Robust optimization design method of cam mechanism based on improved red-mouth blue-magpie optimization algorithm

Abstract

The invention discloses a robust optimization design method of a cam mechanism based on an improved red-mouth blue-magpie optimization algorithm. The method comprises the following steps: S1, establishing a mathematical optimization model of a bias direct-acting push rod cam mechanism; s2, establishing a robust optimization design model of the bias direct-acting push rod cam mechanism; s3, setting parameters of a red-mouth blue-magpie algorithm, and initializing a population based on a Halton sequence; s4, selecting the frontier solution through non-dominated sorting, and storing the frontier solution in a food file; s5, updating the population by simulating prey searching and prey attacking behaviors of the red-beaked blue magpies in the small group or the cluster; s6, calculating a population fitness value and a constraint violation value, and selecting a frontier solution through non-dominated sorting to update the food archive; and S7, repeating S5 to S6 until the maximum evolution algebra is reached, and outputting the optimal design parameter set of the robust optimization design model of the bias direct-acting push rod cam mechanism, so that the good performance of the cam mechanism can be ensured to a certain extent under the influence of uncertain factors, and the obtained conclusion has an engineering design reference value.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical design, manufacturing and automation, and particularly to a robust optimization design method for a cam mechanism based on an improved red-billed blue magpie optimization algorithm. Background Technique

[0002] A cam mechanism can convert rotational motion into linear motion or reciprocating motion, playing a core role in the fields of mechanical design and automation, and is widely used in the automotive industry, packaging machinery, printing machinery, medical equipment and other fields. The motion performance of the cam mechanism directly affects the running accuracy and stability of the mechanical equipment. In actual operation, the cam mechanism is affected by dynamic loads, friction and wear, and these factors will reduce its service life. When using traditional deterministic design methods to design the cam mechanism, the design state, design goal, design constraints and design model are all deterministic, without considering various uncertain sources that may cause changes. In practical applications, the cam mechanism is affected by various uncontrollable factors, such as manufacturing errors, assembly errors and changes in the working environment. Conducting a robust optimization design for the cam mechanism can, by adjusting the design variables and controlling the tolerances, enable the mechanism to still maintain good performance under the influence of these uncertain factors.

[0003] Swarm intelligence optimization algorithms are a class of meta-heuristic optimization algorithms that simulate the behavior of natural biological groups. These algorithms simulate the collaborative behavior of biological groups and achieve the optimization solution of complex problems through simple interactions and information sharing among group members. The red-billed blue magpie optimization algorithm is an efficient, flexible and easy-to-implement meta-heuristic optimization algorithm. By simulating the foraging behavior of the red-billed blue magpie, it has the characteristics of strong global search ability, fast convergence speed, good robustness and a balance between exploration and exploitation, and is applicable to a variety of complex optimization problems. However, the standard red-billed blue magpie optimization algorithm does not have the ability to compare the performance of multi-objective solutions, and there are problems such as insufficient population diversity. Summary of the Invention

[0004] Object of the Invention: The present invention aims to solve some problems existing in the prior art, and particularly innovatively proposes a robust optimization design method for a cam mechanism based on an improved red-billed blue magpie optimization algorithm, which can perform a robust optimization design on multiple objectives of the cam mechanism.

[0005] Technical Solution: To achieve the above object, the present invention provides a robust optimization design method for a cam mechanism based on an improved red-billed blue magpie optimization algorithm, including the following steps:

[0006] Step 1: Taking the base circle radius R of the offset translating roller follower cam mechanism b and the cam roller radius R g, the eccentricity e, the distance q between the cam center and the follower bearing, the length b of the follower bearing, and the cam thickness t are design variables D, D ∈ {R b , R g , e, q, b, t}, with the maximum contact stress ζ max between the cam and the roller as the design objective, and a mathematical optimization model of the offset translating roller follower cam mechanism is constructed according to the geometric, kinematic, and force constraints that the design parameters need to satisfy;

[0007] Step 2: Considering the machining errors generated during the manufacturing of each component of the offset translating roller follower cam mechanism, the local expansion method is used to perform Taylor expansion of the objective function and constraint conditions of the mathematical optimization model of the offset translating roller follower cam mechanism near the mean value of the random variables, and the variables of the probability distribution are quantized uncertainly to obtain an effective approximate moment estimate, and the mathematical optimization model in Step 1 is transformed into a robust optimization design model of the offset translating roller follower cam mechanism with the mean value μ ζmax of the maximum contact stress between the cam and the roller and the variance as the design objective;

[0008] Step 3: Improve the parameter initialization of the red-billed blue magpie optimization algorithm, set the population size N of the red-billed blue magpie, select the auxiliary parameter ε, the maximum number of generations G, and initialize the population through the Halton sequence within the range of the design variables:

[0009] x i,j = lb + Halton × (ub - lb) (1)

[0010] where x i,j is the j-th dimension of the i-th individual in the population, lb and ub are the upper and lower bounds of the j-th dimension, and Halton is the Halton sequence;

[0011] Step 4: Calculate the fitness value of each individual in the population in the fitness function μ ζmax and , and the constraint violation value of the individual, and compare the superiority and inferiority of the individuals through fast non-dominated sorting according to the population fitness value and the constraint violation value, and store the solutions on the Pareto front after sorting in the food archive Archive as the position of the initial best food;

[0012] Step 5: Update the population by simulating the foraging behavior of the red-billed blue magpie in small groups or clusters to find and attack prey, where the small groups or clusters are randomly selected according to the auxiliary parameter ε, and the specific operations are as follows:

[0013] (1) Search for food: Simulate the behavior of the red-billed blue magpie searching for food in small groups or clusters, and update the position by randomly selecting some individuals to simulate its search ability in different environments;

[0014] Small group search:

[0015]

[0016] Swarm search:

[0017]

[0018] Among them, p and q respectively represent the number of individuals in the small group and the swarm, p ∈ [2, 5], q ∈ [10, N], X i (t) is the i-th individual of the population in the t-th generation, X rs (t) is an individual randomly selected in the current generation, X m (t) is an individual randomly selected to enter the small group or the swarm, Rand1 and Rand2 represent random numbers from 0 to 1;

[0019] (2) Attack the prey: Simulate the behavior of the red-billed blue magpie attacking the prey in the small group or the swarm, and update the individual position by quickly approaching the food position;

[0020] Small group attack:

[0021]

[0022] Swarm attack:

[0023]

[0024] Among them, X food (t) is a position randomly selected from the food archive, CF = (1 - (t / G)) 2×t / G , Randn1 and Randn2 represent random numbers generated from a standard normal distribution;

[0025] Step 6: Calculate the fitness value of each individual in the population and the constraint violation value of the individual, merge the new population with the food archive, perform a fast non-dominated sorting based on the population fitness value and the constraint violation value to compare the advantages and disadvantages of individuals, and store the solutions on the Pareto front as the new best food positions in the food archive Archive;

[0026] Step 7: Repeat Step 5 to Step 6 until the maximum number of generations G is reached, and output the set of the best design parameters of the robust optimization design model of the offset translating push rod cam mechanism.

[0027] Preferably, the maximum contact stress ζ between the cam and the roller in Step 1 max :

[0028]

[0029] Among them, the Poisson coefficients v1 and v2, the elastic moduli E1 and E2, and the normal force F in the contact area between the follower and the cam n are calculated as follows:

[0030]

[0031] In the formula, P is the total force acting on the follower, and this force is the algebraic sum of the applied force F0, the inertial force F i = Ms” and the spring force F s = k(s'+γ), the mass M of the follower, the elastic coefficient k, the initial spring compression γ, the pressure angle c = q - (a + s), where s, s', s” are the displacement, velocity, and acceleration of the follower respectively, q is the distance between the cam center and the follower bearing, μ is the friction coefficient, and ɑ is the vertical distance from the roller center to the cam rotation center.

[0032] Preferably, the geometric, kinematic, and force constraints that the design parameters in step 1 need to satisfy are specifically defined as:

[0033]

[0034] Among them, ɑ is the vertical distance from the roller center to the cam rotation center, and ζ p is the allowable contact stress, is the pressure angle, L is the length of the follower, h is the stroke of the follower, and η min is the minimum efficiency of the cam mechanism, and ρ min is the minimum radius of curvature. The calculation of the mechanism efficiency and the radius of curvature is as follows:

[0035]

[0036] Among them, μ is the friction coefficient, and s, s', s” are the displacement, velocity, and acceleration of the follower respectively.

[0037] 4. A robust optimization design method for a cam mechanism based on an improved red-billed blue magpie optimization algorithm according to claim 1, characterized in that the robust optimization design model of the offset translating roller follower cam mechanism in step 2:

[0038]

[0039] Among them, μ f and respectively represent the mean and variance of the target affected by uncertain variables, and μ gi and σ gi respectively represent the constraints g i(i = 1, 2, ···, p) Based on the mean and standard deviation affected by uncertain variables, the larger the value of parameter m, the stronger the constraint reliability; the moment estimation retaining the first-order term is shown as follows:

[0040] μ f =f(μ D ) (12)

[0041]

[0042] In the formula, μ D is the mean of the uncertain variable, is the value obtained by substituting the partial derivative of f at variable d into μ D , is the standard deviation at d.

[0043] Preferably, the processing of the constraint violation value in step 4:

[0044]

[0045] Among them, g is the inequality constraint, h is the equality constraint, l and k are the numbers of the inequality constraint and the equality constraint respectively, θ is a tolerance close to 0, and when it is a feasible solution, SVC = 0; otherwise, it is an infeasible solution.

[0046] Preferably, the comparison criterion for the superiority and inferiority of individuals in step 4:

[0047] There exist solutions X i 、X j , when the solution X i constraint-dominates the solution X j , the following conditions need to be satisfied:

[0048] (1) The solutions X i 、X j are both infeasible solutions, and SVC(X i ) < SVC(X j );

[0049] (2) The solution X i is a feasible solution, and X j is an infeasible solution;

[0050] (3) The solutions X i 、X j are both feasible solutions, and

[0051] The beneficial effects of the present invention:

[0052] In the improved red-billed blue magpie optimization algorithm of the present invention, the population initialization method combined with the Halton sequence can significantly increase the diversity of the initial population. The addition of fast non-dominated sorting and the food archive Archive can help the algorithm solve the multi-objective optimization problem of the robust optimization design of the cam mechanism. Finally, the optimal design parameter set considering the machining error is obtained, realizing the robust optimization design of the offset translating roller follower cam mechanism. The conclusions obtained have reference value for engineering design. Description of the Drawings

[0053] The drawings described herein are used to provide a further understanding of the present invention and form a part of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention.

[0054] Figure 1 It is a flow chart of the robust optimization design method of the cam mechanism based on the improved red-billed blue magpie optimization algorithm;

[0055] Figure 2 It is a structural schematic diagram of the offset translating roller follower cam mechanism. Detailed Embodiments

[0056] This part will describe in detail the specific embodiments of the present invention. The preferred embodiments of the present invention are shown in the drawings. The function of the drawings is to supplement the description of the text part of the specification, enabling people to intuitively and vividly understand each technical feature and the overall technical solution of the present invention, but it cannot be understood as a limitation to the protection scope of the present invention.

[0057] Refer to Figure 1 - Figure 2 , the present invention provides a robust optimization design method of a cam mechanism based on an improved red-billed blue magpie optimization algorithm, which can perform robust optimization design on multiple objectives of the cam mechanism, including the following steps: S1: Establish a mathematical optimization model of the offset translating roller follower cam mechanism; S2: Considering the machining errors generated during the manufacturing of each component of the cam mechanism, establish a robust optimization design model of the offset translating roller follower cam mechanism using the local expansion method; S3: Set the parameters of the red-billed blue magpie algorithm and initialize the population based on the Halton sequence; S4: Calculate the population fitness value and the constraint violation value, and select the non-dominated solutions through non-dominated sorting and store them in the food archive; S5: Update the population by simulating the foraging behavior of the red-billed blue magpie in small groups or clusters to find and attack prey; S6: Combine the food archive and the new population, calculate the population fitness value and the constraint violation value, and select the non-dominated solutions through non-dominated sorting to update the food archive; S7: Repeat S5-S6 until the maximum number of generations of evolution is reached, and output the optimal design parameter set of the robust optimization design model of the offset translating roller follower cam mechanism, etc.

[0058] A robust optimization design method of a cam mechanism based on an improved red-billed blue magpie optimization algorithm specifically includes the following steps:

[0059] Step 1: As Figure 2 , according to the motion law s = f(t) of the follower displacement s with respect to time t provided by the design requirements, the follower load F0, the follower mass M, the follower length L, the Poisson coefficients v1 and v2, the elastic moduli E1 and E2, the friction coefficient μ, and the allowable contact stress ζ p , the elastic coefficient k, the initial spring compression γ, and the base circle radius R of the offset translating roller follower cam mechanism b , the cam roller radius R g , the eccentricity e, the distance q between the cam center and the follower bearing, the follower bearing length b, and the cam thickness t are used as design variables. Based on the geometric, motion, and force constraints that the design parameters need to satisfy, a mathematical optimization model for minimizing the maximum contact stress ζ between the cam and the roller of the offset translating roller follower cam mechanism is constructed: max :

[0060] (1) The maximum contact stress ζ between the cam and the roller max is defined as:

[0061]

[0062] where the normal force F in the contact area between the follower and the cam n is calculated as follows:

[0063]

[0064] In the formula, P is the total force acting on the follower. This force is the algebraic sum of the external force F0, the inertial force F i = Ms” and the spring force F s = k(s'+γ), the follower mass M, the elastic coefficient k, the initial spring compression γ, the pressure angle c = q-(a + s), s, s', and s” are the follower velocity, acceleration respectively, q is the distance between the cam center and the follower bearing, μ is the friction coefficient, and ɑ is the vertical distance from the roller center to the cam rotation center;

[0065] (2) The geometric, motion, and force constraints that the design parameters need to satisfy are specifically defined as:

[0066]

[0067] where ζ p is the allowable contact stress, L is the follower length, h is the follower stroke, η min is the minimum efficiency of the cam mechanism, ρ min is the minimum radius of curvature. The calculation of the mechanism efficiency and the radius of curvature is as follows:

[0068]

[0069] Step 2: Considering the machining errors generated during the manufacturing of each component of the cam mechanism, the objective function and constraint conditions of the mathematical optimization model of the offset translating roller follower cam mechanism are Taylor-expanded near the mean value of the design variables D ∈ {R b , R g , e, q, b, t}, and the variables with probability distributions are subjected to uncertainty quantification to obtain effective approximate moment estimates, thus obtaining the robust optimization design model of the offset translating roller follower cam mechanism:

[0070]

[0071] where μ f and represent the mean and variance of the objective affected by the uncertain variables respectively, μ gi and σ gi represent the mean and standard deviation of the constraint g i (i = 1, 2, ···, p) affected by the uncertain variables respectively. The larger the value of the parameter m, the stronger the constraint reliability (in this invention, m = 3 is taken). The moment estimate retaining the first-order term is shown as follows:

[0072] μ f = f(μ D ) (15)

[0073]

[0074] In the formula, μ D is the mean value of the uncertain variable, is the value obtained by substituting the partial derivative of f at the variable d into μ D , is the standard deviation at d;

[0075] Step 3: Perform the initial parameter setting of the improved red-billed blue magpie optimization algorithm, set the population size N of the red-billed blue magpie, select the auxiliary parameter ε, the maximum number of generations G, and initialize the population through the Halton sequence within the range of the design variables:

[0076] x i,j = lb + Halton × (ub - lb) (17)

[0077] where x i,j is the j-th dimension of the i-th individual in the population, lb and ub are the upper and lower bounds of the j-th dimension, and Halton is the Halton sequence;

[0078] Step 4: Calculate the fitness function μ ζmax for each individual in the population and The fitness value and the constraint violation value of the individual are used, and the individuals are sorted in terms of superiority and inferiority through fast non-dominated sorting based on the population fitness value and the constraint violation value. The solutions on the Pareto front after sorting are stored in the food archive Archive as the positions of the initial best foods.

[0079] (1) Handling of constraint violation values

[0080]

[0081] Among them, g is the inequality constraint, h is the equality constraint, l and k are the numbers of the inequality constraint and the equality constraint respectively, and θ is a tolerance close to 0. When it is a feasible solution, SVC = 0; otherwise, it is an infeasible solution.

[0082] (2) Comparison criteria for individual superiority and inferiority

[0083] There exist solutions X i and X j . When the solution X i constraint-dominates the solution X j , the following conditions need to be satisfied:

[0084] 1) The solutions X i and X j are both infeasible solutions, and SVC(X i ) < SVC(X j );

[0085] 2) The solution X i is a feasible solution, and X j is an infeasible solution;

[0086] 3) The solutions X i and X j are both feasible solutions, and

[0087] Step 5: Update the population by simulating the foraging behavior of red-billed blue magpies to search for prey and attack prey in small groups or clusters (randomly select small groups or clusters according to ε). The specific operations are as follows:

[0088] (1) Search for food: Simulate the behavior of red-billed blue magpies searching for food in small groups or clusters. By randomly selecting some individuals for position update, simulate their search ability in different environments.

[0089] Small group search:

[0090]

[0091] Cluster search:

[0092]

[0093] Among them, p and q represent the number of individuals in the small group and the cluster respectively, p ∈ [2, 5], q ∈ [10, N], X i (t) is the i-th individual in the population in the t-th generation, X rs (t) is the randomly selected individual in the current generation, X m (t) is the individual randomly selected to enter the small group or the cluster, and Rand1 and Rand2 represent random numbers from 0 to 1;

[0094] (2) Attack the prey: Simulate the behavior of the red-billed blue magpie attacking the prey in the small group or the cluster, and update the individual position by quickly approaching the food position.

[0095] Small group attack:

[0096]

[0097] Cluster attack:

[0098]

[0099] Among them, X food (t) is a randomly selected position in the food archive, CF = (1 - (t / G)) 2×t / G , and Randn1 and Randn2 represent random numbers generated from a standard normal distribution.

[0100] Step 6: Calculate the fitness value of each individual in the population and the constraint violation value of the individual, merge the new population with the food archive, perform a fast non-dominated sorting according to the population fitness value and the constraint violation value, and store the solutions on the Pareto front as the new best food positions in the food archive Archive;

[0101] Step 7: Repeat Step 5 to Step 6 until the maximum number of generations G is reached, and output the set of the best design parameters of the robust optimization design model of the offset translating roller follower cam mechanism.

[0102] In the cam mechanism robust optimization design method based on the improved red-billed blue magpie optimization algorithm, this patent establishes a robust optimization design model of the offset translating roller follower cam mechanism. Combining the population initialization method of the Halton sequence on the basis of the standard red-billed blue magpie optimization algorithm significantly increases the diversity of the early population. Adding the fast non-dominated sorting and the food archive strategy helps the algorithm solve the problem of mutual exclusion between the multi-objective optimization goals of the cam mechanism robust optimization design. Finally, the set of the best design parameters considering the machining error is obtained, realizing the robust optimization design of the offset translating roller follower cam mechanism. To a certain extent, it can ensure good performance under the influence of uncertain factors of the cam mechanism, and the obtained conclusions have reference value for engineering design.

[0103] On the premise of no conflict, those skilled in the art can freely combine and superimpose the above additional technical features.

[0104] The above description is only the preferred implementation mode of the present invention. As long as the technical solutions that achieve the purpose of the present invention by basically the same means fall within the protection scope of the present invention.

Claims

1. A robust optimization design method for cam mechanisms based on an improved red-billed blue magpie optimization algorithm, characterized in that: It includes the following steps: Step 1: Take the base circle radius R of the offset translating roller follower cam mechanism b , the cam roller radius R g , the eccentricity e, the distance q between the cam center and the follower bearing, the length b of the follower bearing, and the cam thickness t as the design variables D, D ∈ {R b , R g , e, q, b, t}, take the maximum contact stress ζ max between the cam and the roller as the design objective, and construct a mathematical optimization model of the offset translating roller follower cam mechanism according to the geometric, kinematic and force constraints that the design parameters need to satisfy; Step 2: Considering the manufacturing errors generated during the production of each component of the offset translating roller follower cam mechanism, the objective function and constraint conditions of the mathematical optimization model of the offset translating roller follower cam mechanism are Taylor-expanded near the mean value of the random variables using the local expansion method. The variables of the probability distribution are subjected to uncertainty quantification to obtain an effective approximate moment estimate, and the mathematical optimization model in Step 1 is transformed into a robust optimization design model of the offset translating roller follower cam mechanism with the mean value μ ζmax and variance of the maximum contact stress between the cam and the roller as the design objective; Step 3: Improve the parameter initialization of the Red-billed Blue Magpie optimization algorithm, set the population size N of the Red-billed Blue Magpie, select the auxiliary parameter ε, the maximum number of generations G, and initialize the population through the Halton sequence within the range of design variables: x i,j = lb + Halton × (ub - lb)(1) where x i,j is the j-th dimension of the i-th individual in the population, lb and ub are the upper and lower bounds of the j-th dimension, and Halton is the Halton sequence; Step 4: Calculate the fitness value of each individual in the population in the fitness function μ ζmax and the fitness value of the individual and the constraint violation value of the individual, and perform fast non-dominated sorting based on the population fitness value and the constraint violation value to compare the pros and cons of individuals. Store the solutions on the Pareto front after sorting in the food archive Archive as the position of the initial best food; Step 5: Update the population by simulating the foraging and attacking behaviors of the Red-billed Blue Magpie in small groups or clusters. Among them, the small group or cluster is randomly selected according to the auxiliary parameter ε. The specific operations are as follows: (1) Search for food: Simulate the behavior of the Red-billed Blue Magpie searching for food in small groups or clusters. Update the positions of some individuals randomly to simulate its search ability in different environments; Small group search: Cluster search: Among them, p and q represent the number of individuals in the small group and the cluster respectively, p ∈ [2, 5], q ∈ [10, N], X i (t) is the i-th individual of the population in the t-th generation, X rs (t) is the randomly selected individual in the current generation, X m (t) is the individual randomly selected to enter the small group or the cluster, and Rand1 and Rand2 represent random numbers from 0 to 1; (2) Attack prey: Simulate the behavior of the Red-billed Blue Magpie attacking prey in small groups or clusters. Update the individual positions by quickly approaching the food position; Small group attack: Cluster attack: where X food (t) is a position randomly selected from the food archive, and CF = (1 - (t / G)) 2×t / G , and Randn1 and Randn2 represent random numbers generated from a standard normal distribution; Step 6: Calculate the fitness value of each individual in the population and the constraint violation value of the individual. Merge the new population with the food archive. Compare the superiority and inferiority of individuals through fast non-dominated sorting based on the population fitness value and the constraint violation value. Store the solutions on the Pareto front as the new best food positions in the food archive Archive; Step 7: Repeat Step 5 to Step 6 until the maximum number of generations G is reached, and output the set of the best design parameters of the robust optimization design model of the offset translating pushrod cam mechanism.

2. A robust optimization design method for a cam mechanism based on an improved red-billed blue magpie optimization algorithm according to claim 1, characterized in that: The maximum contact stress ζ between the cam and the roller in Step 1 max : Among them, the Poisson coefficients v1 and v2, the elastic moduli E1 and E2, and the normal force F in the contact area between the follower and the cam n are calculated as follows: Wherein, P is the total force acting on the follower, and this force is the algebraic sum of the applied force F0, the inertial force F i = Ms”, and the spring force F s = k(s'+γ), the mass M of the follower, the elastic coefficient k, the initial spring compression γ, pressure angle c = q - (a + s), s, s', s” are the displacement, velocity, and acceleration of the follower respectively, q is the distance between the cam center and the follower bearing, μ is the friction coefficient, and ɑ is the perpendicular distance from the roller center to the cam rotation center.

3. A robust optimization design method for a cam mechanism based on an improved red-billed blue magpie optimization algorithm according to claim 1, characterized in that: The geometric, kinematic, and force constraint conditions that the design parameters in Step 1 need to satisfy are specifically defined as: Among them, ɑ is the vertical distance from the center of the roller to the center of rotation of the cam, ζ p is the allowable contact stress, is the pressure angle, L is the length of the follower, h is the stroke of the follower, η min is the minimum efficiency of the cam mechanism, ρ min is the minimum radius of curvature. The calculation of the mechanism efficiency and the radius of curvature is as follows: Among them, μ is the friction coefficient, s, s', and s'' are the displacement, velocity, and acceleration of the follower respectively.

4. A robust optimization design method for a cam mechanism based on an improved red-billed blue magpie optimization algorithm according to claim 1, characterized in that: The robust optimization design model of the offset translating pushrod cam mechanism in Step 2: Among them, μ f and represent the mean and variance of the target affected by the uncertain variable respectively, and represent the mean and standard deviation of the constraint g i (i = 1, 2, ···, p) affected by the uncertain variable respectively. The larger the value of the parameter m, the stronger the reliability of the constraint. The moment estimation of retaining the first-order term is shown as follows: μ f = f(μ D )(12) where μ D is the mean of the uncertain variables, is the value obtained by substituting the partial derivative of f at the variable d with μ D , is the standard deviation at d.

5. A robust optimization design method for a cam mechanism based on an improved red-billed blue magpie optimization algorithm, as claimed in claim 1, wherein: The handling of the constraint violation value in Step 4: Among them, g is the inequality constraint, h is the equality constraint, l and k are the numbers of the inequality constraint and the equality constraint respectively, θ is a tolerance close to 0. When it is a feasible solution, SVC = 0; otherwise, it is an infeasible solution.

6. A robust optimization design method for a cam mechanism based on an improved red-billed blue magpie optimization algorithm according to claim 1, characterized in that: The comparison criterion for the superiority and inferiority of individuals in Step 4: There exists a solution X i , X j , when the solution X i is constraint-dominated by the solution X j the following conditions must be satisfied: (1) Solution X i and X j are both infeasible solutions, and SVC(X i ) < SVC(X j ); (2) Solution X i is a feasible solution, X j is an infeasible solution; (3) Solution X i and X j are both feasible solutions, and X i < X j .

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