refined and set to 0.5-0.8mm. The mesh size of the hard matrix part is reduced to speed up the analysis process; the impact block is set as a rigid body and will not deform, so the mesh size is set to 5mm to speed up the analysis process; After completing the above pre-processing, simulation is performed, and after completing the simulation, post-processing is performed, and the data is imported into the origin software for curve drawing. The impact force-time curve and energy-time curve are obtained, and the impact force peak value and energy absorption peak value are calculated.

5. The method for optimizing the structural parameters of a multi-angular conformal PDC tooth according to claim 1, characterized in that: Step S4 is specifically as follows: The five factors of ridge angle, fillet, edge height, edge and side angle in the multi-angle conformal PDC tooth structure are taken as design factors, and the crushing specific energy, average cutting force, impact force peak and energy absorption peak are taken as optimization targets. The 12 groups of data obtained in S3 are imported into the Plackett-Burmans module in the Design-Expert software, and the test data are analyzed for significance to obtain the significance test results. The significance results are measured by the size of the p value. The p value of the first and second terms of the variable is observed. If the p value is less than 0.05, it means that the factor represented by this variable has a significant effect on the test results. Otherwise, the factor has no obvious effect on the response target. After the analysis is completed, the design factors that have significant influence on the crushing specific energy, average cutting force, impact force peak and energy absorption peak among the five factors are ridge angle, fillet, edge and side angle, which are determined as key structural parameters.

6. The method for optimizing the structural parameters of a multi-angular conformal PDC tooth according to claim 1, characterized in that: Step S5 is specifically as follows: Obtain sample data, and obtain the structural parameters with significant influence, such as ridge angle, fillet, edge angle and side angle, according to the significance analysis in S4. On this basis, perform optimal Latin hypercube sampling. Select the DOE module and EXCEL module in the Isight software and connect the two together. Add the four columns A, B, D, and E in EXCEL to DOE, and select optimal Latin hypercube sampling in DOE. According to the empirical formula, determine the sampling number as 60, and then click Generate to obtain the sampling table, and obtain N=60 groups of test data to form Experimental Table B.

7. The method for optimizing the structural parameters of a multi-angular conformal PDC tooth according to claim 6, characterized in that: Step S6 is specifically as follows: in ABAQUS software, the scheme combinations in the S5 sampling table are subjected to cutting simulation and impact simulation according to step S3 to obtain four response data of each group, which are filled into the corresponding columns in the table to complete test table B.

8. The method for optimizing the structural parameters of a multi-angular conformal PDC tooth according to claim 7, characterized in that: Step S7 is specifically as follows: The simulation data obtained in S6 are subjected to grey correlation analysis to construct the CPO-SVR proxy model. The 60 groups of data are divided into 50 training sets and 10 test sets. The CPO-SVR proxy model is used to complete the training and prediction of the data. The root mean square error (RMSE) and the determination coefficient (R) are used to calculate the predicted value. 2 Verify the model validity and proceed to the next step if the model is valid; S7.1 Grey correlation analysis S7.1.1 Normalize the raw data Since the responses are not of the same type, the test response values ​​need to be normalized to between [0,1]; the smaller the crushing specific energy and average cutting force, the better, while the larger the impact force and energy absorption, the better. The peak impact force and energy absorption peak can be turned into negative numbers, so they can be normalized using formula (1); In formula (2), B ik It represents the normalized response value of the i-th group test when the index is k, where k=1 means the index is the crushing specific energy, k=2 means the index is the average cutting force, k=3 means the index is the impact force peak, k=4 means the index is the energy absorption peak, L k represents all test response values ​​with index k, L ik It indicates the test response value of group i when the index is k; S7.1.2 Determine the reference sequence Use B 0k It represents the reference sequence, which means the optimal value obtained when the indicator k is sampled. The first two indicators in this paper are as small as possible, so the reference sequence is the minimum response value corresponding to each indicator. After normalization, B is obtained. 0k ={1,1}, the latter two indicators are as large as possible, so the reference sequence is the maximum response value corresponding to each indicator, and B is obtained after normalization. 0k ={0,0}; S7.1.3 Calculation of grey correlation coefficient The specific steps are as follows: D ik =|B 0k -B ik | (3) In formulas (3)-(6), Δ ik Indicates the deviation sequence of the index k, the i-th group of experiments; Δ min It means to search for the deviation sequence by k, where k = 1, 2, 3, 4, and then search by i, where i = 1, 2, 3...n1, n1 is the optimal Latin hypercube sampling number, which is 60, and get the minimum value Δ of the deviation sequence min ; Δ max It means that the deviation sequence is first searched by k, and then searched by i to obtain the maximum value Δ of the deviation sequence max ;μ ik When the index is k, the grey correlation coefficient of the i-th group of data, ξ represents the resolution coefficient, which is usually 0.5; S7.1.4 Determine the weight of each response using the entropy weight method The specific calculation process is as follows: D k =1-e k (9) In formulas (7)-(10), the k-th index represents the proportion of the i-th group of tests, which is the normalized data calculated by formula (2); k is the information entropy of indicator k. The smaller the information entropy, the greater the discrete degree of the indicator, and the greater the objective weight of the indicator. In addition, because we need to calculate lnp ik , if B ik is 0, then P ik The computer cannot calculate it because it is 0. Therefore, the translation method is used. For the indicator column that appears 0 during the normalization process, a translation amount is added to the column data at the same time. The translation amount is the absolute value of the minimum value of the column data plus 0.01, and the new B is obtained. ik , which can solve this problem; D k is the information redundancy of index k; m2 is the number of indicators, which is 4; w k is the weight of indicator k; S7.1.5 Calculation of grey relational degree Convert each group of response values ​​into the corresponding grey correlation degree. The higher the grey correlation degree, the more it meets the requirements. The calculation process is as follows: In formula (11), h ik Indicates that the index is k, the grey relational degree corresponding to the i-th group of experiments, m2 is the number of indicators, which is 4; W k represents the objective weight of indicator k, U ik The index is k, and the grey correlation coefficient corresponding to the i-th group of experiments; S7.2 Construction of CPO-SVR surrogate model Crested Porcupine Optimization (CPO) The initial population search process of CPO is: In formula (12): X i is the i-th solution to be selected in the search space; L, U are the lower and upper limits of the search range; r is a random number between 0 and 1; N is the population size; The CPO algorithm uses the cyclic population reduction technique (CPR). The mathematical model of cyclic reduction is as follows: In formula (13): N min is the minimum number of newly generated populations, t is the current function evaluation, T is the number of cycles, and T max is the maximum number of function evaluation loops, % is the remainder or modulus operator; The CPO algorithm is inspired by the various defensive behaviors of crested porcupines in nature, which includes four different protection mechanisms: vision, hearing, smell and physical attack, to identify the aggressiveness of alien species; The entire optimization process of the four defense strategies in the CPO algorithm is as follows: (1) When the crested porcupine first realizes the existence of alien species, it activates the first defense strategy. At this time, for the crested porcupine, the alien species has two possibilities: continue to approach or stay away. If mathematical methods are used to simulate these two situations, the normal distribution can be used to generate random values ​​and judge the size. If the absolute value is less than 1, the crested porcupine will continue to approach, otherwise it will stay away. The mathematical model is as follows: In formula (14): are the positions of the i-th individual at iterations t and t+1 respectively; τ1 and τ2 are random numbers from a normal distribution and random values ​​in the interval [0, 1] respectively; is the best solution obtained; Represents the vector generated between the current individual and the random individual; (2) When the alien species approach to a certain extent, the second defense strategy is launched. The crested porcupine starts to make noise to warn the alien species, and the sound will increase as the distance shortens. The mathematical model is as follows: In formula (15), r1 and r2 are two random positive integers in [1, N]; U1 is the three possible situations in the simulation strategy; τ3 is a randomly generated value between 0 and 1; (3) In order to prevent alien species from approaching further, the crested porcupine will launch a third defense strategy, secreting a foul odor in the surrounding area to warn alien species; the mathematical model is as follows: In formula (16), δ is the parameter for controlling the direction; γ t It is a defense factor; is the odor diffusion factor; (4) If the above three defense strategies fail to prevent the alien species from approaching, the crested porcupine will launch the fourth defense strategy and launch a physical attack on the alien species; its mathematical model is as follows: In formula (17): α is the convergence factor; F is the average force of CP on the i-th alien species; Support Vector Machine Regression Model (SVR) The principle of the SVR model is as follows: The decision function expression of the SVR regression model is: m k (t)=A k (t)cos(φ k (t)) (18) In formula (19), D(f) is the optimal linear regression plane; C is the penalty factor; R ε is the ε control error function; the optimization problem can be simplified as: In formula (20): is a regularization term used to control the complexity of the model; C is a regularization parameter used to balance the complexity of the model and the training error; ξ j , is the relaxation factor; W T is the hyperplane coefficient vector; is the nonlinear mapping function; b is the bias; The Lagrange equation and duality theory are used to transform equation (20) into the following formula: The optimal solution can be expressed as: In formula (22), x is the input feature vector; x j is the support vector in the training set; a r , is the Lagrange multiplier used to control the influence of the support vector; K(x r , x j ) is the kernel function, which is used to map the input data into a high-dimensional space; S7.3 Construction of CPO-SVR surrogate model The specific steps are as follows: S7.3.1 Select 60 sets of sample data obtained by optimal Latin hypercube sampling, randomly select 50 sets of samples as training sets, and the remaining 10 sets of samples as test sets. Use the mapminmax program in Matlab to normalize the inputs of the training set and the test set, and name the normalization method inputs. Similarly, normalize the outputs of the training set and the test set, and name the normalization method outputs. S7.3.2 Set the parameters of the CPO optimization algorithm, including the number of CPs, the number of iterations, the number of parameters to be optimized, the upper and lower limits of the parameters to be optimized, and the fitness function. Define the fitness function fitSVM: use 5-fold cross validation, use radial basis function (RBF) as the kernel function of SVM, set the penalty parameter C of SVM, the parameter gamma of the RBF kernel, and specify the type of SVM as epsilon-SVR (regression type); S7.3.3 Use the libsvmtrain function to train the SVR model and perform cross-validation. The regularization parameter C of the SVM and the parameter gamma of the RBF kernel are determined by the best position obtained by the CPO algorithm. S7.3.4 Use the trained SVR model to predict the training set and the test set, and use the mapminmax function to denormalize the prediction results from the normalized state to obtain the predicted values ​​of the original data; S7.3.5 Utilization of the coefficient of determination R 2 The model training accuracy is tested with the root mean square error (RMSE). If the accuracy meets the requirement, continue training. If not, retrain the network. S7.3.6 When the accuracy of the training set model meets the requirements, the model parameters are imported in the same way as in S7.3.4, combined with the test set data to obtain the model output, and the model output is denormalized to obtain the predicted value of the test set; S7.3.7 is the same as S7.3.

5. Check the model. If the accuracy requirement is met, the training ends. Otherwise, return to S7.3.1 to retrain the network. S7.4CPO-SVR model accuracy test The root mean square error (RMSE) and the coefficient of determination (R 2 ) to test the accuracy of the neural network, and the specific implementation is as follows: In formulas (23)-(24), RMSE represents the root mean square error, m3 represents the number of samples tested, and y i and Represent the true value and predicted value of the i-th group of samples, R 2 represents the coefficient of determination, Represents the average value of the samples in group m3; RMSE is required to be less than 0.2, R 2 If it is greater than 0.8, it means that the accuracy of model training meets the requirements and is determined to be an available model.

9. The method for optimizing the flash groove parameters and forging process parameters of a hinge beam forging die according to claim 8, characterized in that: Step S8 is as follows: on the premise that the accuracy of the CPO-SVR model constructed in S7 meets the requirements, it is combined with the Hippo optimization algorithm to seek the optimal response and the optimal values ​​of its corresponding structural parameters in the feasible domain; Hippo optimization algorithm The algorithm simulates a hippopotamus’ position updates in a river or pond, its defense strategies against predators, and its avoidance methods; (1) In the initialization phase, the hippopotamus are candidate solutions to the optimization problem, which means that the position of each hippopotamus in the search space is updated to represent the value of the decision variable; The vector formula for generating decision variables is: X(:,i)=X min (i)+r1×(X max (i)-X min (i)) (25) In formula (25), X(:,i) represents the position of the i-th candidate solution; r1 represents a random number in the interval [0,1]; X min (i) X max (i) represents the lower and upper limits of the i-th decision variable respectively; (2) Exploration phase In the optimization process of this study, the exploration is divided into two phases; Exploration phase 1: The position of hippos in the river or pond is updated: hippos tend to gather close to each other, and the dominant hippo is determined iteratively based on the objective function value; the position formula of male hippos in the group is: X_P1(i,:)=X(i,:)+r2×(D hippo -I1X(i,:)) (26) In formula (26), X_P1(i,:) represents the position of the male hippopotamus; D hippo represents the position of the dominant male hippopotamus; r2 is a random number in the interval [0, 1]; I1 represents a random number in the interval [1, 2]; When the juvenile hippopotamus is far away from the mother hippopotamus, the position update formula of male and female or juvenile hippopotamus in the group is: In formula (27), X_P2(i,:) represents the position of the female or juvenile hippopotamus in the group; r5 represents a random vector; MG i represents the average value of randomly selected hippos; T represents the selection probability; I2 represents a random number in the interval [1, 2]; Exploration Stage 2 Hippopotamus defending against predators: When a hippopotamus is attacked by a predator or other creatures invading its territory, it triggers a defensive response, using their terrifying jaws to make sounds to deter and repel the attacker; the location of the predator or other creature invading the hippopotamus' territory is: In formula (28): X_P3(i,:) represents the location of the predator or other organism invading the hippopotamus’ territory; represents a random vector with Levy distribution, which is used to describe the mutation of the predator position when attacking hippopotamus; predator j Represents the position of the predator in the search space; represents the distance from the i-th hippopotamus to the predator; b, c, d, and g all represent uniformly distributed random numbers, but their value intervals are different. The value interval of b is [2,4], the value interval of c is [1,1.5], the value interval of d is [2,3], and the value interval of g is [2,4]; r9 is a random variable in the interval [-1,1]; factors that contribute to hippos' defensive behaviors to protect themselves from predators; F i is the objective function value; (3) Hippos escape from predators during the development phase: Warnings are ineffective. Lone, sick, and immature hippos are easily attacked by predators. Hippos seek to stay away from predators. The safe locations that hippos search for in order to find the nearest safe place are: In formula (29): X_P4(i,:) represents the location of the hippopotamus to find the nearest safe place; r 10 Represents a random number in the interval [0, 1]; r 11 Represents a random number that conforms to the normal distribution; t is the current iteration number; The specific steps for seeking the optimal response and the optimal values ​​of its corresponding structural parameters are as follows: S8.11 Set the total number of hippo populations, the maximum number of iterations, the problem dimension, and the upper and lower bounds of the parameters; S8.12 Use formula (25) to initialize the initial position of each hippopotamus. The position is usually randomly initialized within the constraints of the problem. S8.13 uses the CPO-SVR agent model as the objective function to minimize and evaluates the fitness of each hippopotamus according to its position; S8.14 updates the position of the hippopotamus, determines the dominant hippopotamus according to the fitness value of the objective function, that is, finds the current optimal solution, and uses formula (26) to update the position of male hippopotamus and tend to move closer to the dominant male hippopotamus. Use formula (27) to update the position of female and juvenile hippopotamus, which depends on the average position of some randomly selected hippopotamus in the group, and is simulated in the algorithm by moving towards the local optimal solution; S8.15 When a predator or other creature invades the hippopotamus's territory, the hippopotamus will trigger a defensive response and update its position using formula (28); S8.16 If the warning is ineffective, the hippopotamus will look for the nearest safe place to escape the predator and update its position using formula (29). In the algorithm, this can be achieved by randomly moving to other areas of the search space to avoid local optimality; S8.17 The algorithm repeats the above steps until the maximum number of iterations or other termination conditions are reached; At the end of the S8.18 algorithm, the position of the hippopotamus with the highest fitness and the current value of each factor are output as the optimal solution to the problem.

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