Method for predicting instability characteristic of planet row needle bearing retainer

Abstract

The invention relates to a method for predicting the instability characteristic of a planet row needle bearing retainer, belongs to the technical field of bearing characteristic analysis, and solves the problems that in the prior art, the research on the instability of a bearing retainer is mostly limited to a self-rotation working condition, and prediction is carried out only through a dynamic modeling or testing method; the prediction method comprises the following steps of: firstly, establishing a coordinate system of a planetary gear set, and constructing an index for describing the instability characteristic of the retainer on the basis of the coordinate system; using the kinetic model to form training data of the proxy model; furthermore, a construction and training method of the proxy model is provided, the instability characteristic of the planet row needle bearing retainer can be rapidly obtained, a large amount of dynamic calculation involved in the bearing optimization design process can be replaced, consumption of calculation resources and time can be reduced, and therefore rapid optimization design of the high-performance planet row needle bearing is supported.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of bearing characteristic analysis, and particularly relates to a planetary row needle bearing cage instability characteristic prediction method. BACKGROUND

[0002] The needle bearing is used for supporting the planetary wheel and the planetary carrier pin shaft in the planetary row, and under the extreme service condition of high centrifugal acceleration, the cage is prone to instability, on the one hand, due to the reciprocating impact of the roller on the cage under the action of centrifugal force, and on the other hand, due to the more complex movement state of the cage itself under the action of centrifugal force. Therefore, the cage instability is an important content that must be considered in the bearing design under the high centrifugal acceleration condition, and therefore it is necessary to study a method capable of quickly predicting the instability characteristic of the bearing cage. SUMMARY

[0003] In view of the above problems, the present application provides a planetary row needle bearing cage instability characteristic prediction method, which solves the problem that the research on the instability of the bearing cage in the prior art is mostly limited to only the rotation condition, and the instability is predicted by the method of dynamics modeling. These methods have the following disadvantages: 1) the bearing dynamics characteristics of only the rotation condition and the planetary row co-rotation coupling condition are different, and the instability law of the cage is different, and the original method cannot be applied; 2) the method of dynamics modeling is extremely time-consuming, and a single calculation often consumes several days of time, and therefore it cannot be used for analyzing the instability characteristic of the cage in the bearing optimization design process. Therefore, the prior art cannot support the technical problem of quickly predicting the instability characteristic of the planetary row needle bearing cage.

[0004] The present application provides a planetary row needle bearing cage instability characteristic prediction method, and the specific steps are as follows: S1, establishing a planetary carrier coordinate system and a bearing coordinate system of a planetary gear set; Wherein, the planetary gear set comprises a sun gear, a planetary carrier, a cage, a roller, a planetary wheel, a ring gear, a pin shaft and a planetary row needle bearing; S2, constructing the coordinates of the key components of the planetary gear set in the bearing coordinate system and the coordinates in the planetary carrier coordinate system; Wherein, the key components are the cage and / or the planetary wheel; S3, based on the positions of the cage center relative to the planetary wheel center and the pin shaft, respectively, under the coordinates of the key components in the bearing coordinate system and the coordinates in the planetary carrier coordinate system, obtaining a cage instability characteristic index model of the cage center; S4, obtaining the working condition points and parameter points of the planetary row needle bearing in the simulated planetary gear set, and obtaining a simulation instability characteristic index of the cage under the cage instability characteristic index model of the cage center, to form training data; S5, establishing a surrogate model; S6, training the best coefficient vector of the agent model based on the training data; based on the best coefficient vector, obtaining the trained agent model; S7, inputting the input parameter matrix of the star row needle bearing to be tested into the trained agent model to obtain the instability characteristic prediction result of the star row needle bearing cage.

[0005] Optionally, the key component j is the cage and / or the planet wheel.

[0006] Optionally, the instability characteristic index of the cage center of the cage includes the average radius of the movement trajectory of the cage center relative to the center of the planet wheel, the average radius of the movement trajectory of the pin shaft, and the average speed of the pin shaft.

[0007] Optionally, the specific steps of S3 are as follows: S31, obtaining the coordinates of the pin shaft in the planet carrier coordinate system; S32, obtaining the movement trajectory of the cage center relative to the center of the planet wheel and the movement trajectory of the pin shaft; S33, obtaining the radius of the movement trajectory of the cage center relative to the center of the planet wheel and the radius of the movement trajectory of the cage center relative to the pin shaft; S34, obtaining the relative speed of the cage center relative to the pin shaft based on the planet carrier coordinate system; S35, based on the values obtained in S31 to S34, obtaining the average radius of the movement trajectory of the cage center relative to the center of the planet wheel, the average radius of the movement trajectory relative to the pin shaft, and the average speed relative to the pin shaft, as the instability characteristic index model of the cage.

[0008] Optionally, the expression of the agent model is:

[0009] wherein, indicates the instability characteristic index of the input parameter matrix S, such as the average radius and the average speed; indicates the trace of the matrix; indicates the input parameter matrix; is a coefficient matrix; indicates the deviation.

[0010] Optionally, the input parameter matrix includes a plurality of input parameter combinations, and the input parameter combination includes the working condition point and the parameter point of the bearing.

[0011] Optionally, the specific steps of S6 are as follows: S61, performing quadratic regression on each input parameter combination to obtain the instability characteristic index initial value of each input parameter combination of the coefficient matrix, which is used to form the initial coefficient vector; S62, simultaneously performing two cycles on the initial coefficient vector: cycle 1 and cycle 2, both of which include a plurality of particle swarm algorithm-based processes, each of which takes the previous result as the initial value, to obtain a first optimization result and a second optimization result; S63, performing a third cycle based on the first optimization result and the second optimization result obtained in S62 to obtain an optimal optimization result; S64, based on the optimal optimization result, performing a fourth cycle to obtain an optimal coefficient vector; and based on the optimal coefficient vector, obtaining a trained proxy model.

[0012] Compared with the prior art, the present application has at least the following beneficial effects: The prediction method of the present application can quickly obtain the instability characteristics of the planet row needle bearing cage, can replace a large number of dynamic calculations involved in the bearing optimization design process, can reduce the consumption of computing resources and time, and thus supports the rapid optimization design of high-performance planet row needle bearings. BRIEF DESCRIPTION OF DRAWINGS

[0013] The accompanying drawings are only for the purpose of illustrating specific embodiments and are not considered to be limiting to the present application.

[0014] Figure 1 FIG. 1 is a schematic diagram of the structure of a planet gear set and a planet row needle bearing of the present application; Figure 2 FIG. 2 is a schematic diagram of the planet carrier coordinate system and the bearing coordinate system of the present application; Figure 3 FIG. 3 is a process principle diagram of the optimal coefficient vector of the trained proxy model of the planet row needle bearing cage instability characteristic prediction method of the present application; Figure 4 FIG. 4 is a schematic diagram of the selection of bearing design parameters of the planet row needle bearing cage instability characteristic prediction method of the present application; Figure 5 FIG. 5 is a principle diagram of the selection of bearing working conditions of the planet row needle bearing cage instability characteristic prediction method of the present application.

[0015] REFERENCE NUMERALS: 1. sun gear; 2. planet carrier; 3. cage; 4. roller; 5. planet gear; 6. ring gear; 7. pin shaft; 8. planet row needle bearing. DETAILED DESCRIPTION

[0016] In order to enable the above-mentioned objects, features and advantages of the present application to be clearer, the present application will be further described below in detail with reference to the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present application and the features in the embodiments can be combined with each other without conflict. In addition, the present application can also be implemented in other ways different from those described herein, and therefore the protection scope of the present application is not limited by the specific embodiments disclosed below.

[0017] One specific embodiment of the present application, as shown in Figures 1-5 , discloses a method for predicting the instability characteristics of a planetary row needle bearing cage, and the specific steps are as follows: S1, as shown in Figure 1 , establish the planetary gear set planetary carrier coordinate system (O C XY) and the bearing coordinate system (O P xy).

[0018] Further, the planetary gear set includes a sun gear 1, a planetary carrier 2, a cage 3, a roller 4, a planetary gear 5, a ring gear 6 and a planetary row needle bearing 8; the planetary row needle bearing 8 includes the cage 3 and the roller 4; the planetary carrier 2 is arranged on the outer side of the sun gear 1, the inner side of the ring gear 6, the sun gear 1 and the planetary carrier 2 are drivingly connected through the planetary gear 5, the ring gear 6 and the planetary carrier 2 are drivingly connected through the planetary gear 5; the planetary row needle bearing 8 is arranged between the planetary gear 5 and the planetary carrier 2; the planetary row needle bearing 8 includes a cage 3, and a plurality of rollers 4 are evenly distributed on the cage 3.

[0019] Specifically, the origin of the planetary carrier coordinate system (O C XY) is located at the theoretical center of the sun gear 1, the Y direction of the planetary carrier coordinate system is determined by the negative gravity direction, and the X axis is rotated 90 degrees clockwise from the Y axis; the origin of the bearing coordinate system (O P xy) is located at the theoretical center of the planetary row needle bearing 8, the X axis direction of the bearing coordinate system is from the theoretical center O C of the sun gear 1 to the theoretical center O P of the planetary row needle bearing 8.

[0020] Further, in the planetary carrier coordinate system, the position coordinates of the sun gear 1 (0, 0, Φ S ), the position coordinates of the planetary carrier 2 (0, 0, Φ C ) and the position coordinates of the ring gear 6 (0, 0, Φ R ) are determined, wherein Φ S represents the angle of rotation of the sun gear 1; Φ C represents the angle of rotation of the planetary carrier 2; Φ R represents the angle of rotation of the ring gear 6. Further, in the bearing coordinate system, the position coordinates of the planetary gear 5 (x P, y P , θ P ) and the position coordinates (x g , y g , θ g ) of the cage, wherein x P , y P and θ P represent the coordinates of the x-axis, the y-axis and the angle of rotation of the planet wheel 5 in the bearing coordinate system, respectively; x g , y g and θ g represent the coordinates of the x-axis, the y-axis and the angle of rotation of the cage 3 in the bearing coordinate system, respectively.

[0021] S2, the coordinates (x j (t), y j (t)) in the bearing coordinate system and the coordinates (X j (t), Y j (t)) in the planet carrier coordinate system of the key component j at time t when the planetary gear set is constructed.

[0022] Further, the expression of the coordinates (X j (t), Y j (t)) of the key component j in the planet carrier coordinate system at time t is:

[0023]

[0024] wherein, represents the distance between the origin of the bearing coordinate system and the origin of the planet carrier coordinate system; represents the rotation angle of the key component j in the planet carrier coordinate system at time t; represents the x-axis coordinate of the key component j in the planet carrier coordinate system at time t; represents the y-axis coordinate of the key component j in the planet carrier coordinate system at time t; is the rotation speed of the planet carrier.

[0025] wherein x j (t) represents the coordinate of the x-axis of the key component j in the bearing coordinate system at time t; y j (t) represents the coordinate of the y-axis of the key component j in the bearing coordinate system at time t.

[0026] Specifically, the key component j is the cage and / or the planet wheel, j is g or p, when j is g, it represents the cage; when j is p, it represents the planet wheel.

[0027] S3, based on the positions of the cage 3 center relative to the planetary gear 5 center and the pin shaft 7, respectively, under the coordinates of the bearing coordinate system and the coordinates of the planetary gear coordinate system, obtaining a cage instability characteristic index model.

[0028] Further, the S3 specifically comprises: S31, obtaining the coordinates (X C (t), Y C (t)) of the pin shaft under the planetary gear coordinate system, expressed as:

[0029] wherein, represents the x-axis coordinate of the pin shaft under the planetary gear coordinate system at time t; represents the y-axis coordinate of the pin shaft under the planetary gear coordinate system at time t; represents the rotation angle of the planetary gear under the planetary gear coordinate system at time t.

[0030] S32, obtaining the motion trajectory of the cage center relative to the planetary gear center and the motion trajectory of the cage center relative to the pin shaft, expressed as:

[0031] wherein, represents the relative position of the cage relative to the planetary gear in the X direction under the planetary gear coordinate system at time t; represents the relative position of the cage relative to the planetary gear in the Y direction under the planetary gear coordinate system at time t; represents the X-axis coordinate of the cage under the planetary gear coordinate system at time t; represents the X-axis coordinate of the planetary gear under the planetary gear coordinate system at time t; represents the relative position of the cage relative to the pin shaft in the X direction under the planetary gear coordinate system at time t; represents the relative position of the cage relative to the pin shaft in the Y direction under the planetary gear coordinate system at time t; represents the X-axis coordinate of the pin shaft under the planetary gear coordinate system at time t; represents the Y-axis coordinate of the cage under the planetary gear coordinate system at time t; represents the Y-axis coordinate of the planetary gear under the planetary gear coordinate system at time t; represents the Y-axis coordinate of the pin shaft under the planetary gear coordinate system at time t.

[0032] S33, obtaining the radius of the motion trajectory of the cage center relative to the planetary gear center and the radius of the motion trajectory of the cage center relative to the pin shaft, expressed as:

[0033]

[0034] wherein, is the radius of the trajectory of the center of the cage relative to the center of the planet gear at time t, is the radius of the trajectory of the center of the cage relative to the pin shaft at time t.

[0035] S34, obtaining the relative speed of the center of the cage relative to the pin shaft based on the planetary carrier coordinate system , the expression is:

[0036] wherein, represents the speed component of the cage on the X-axis of the planetary carrier coordinate system at time t; represents the speed component of the pin shaft on the X-axis of the planetary carrier coordinate system at time t; represents the speed component of the cage on the Y-axis of the planetary carrier coordinate system at time t; represents the speed component of the pin shaft on the Y-axis of the planetary carrier coordinate system at time t.

[0037] S35, based on the values obtained in S31 to S34, respectively obtaining the average radius of the trajectory of the center of the cage relative to the center of the planet gear , the average radius of the trajectory of the center of the cage relative to the pin shaft , the average value of the speed of the center of the cage relative to the pin shaft as the instability characteristic index model of the cage.

[0038] S4, obtaining the working points and parameter points of the planetary row needle bearing in the simulation planetary gear set, and obtaining the simulation instability characteristic index of the cage under the instability characteristic index model of the cage at the center of the cage, forming training data.

[0039] Further, S4 specifically includes: S41, establishing a planetary row dynamics model containing planetary needle bearings in the dynamics simulation software.

[0040] S42, within the working range of the planetary row needle bearing, uniformly selecting parameter points and corresponding working points, performing dynamics simulation on the planetary row dynamics model of S41, extracting the coordinates (x j (t), y j (t)) of the key components j at time t in the bearing coordinate system; extracting the rotation angle of the planetary carrier at time t in the planetary carrier coordinate system, and obtaining the instability characteristic index of the cage according to the instability characteristic index model of the cage in S3.

[0041] Specifically, within the design range of bearing parameters (such as bearing radial clearance, pocket clearance, guide clearance, etc.), design parameter points (such as the radial clearance design range of the bearing is 0-50 μm, and 0 μm, 10 μm, 20 μm, 30 μm, 40 μm, and 50 μm are uniformly selected to obtain 0-1000 rpm, 0-2000 rpm, 0-3000 rpm, …, respectively, to form a combination for simulation), dynamic simulation is carried out. After the simulation is completed, the positions of the cage, the planet wheel and the pin shaft corresponding to the working condition points and the parameter points are extracted, the coordinates (x j (t), y j (t)) of the key components j at time t in the bearing coordinate system are extracted; the rotation angle of the planet carrier at time t in the planet carrier coordinate system is extracted; the simulation average radius of the motion trajectory of the cage center relative to the planet wheel center is obtained according to S3, the simulation average radius of the motion trajectory of the cage center relative to the pin shaft, the simulation average speed relative to the pin shaft, and the training data are formed.

[0042] S5, establish a proxy model.

[0043] Specifically, the expression of the proxy model is:

[0044] wherein, indicates the instability characteristic index of the input parameter matrix S, such as the average radius, the average speed; indicates the trace of the matrix; indicates the input parameter matrix; is a coefficient matrix; indicates the bias.

[0045] Specifically, the input parameter matrix includes multiple groups of input parameter combinations, and the input parameter combination includes the working condition points and the parameter points of the bearing.

[0046] Further, the expression of the coefficient matrix is:

[0047] wherein, indicates the coefficient of the first row and the first column; l indicates the coefficient of the i th, the first column; l indicates the coefficient of the i th row and the i l th column; l indicates the coefficient of the i th row and the i l th column.​​​l The coefficients of the column; Indicates the first l line, number l The coefficients of the column.

[0048] S6. Train the optimal coefficient vector K of the surrogate model using the Particle Swarm Optimization (PSA) algorithm based on the training data. best .

[0049] Furthermore, such as Figure 2 As shown, S6 specifically includes: S61, the first combination of input parameters Input parameters Perform a quadratic regression to obtain initial values ​​for the instability characteristic indices of each input parameter combination in the coefficient matrix, which are then used to form the initial coefficient vector. The expression is:

[0050] in, The first element of the coefficient matrix represents the first element of the coefficient matrix. Input parameters The initial value of the instability index; and They represent the first l line, number l The coefficients of the column, and the first The coefficient of the first row and first column; Indicates the first l The coefficient of the second row and the second column.

[0051] S62, Regarding the initial coefficient vector Two loops are executed simultaneously: loop 1 and loop 2. Each loop contains 5 processes based on the particle swarm optimization algorithm. Each process uses the result of the previous one as the initial value to obtain the first optimization result K1 and the second optimization result K2.

[0052] Furthermore, when performing the particle swarm optimization algorithm, the search range is:

[0053] in, This is the regional coefficient, and its value is 5 in both loop 1 and loop 2. Represents the coefficient matrix Minimum value of each parameter; Represents the coefficient matrix The maximum value of each parameter.

[0054] S63, the first optimization result K obtained based on S62 1 Second optimization result K 2 Execute the third loop to obtain the optimal optimization result K.3 The specific steps are as follows: If the difference between the determination coefficients of the first optimization result K1 and the second optimization result K2 is less than or equal to the threshold, execute loop A: Loop A contains 3 search processes based on the particle swarm optimization algorithm, with region coefficients... The value is 3; otherwise, loop B is executed, which includes 5 search processes based on the particle swarm optimization algorithm, with a region coefficient of 3. The value is 5; the optimal optimization result K is obtained. 3 .

[0055] Furthermore, the first optimization result K 1 Second optimization result K 2 The expression for the difference between the coefficients of determination is: .

[0056] S64, Based on the optimal optimization result K 3 Execute the fourth loop: in the first optimization result K 1 The second optimization result K 2 and the optimal optimization result K 3 Choose the one with the larger coefficient of determination as the temporary maximum optimization result. If the temporary maximum optimization result If the difference between the coefficient of determination of the optimal result K3 and the coefficient of determination of the optimal result K3 is less than the threshold, execute loop A; otherwise, execute loop B to obtain the optimal result K. 4 , is the optimal coefficient vector To obtain a trained agent model; This represents the coefficient of determination corresponding to the first optimization result K1; This represents the determination coefficient corresponding to the second optimization result K2.

[0057] Furthermore, the temporary maximum optimization result The expression for the difference between the determination coefficient of the optimal optimization result K3 and the coefficient of determination is:

[0058] Furthermore, using the coefficient of determination The expression is:

[0059] in, m It is the amount of training data. Indicates the first i The actual indicators of a combination of parameters; Indicates the first i Predictive indicators based on a combination of parameters; This represents the average value of the actual indicator.

[0060] It can be understood that when the optimization result K (K 1 or K 2 or K 3 or K best,3 or K best ) is brought into the expression of the surrogate model, the predicted indicators corresponding to all parameter combinations can be obtained , and on this basis, the determination coefficient corresponding to the optimization result K can be obtained, which can be written as R 2 (K).

[0061] S7, input the input parameter matrix of the star row needle bearing to be tested into the trained surrogate model, and obtain the instability characteristic prediction result of the star row needle bearing retainer.

[0062] In order to illustrate the effectiveness of the method of the present application, the above technical solutions of the present application are described in detail through two specific examples as follows: Example 1 For the case that the bearing revolution speed is 3000 rpm and the torque is 610 Nm, a group of bearing design parameters (pocket clearance, radial clearance) are set, as shown in Figure 4 , the circles are training data (results obtained by a dynamic simulation model), and the square frame is a test set, which is used to analyze the accuracy of the surrogate model.

[0063] The model is trained using the training set data, and the training process is as shown in Figure 3 , and the optimal coefficient vector is obtained as follows:

[0064] Among them, the superscripts A, B and C of K respectively represent the average radius of the movement track of the retainer center relative to the planetary wheel center, the average radius of the movement track of the retainer center relative to the pin shaft, and the optimal coefficient vector corresponding to the rotation speed index of the pin shaft.

[0065] Example 2 For the case that the radial clearance is 30 μm and the pocket clearance is 50 μm, a group of working conditions are set, as shown in Figure 5 , the circles are training data (results obtained by a dynamic simulation model), and the square frame is a test set, which is used to analyze the accuracy of the surrogate model.

[0066] The model is trained using the training set data, and the training process is as shown in Figure 3 , and the optimal coefficient vector is obtained as follows:

[0067] Wherein, the superscript D, E, F of K respectively represents the average radius of the motion track of the cage center relative to the planetary wheel center, the average radius of the motion track of the cage center relative to the pin shaft, and the optimal coefficient vector corresponding to the rotation speed index of the pin shaft.

[0068] Referring to Figure 4 Wherein the circles are training data and the square boxes are test sets; referring to Figure 5 Wherein the circles are training data and the square boxes are test sets.

[0069] The above merely describes the preferred embodiments of the present application, but the protection scope of the present application is not limited to this. Any changes or replacements within the technical range disclosed by the present application can be easily thought of by those skilled in the art, and should be covered within the protection scope of the present application.

Claims

1. A method for predicting the instability characteristics of a planetary needle roller bearing cage, characterized in that, The specific steps are as follows: S1, establishing a planetary carrier coordinate system and a bearing coordinate system of a planetary gear set; The planetary gear set comprises a sun gear, a planetary carrier, a retainer, a roller, a planet gear, a ring gear, a pin shaft and a planetary row needle bearing; S2, constructing the coordinates of the key components of the planetary gear set in the bearing coordinate system and the coordinates of the planetary carrier coordinate system; The key components are the retainer and / or the planet gear; S3, based on the positions of the retainer center relative to the planet gear center and the pin shaft, obtaining a retainer instability characteristic index model of the retainer center under the coordinates of the key components in the bearing coordinate system and the planetary carrier coordinate system; S4, obtaining the working condition points and parameter points of the planetary row needle bearing in the simulation planetary gear set, and obtaining the simulation instability characteristic index of the retainer under the retainer instability characteristic index model of the retainer center, to form training data; S5, establishing a surrogate model; S6, training the best coefficient vector of the surrogate model based on the training data; based on the best coefficient vector, obtaining the trained surrogate model; S7, inputting the input parameter matrix of the to-be-tested planetary row needle bearing into the trained surrogate model to obtain the prediction result of the instability characteristic of the planetary row needle bearing retainer.

2. The planetary row needle bearing cage instability characteristic prediction method of claim 1, wherein, The key component j is the retainer and / or the planet gear.

3. The planetary row needle bearing cage instability characteristic prediction method of claim 2, wherein, The retainer instability characteristic index of the retainer center includes the average radius of the movement trajectory of the retainer center relative to the planet gear center, the average radius of the movement trajectory of the pin shaft, and the average speed of the pin shaft.

4. The planetary row needle bearing cage instability characteristic prediction method of claim 3, wherein, The specific steps of S3 are as follows: S31, obtaining the coordinates of the pin shaft in the planetary carrier coordinate system; S32, obtaining the movement trajectory of the retainer center relative to the planet gear center and the movement trajectory of the pin shaft; S33, obtaining the radius of the movement trajectory of the retainer center relative to the planet gear center and the radius of the movement trajectory of the retainer center relative to the pin shaft; S34, obtaining the relative speed of the retainer center relative to the pin shaft based on the planetary carrier coordinate system; S35, based on the values obtained from S31 to S34, obtaining the average radius of the movement trajectory of the retainer center relative to the planet gear center, the average radius of the movement trajectory relative to the pin shaft, and the average speed relative to the pin shaft, as the instability characteristic index model of the retainer.

5. The planetary row needle bearing cage instability characteristic prediction method of claim 1, wherein, The expression of the surrogate model is: wherein, denotes an instability characteristic indicator of the input parameter matrix S; denotes the trace of a matrix; is the coefficient matrix; denotes the bias.

6. The planetary row needle bearing cage instability characteristic prediction method of claim 5, wherein, The input parameter matrix includes multiple input parameter combinations, and the input parameter combination includes the working condition points and parameter points of the bearing.

7. The planetary row needle bearing cage instability characteristic prediction method of claim 1, wherein, The specific steps of S6 are as follows: S61, performing quadratic regression on each input parameter combination to obtain the initial value of the instability characteristic index of each input parameter combination of the coefficient matrix, which is used to form the initial coefficient vector; S62, performing two loops on the initial coefficient vector simultaneously: loop 1 and loop 2, both of which include multiple processes based on the particle swarm algorithm, and each process takes the result of the previous process as the initial value to obtain the first optimization result and the second optimization result; S63, based on the first optimization result and the second optimization result obtained from S62, performing a third loop to obtain the optimal optimization result; S64, based on the optimal optimization result, performing a fourth loop to obtain the best coefficient vector; based on the best coefficient vector, obtaining the trained surrogate model.

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