Improved artificial bee colony algorithm based on Taguchi method for inverse solver of robotic arm

Abstract

The present invention discloses a robotic arm inverse kinematics device that integrates the Taguchi method with an improved artificial bee colony algorithm. After completing the kinematic modeling of the robotic arm, the method needs to apply the kinematic model and constraints to construct a fitness function for the problem, then use the improved artificial bee colony algorithm to search for the inverse kinematics solution of the robotic arm, and finally use the Taguchi method to screen the important parameters of the improved artificial bee colony algorithm. The method introduces a new intelligent swarm algorithm, an improved algorithm of the artificial bee colony algorithm, to solve the inverse kinematics problem of the robotic arm. By considering the swarm movement speed and introducing relevant parameters, the algorithm's solution accuracy for the problem is effectively improved, and the shortcoming of falling into local optimality in solving the robotic arm inverse kinematics problem is improved. At the same time, applying the Taguchi method to select the most appropriate algorithm parameters can obtain better solution results.

Description

Technical Field

[0001] The invention belongs to the technical field of mechanical arm kinematics. Background Art

[0002] Robot kinematics is a crucial component of robotics research, and its inverse kinematics module forms the foundation for subsequent trajectory planning and control research. Solving inverse kinematics for robotic arms presents multiple solutions, and numerous approaches are available. The versatility, robustness, and efficiency of a solution are crucial criteria for determining its success.

[0003] Compared to forward kinematics, the study of inverse kinematics for manipulators—the task of calculating a series of joint angles that meet the desired end-effector position given a known desired position—is much more challenging. Solving inverse kinematics is inherently a nonlinear, highly coupled, and complex problem, and therefore lacks a universal solution algorithm.

[0004] For robotic arms with lower complexity, inverse kinematics can typically be solved using analytical methods (which can be categorized as algebraic or geometric) and numerical methods. Specifically, after completing the kinematic modeling of the target robot and obtaining analytical expressions, the solution can be achieved through geometric analysis, trigonometric transformations, and other methods. However, analytical methods can only be used for robotic arms that meet the Pieper criterion, lack versatility, and are unable to solve complex inverse kinematics problems with high degrees of freedom.

[0005] With the development of intelligent optimization algorithms, various algorithms have been applied to inverse kinematics for robotic arms, proposing new solutions to the problem. Swarm intelligence algorithms such as the particle swarm optimization algorithm, the sparrow search algorithm, and the fruit fly optimization algorithm, as well as their improved algorithms, have been applied to inverse kinematics problems. The artificial bee colony algorithm (ABA), a swarm intelligence optimization algorithm that draws on the wisdom of honey bees, has been widely used to solve numerous practical problems due to its advantages of having few parameters, a fast solution process, and low complexity. However, when applied to solving inverse kinematics problems for robotic arms, the ABA still suffers from the problem of being trapped in local optima, and its solution accuracy and stability need to be improved. Summary of the Invention

[0006] The purpose of the present invention is to propose an inverse kinematics solver of a hybrid Taguchi method and a speed-assisted artificial bee colony algorithm, which improves the efficiency and stability of the inverse kinematics solution of a manipulator.

[0007] The steps of the present invention are:

[0008] S1. Design and improve the artificial bee colony algorithm inverse kinematics solver:

[0009] Bees are divided into collecting bees, observing bees and scout bees. The individual movement speed is introduced to improve the nectar source location update method of the algorithm. The maximum distance ratio is added during initialization. Used to combine upper and lower bounds of the position and Get the speed limit:

[0010] (3)

[0011] At the same time, the weight coefficient is added to adjust the speed parameter, and the abstention limit coefficient is introduced to set the abstention limit parameter:

[0012] (4)

[0013] in Is a function that performs rounding;

[0014] The specific solving process of the solver is as follows:

[0015] Step 4.1: Initialize the honey source position within the robot workspace, i.e., the constraint range, based on the forward kinematics model ,in, It is an n-dimensional nectar source location information, N is the number of nectar sources, and the number of iterations of the algorithm , population number , acceleration coefficient and weight coefficient The parameters are set, and the fitness value of each nectar source is calculated according to the fitness function to judge the quality of the nectar source;

[0016] Step 4.2: Align the honey bees with the nectar sources initialized in step 4.1 one by one, and then update the nectar sources according to formula (5):

[0017] (5)

[0018] in, To adjust the weight coefficient of movement, is the acceleration coefficient, for The speed and position of the individual, for remove The speed and position of a random individual outside the

[0019] The updated speed and position need to be within the speed constraint boundary Compare, if it is within the range, keep it, otherwise take the boundary value. After completing the position update, the quality of the nectar source is judged by calculating the fitness value and the best nectar source is retained. At the same time, it is necessary to record the number of times the nectar source cannot be updated to a better fitness value. ;

[0020] Step 4.3: Calculate the sharing probability of the information obtained by the bees, and then share the information obtained by the bees with the employed bees and the observer bees based on this probability; the observer bees use the iterative strategy of formula (5) to update the nectar source information based on the nectar source information provided by the bees, and record the number of times the nectar source cannot be updated to a better fitness. To determine whether the nectar source is exhausted;

[0021] Step 4.4: Based on the parameters recorded in Step 4.2 and Step 4.3 Limiting the number of times you give up nectar sources For comparison, if , then continue to explore the existing nectar sources, otherwise if When the abandonment limit is reached, it means that the nectar source has been exhausted and there is no value in further development. In this case, the employed bees and observer bees need to be converted into scout bees, abandon the exhausted nectar source, and reinitialize the nectar source to obtain new nectar source information.

[0022] Step 4.5: The best nectar source is retained and the search cutoff condition is determined. If the search cutoff condition is met, the algorithm stops and the final population, i.e., the optimized solution, is output. Otherwise, the algorithm returns to step 4.2 to continue updating the nectar source location.

[0023] Step 5: Apply Taguchi method to optimize parameters:

[0024] The population size was selected for the improved artificial bee algorithm , Waiver Limitation Coefficient , maximum distance ratio , maximum weight coefficient Four parameters are used as influencing factors, and each influencing factor is divided into three levels. Based on this, an orthogonal array of influencing factors is obtained; finally, the quality of each experiment of the orthogonal array is measured by introducing the signal-to-noise ratio.

[0025] The present invention has a wide range of applications, and the convergence speed of the fitness function during the iteration process is improved compared with the basic artificial bee colony algorithm solver, thereby improving the efficiency and solution stability of the inverse kinematics of the robotic arm. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 This is a schematic diagram of the relationship between the three types of bee colonies in the artificial bee colony algorithm;

[0027] Figure 2 This is a simplified diagram of the macro-micro robotic arm;

[0028] Figure 3 Schematic diagram of the coordinates of the macro-micro robotic arm;

[0029] Figure 4This is the workflow diagram for the solver application proposed in this paper;

[0030] Figure 5 This is a graph showing the results of experiments on orthogonal arrays;

[0031] Figure 6 is the signal-to-noise ratio of the 9 groups of parameters of the orthogonal array;

[0032] Figure 7 Comparison of the solver's performance before and after introducing the speed factor to assist optimization in the artificial bee colony algorithm. DETAILED DESCRIPTION

[0033] The present invention is achieved through the following technical solution, and the specific steps are as follows:

[0034] Step 1: Coordinate establishment and parameter definition:

[0035] Perform structural analysis on the robotic arm (n degrees of freedom) that requires inverse solution, clarify the rod length, joint angle, and constraint information of each joint angle during specific work, and establish a rectangular coordinate system at each joint based on its specific characteristics and the principles of kinematic analysis.

[0036] Step 2: Establishment of robotic arm kinematic model:

[0037] Based on step 1, the forward kinematic model of the manipulator is established using the DH modeling or homogeneous transformation matrix method. The transformation matrix between the manipulator's end position and the reference coordinate system is obtained by multiplying the transformation relationship between two adjacent joint angles in sequence:

[0038] (1)

[0039] in, An independent variable is the joint angle of the robot arm The function represents the transformation matrix of the coordinate system of the end of the manipulator relative to the base coordinates; is the posture matrix of the end of the manipulator, which represents the spatial posture of the end of the manipulator in the reference base coordinates; is the position vector of the end of the manipulator, which represents the spatial position of the end of the manipulator in the reference base coordinates.

[0040] Step 3: Construct the fitness function and specify the constraints:

[0041] In order to judge the quality of the joint angle parameters, a fitness function is constructed with the minimum posture error of the end arm as the constraint condition. Because the working state of the robot arm is generally a repetitive operation process, the posture error can be ignored and only the error of the end position is considered. In summary, the following fitness function is established:

[0042] (2)

[0043] in, represents the actual position of the end of the robot arm, and is the position coordinate parameter that the end of the robotic arm is expected to reach.

[0044] The essence of the fitness function is the error between the actual position and the desired position. When the calculated parameters can achieve a position that is exactly the same as the desired position, the fitness function is always 0. Therefore, the fitness value can be used to judge the quality of the solution. The closer the fitness value is to 0, the closer it is to the desired position; conversely, the larger the fitness value, the greater the deviation of the solution from the desired position.

[0045] Step 4: Design and improve the artificial bee colony algorithm inverse kinematics solver:

[0046] The artificial bee colony algorithm is a swarm intelligence heuristic algorithm. It refers to the nectar-gathering process of a bee colony. In order to find the nectar source with the most nectar (that is, the optimal solution in the actual problem), the bees are divided into three types: gathering bees, observing bees, and scout bees. The relationship between the three is as follows: Figure 1 shown.

[0047] Based on the artificial bee colony algorithm, the individual movement speed is introduced to improve the nectar source location update method of the algorithm, and a maximum distance ratio is added during initialization. Used to combine upper and lower bounds of the position and Get the speed limit:

[0048] (3).

[0049] At the same time, increase the weight coefficient Used to adjust speed parameters and introduce abstention restriction coefficient Restrictions on waivers To set it up:

[0050] (4)

[0051] Where is the function that performs rounding.

[0052] The specific solving process of the solver is as follows:

[0053] Step 4.1: Based on the forward kinematic model in step 2, initialize the honey source position within the manipulator workspace, i.e., the constraint range. ,in, It is an n-dimensional nectar source location information, N is the number of nectar sources, and the number of iterations of the algorithm , population number , acceleration coefficient and weight coefficient Parameters such as etc. are set, and the fitness value of each nectar source is calculated according to the fitness function to judge the quality of the nectar source.

[0054] Step 4.2: Align the honey bees with the nectar sources initialized in step 4.1 one by one, and then update the nectar sources according to formula (5):

[0055] (5)

[0056] in, To adjust the weight coefficient of movement, is the acceleration coefficient, for The speed and position of the individual, for remove The speed and position of a random individual outside the system. The updated speed and position need to be within the speed constraint boundary. Compare, if it is within the range, keep it, otherwise take the boundary value. After completing the position update, the quality of the nectar source is judged by calculating the fitness value and the best nectar source is retained. At the same time, it is necessary to record the number of times the nectar source cannot be updated to a better fitness value. .

[0057] Step 4.3: Calculate the sharing probability of the information obtained by the bees (including position, speed, fitness value, etc.), and then share the information obtained by the bees with the employed bees and the observer bees based on this probability. The observer bees use the iterative strategy of formula (5) to update the nectar source information based on the nectar source information provided by the bees, and record the number of times the nectar source cannot be updated to a better fitness value. To determine whether the nectar source is exhausted.

[0058] Step 4.4: Based on the parameters recorded in Step 4.2 and Step 4.3 Limiting the number of times you give up nectar sources For comparison, if , then continue to explore the existing nectar sources, otherwise if When the abandonment limit is reached, it means that the nectar source has been exhausted and there is no value in further development. In this case, the employed bees and observer bees need to be converted into scout bees, abandon the exhausted nectar source, and reinitialize the nectar source to obtain new nectar source information.

[0059] Step 4.5: Keep the best nectar source and determine whether the solution cutoff condition is met (the target solution accuracy is reached or the maximum number of iterations is reached). If the search cutoff condition is met, the algorithm stops and outputs the final population, which is the optimized solution; otherwise, return to step 4.2 to continue updating the nectar source location.

[0060] Step 5: Apply Taguchi method to optimize parameters:

[0061] At this point, the inverse kinematics problem of the robotic arm can be solved by the improved algorithm. However, in the specific solution, the efficiency of solving the problem is different due to the adjustment of parameters. Therefore, the Taguchi method is introduced to select the parameters with the best effect.

[0062] The population size was selected for the improved artificial bee algorithm , Waiver Limitation Coefficient , maximum distance ratio , maximum weight coefficient Four parameters are used as influencing factors, and each influencing factor is divided into three levels, and then an orthogonal array of influencing factors is obtained. Finally, by introducing the signal-to-noise ratio ( ,in is the fitness function value) to measure the quality of each experiment of the orthogonal array.

[0063] Taking the macro-micro manipulator for aerospace applications as the research object, the practical application of the inverse kinematics solver of the present invention is introduced.

[0064] Step 1: Coordinate establishment and parameter definition:

[0065] A schematic diagram of the macro-micro robotic arm is shown below: Figure 2 As shown in the figure, it is a four-degree-of-freedom planar working robot arm. The structural analysis of its model is carried out, and according to the coordinate system establishment principle of DH modeling, the rectangular coordinate system is established at each joint. Figure 3 The connecting rod parameters of the macro-micro robotic arm are , , , , the joint angle parameters are .

[0066] Step 2: Establishment of the kinematic model of the macro-micro robotic arm:

[0067] The DH modeling method is used to establish the forward kinematic model of the robotic arm. The DH parameters are shown in Table 1.

[0068] Table 1 DH parameters of macro-micro manipulator

[0069]

[0070] Since the working space of the aerospace macro-micro manipulator is in the same vertical plane, and according to the DH parameter table, there is no link offset and link angle, the expression in formula (1) can be simplified to derive the forward motion model as follows, and the transformation matrix between adjacent links as shown in formula (8) can be written through the parameters:

[0071] (6).

[0072] Then multiply them in sequence to obtain the transformation matrix of the end coordinate system of the macro-micro manipulator relative to the base coordinate:

[0073] (7)

[0074] in, 、 、 , the rest of the abbreviation rules are the same as the above examples.

[0075] Step 3: Construct the fitness function and specify the constraints:

[0076] To determine the quality of the desired joint angle parameters, a fitness function was constructed using the constraint of minimizing the end-of-arm pose error. Because robotic arms typically operate in a repetitive manner, pose errors can be ignored, and only the end-of-arm position error is considered.

[0077] At the same time, considering that it only works in a vertical plane, we can simplify formula (2) by reducing the coordinates of one spatial dimension to obtain the following fitness function:

[0078] (8)

[0079] in, represents the actual position of the end of the robot arm, and is the desired position coordinate parameter for the end of the manipulator. When the position achieved by the calculated parameters is exactly the same as the desired position, the fitness function is always 0. Therefore, the fitness value can be used to judge the quality of the solution. The closer the fitness value is to 0, the closer it is to the desired position; conversely, the larger the fitness value, the greater the deviation from the desired position.

[0080] Step 4: Improve the artificial bee colony algorithm inverse kinematics solver:

[0081] The artificial bee colony algorithm is a swarm intelligence heuristic algorithm. It refers to the nectar-gathering process of a bee colony. In order to find the nectar source with the most nectar (that is, the optimal solution in the actual problem), the bees are divided into three types: gathering bees, observing bees, and scout bees. The relationship between the three is as follows: Figure 1 shown.

[0082] Based on the artificial bee colony algorithm, the individual movement speed is introduced to improve the nectar source location update method of the algorithm, and a maximum distance ratio is added during initialization. Used to combine upper and lower bounds of the position and Get the speed limit:

[0083] (3).

[0084] At the same time, increase the weight coefficient Used to adjust speed parameters and introduce abstention restriction coefficient Restrictions on waivers To set it up:

[0085] (4)

[0086] in is a function for rounding. The solver workflow is shown in Figure 4 .

[0087] The specific process of solving the inverse kinematics problem of the macro-micro manipulator is as follows:

[0088] Step 4.1: Based on the forward kinematic model in step 2, initialize the honey source position within the manipulator workspace, i.e., the constraint range. ,in , is a 4-dimensional honey source location information, each piece of information corresponds to a candidate solution to the inverse problem, the number of honey sources is N, and the number of iterations of the algorithm is , population number , acceleration coefficient and weight coefficient Parameters such as etc. are set, and the fitness value of each nectar source is calculated according to the fitness function to judge the quality of the nectar source.

[0089] Step 4.2: Align the honey bees with the nectar sources initialized in step 4.1 one by one, and then update the nectar sources according to formula (5):

[0090] (5)

[0091] in, To adjust the weight coefficient of movement, is the acceleration coefficient, for The speed and position of the individual, for remove The speed and position of a random individual outside the group are compared. The updated speed and position need to be compared with the set upper and lower bounds. If they are within the range, they are retained. Otherwise, the boundary value is used. After completing the position update, the best nectar source is retained, that is, the best candidate solution at this time, and the number of times the nectar source cannot be updated to a better fitness is recorded. To determine whether the nectar source is exhausted.

[0092] Step 4.3: Calculate the information sharing probability of the bees, and then share the information obtained by the bees with other bees based on this probability. The observation bees update the nectar source information based on the nectar source information provided by the bees, using the update mechanism of formula (5), and record the number of times the nectar source cannot be updated to a better fitness. To determine whether the nectar source is exhausted.

[0093] Step 4.4: Based on the parameters recorded in Step 4.2 and Step 4.3 Limiting the number of times you give up nectar sources For comparison, if , then continue to explore the existing nectar sources, otherwise if When the abandonment limit is reached, it means that the nectar source has been exhausted and there is no value in further development. In this case, the employed bees and observer bees need to be converted into scout bees, abandon the exhausted nectar source, and reinitialize the nectar source to obtain new nectar source information.

[0094] Step 4.5: The best nectar source (the optimal candidate solution at this time) is retained and a determination is made as to whether the search cutoff condition is met. If the search cutoff condition is met, the algorithm stops and the final iterative nectar source location, i.e., the final optimization solution, is output; otherwise, the algorithm returns to step 4.2 to continue updating the nectar source location.

[0095] Step 5: At this point, the improved algorithm can solve the inverse kinematics problem of the robot arm. However, in the specific solution, the efficiency of solving the problem varies due to the adjustment of parameters. Therefore, the Taguchi method is introduced to select the parameters with the best effect.

[0096] For the improved artificial bee colony algorithm, the population size was selected , Waiver Limitation Coefficient , maximum distance ratio , maximum weight coefficient Four parameters are used as influencing factors, and each influencing factor is divided into three levels, as shown in Table 2. Then, the orthogonal array shown in Table 3 is obtained by the Taguchi method.

[0097] Table 2 Influencing factors and levels

[0098]

[0099] Table 3 Solving orthogonal array

[0100]

[0101] According to the nine key factors of the orthogonal array in Table 3, the most appropriate set of parameter values ​​is determined by the indicator SNR as the parameters of the algorithm for solution.

[0102] Step 6: Simulation process of inverse kinematics solution of the macro-micromanipulator. Specifically specify a desired pose and then apply the proposed solver to solve it.

[0103] Step 6.1: Set the desired position of the macro-micro manipulator, initialize the position of the improved artificial bee colony algorithm in the manipulator workspace, and set parameters such as the number of iterations. Specifically, the number of iterations Set it to 200 times, Substituting into equation (9) we can get a pose of the macro-micro manipulator: ,Will Set as the desired pose.

[0104] Step 6.2: After completing the setting of the desired pose, first perform a specific simulation of the inverse solver applied to the problem according to step 4. Then, according to step 5, conduct experiments on the 9 sets of parameters of the orthogonal array to select the most appropriate parameters. Then, set the best parameter configuration in the solver for the inverse solution of other desired poses of the macro-micro manipulator.

[0105] Step 7: Simulation results and analysis:

[0106] After applying the solver to solve, the solution effect is obtained according to the 9 groups of parameters of the orthogonal array (see Figure 5 ) reflects the effect of solving the problem under different parameter conditions, and combined with the signal-to-noise ratio analysis, such as Figure 6 As shown, it shows that the parameter selection when solving the macro-micro manipulator should be the sixth group of parameters (population size , Waiver Limitation Coefficient , maximum distance ratio , maximum weight coefficient ).

[0107] After setting the parameters to the sixth group of parameters, we can get a comparison chart of the effects of the hybrid field method and the improved artificial bee colony algorithm solver on the inverse solution of the macro-micro manipulator with the basic algorithm solution, as shown in Figure 7 As shown in the figure, the first set of parameters with the worst solution effect among the nine sets of parameters is used as a reference. It can be seen that the proposed solver converges faster than the basic artificial bee colony algorithm, and after applying the Taguchi method to optimize the parameters, the solution accuracy is significantly improved by orders of magnitude.

[0108] According to the above simulation analysis results, it can be shown that the designed inverse solver can well solve the inverse kinematics problem of the robotic arm and ensure the accuracy of the inverse kinematics solution of the robotic arm.

[0109] Explanation of symbols of the present invention:

[0110] is the degree of freedom of the robotic arm; is the transformation matrix of the coordinate system of the end of the manipulator relative to the base coordinates, is the desired pose of the end of the robotic arm, Indicates the The joint coordinate system and the The spatial transformation relationship between the joint coordinate systems; is the posture matrix of the end of the robotic arm; is the position vector of the end of the robot arm; They are the normal vector, sliding vector and approach vector in the posture matrix respectively; is the position vector of the end of the robot arm; is the position vector that the end of the robotic arm is expected to reach; is the number of algorithm iterations; are the upper and lower bounds of the joint angle parameters to be solved; N is the number of nectar sources; is the population size of the observation bees in the algorithm; is the waiver restriction coefficient, To limit the number of times you can waive; The number of times the nectar source cannot be updated to a better fitness level; To adjust the weight coefficient of movement, is the maximum weight coefficient; is the acceleration coefficient; is the maximum distance ratio, are the upper and lower bounds of the individual's movement speed; for The speed and position of the individual; for remove The speed and position of a random individual outside the are the connecting rod parameters of the macro-micro robotic arm; is the joint angle parameter of the macro-micro manipulator; yes 、 、 、 、 、 、 、 The abbreviation of .

Claims

1. A robotic arm inverse solver based on an improved artificial bee colony algorithm combined with the Taguchi method, characterized by: The steps are: S1. Design and improve the artificial bee colony algorithm inverse kinematics solver: The individual movement speed is introduced to improve the nectar source location update method of the algorithm, and the maximum distance ratio is added during initialization. Used to combine upper and lower bounds of the position and Get the speed limit: （3） At the same time, the weight coefficient is added to adjust the speed parameter, and the abstention limit coefficient is introduced to set the abstention limit parameter: （4） in Is a function that performs rounding; The specific solving process of the solver is as follows: Step 4.1: Initialize the honey source position within the robot workspace, i.e., the constraint range, based on the forward kinematics model ,in, It is an n-dimensional nectar source location information, N is the number of nectar sources, and the number of iterations of the algorithm , population number , acceleration coefficient and weight coefficient The parameters are set, and the fitness value of each nectar source is calculated according to the fitness function to judge the quality of the nectar source; Step 4.2: Align the honey bees with the nectar sources initialized in step 4.1 one by one, and then update the nectar sources according to formula (5): （5） in, To adjust the weight coefficient of movement, is the acceleration coefficient, for The speed and position of the individual, for remove The speed and position of a random individual outside the The updated speed and position need to be within the speed constraint boundary Compare, if it is within the range, keep it, otherwise take the boundary value, after completing the position update, judge the quality of the nectar source by calculating the fitness value and keep the best nectar source, and at the same time record the number of times the nectar source cannot be updated to a better fitness ; Step 4.3: Calculate the sharing probability of the information obtained by the bees, and then share the information obtained by the bees with the employed bees and the observer bees according to this probability. The observer bees update the nectar source information based on the nectar source information provided by the bees, using the iterative strategy of formula (5), and record the number of times the nectar source cannot be updated to a better fitness. To determine whether the nectar source is exhausted; Step 4.4: Based on the parameters recorded in Step 4.2 and Step 4.3 Limiting the number of times you give up nectar sources For comparison, if , then continue to explore the existing nectar sources, otherwise if When the abandonment limit is reached, it means that the nectar source has been exhausted and there is no value in further development. In this case, the employed bees and observer bees need to be converted into scout bees, abandon the exhausted nectar source, and reinitialize the nectar source to obtain new nectar source information. Step 4.5: The best nectar source is retained and the search cutoff condition is determined. If the search cutoff condition is met, the algorithm stops and the final population, i.e., the optimized solution, is output. Otherwise, the algorithm returns to step 4.2 to continue updating the nectar source location. Step 5: Apply Taguchi method to optimize parameters: The population size was selected for the improved artificial bee algorithm , Waiver Limitation Coefficient , maximum distance ratio , maximum weight coefficient Four parameters are used as influencing factors, and each influencing factor is divided into three levels. Based on this, an orthogonal array of influencing factors is obtained; finally, the quality of each experiment of the orthogonal array is measured by introducing the signal-to-noise ratio.

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