A reliability optimization design method for multi-link shock absorber under impact excitation

Abstract

The application discloses a reliability optimization design method of a multi-link shock isolator under impact excitation, belongs to the technical field of mechanical equipment shock isolation and vibration reduction, and is used for reliability optimization design of a multi-link shock isolator, and comprises the following steps: a dynamic control equation of the multi-link shock isolator is established and solved; global sensitivity index of a dynamic behavior parameter is calculated based on a failure probability of vibration isolation performance, and a sensitivity parameter is extracted; a limit state function of the vibration isolation performance is established; a Kriging surrogate model of the failure probability function is established based on the limit state function; a normalized target function considering the failure probability of the vibration isolation performance is established with high-frequency vibration average transmissibility as a target function; and the normalized target function is solved by using a particle swarm algorithm. The application can reduce the vibration transmissibility of the vibration isolation device, improve the performance robustness of the vibration isolation device, and obtain design parameters of optimal vibration isolation performance by analyzing the multi-link shock isolator under impact excitation and considering constraint conditions of the performance reliability and the dynamic behavior of the vibration isolation device.

Description

Technical Field

[0001] This invention discloses a reliability optimization design method for a multi-link shock absorber under impact excitation, belonging to the field of shock isolation and vibration reduction technology for mechanical equipment. Background Technology

[0002] The vibration isolation and damping performance of a shock absorber largely depends on the selection of its structure, dimensional parameters, and external excitation parameters. However, these parameters inevitably contain uncertainties, thus affecting the reliability of the shock absorber's performance. Multi-link shock absorbers are parallel mechanisms based on the Gauss-Stewart platform. Their high precision and high load-bearing capacity enable them to absorb vibration energy from multi-directional, multi-source excitation environments, and they are widely used in vibration control, precision manufacturing, flight simulation, and other fields.

[0003] In recent years, scholars both domestically and internationally have proposed various multi-link vibration isolators and conducted a series of mechanistic studies on their dynamic characteristics, vibration isolation performance, and structural optimization. These studies include a novel 6-DOF vibration isolation platform, which uses multi-rigid-body system analysis to establish dynamic equations and analyzes the conditions for achieving high static and low dynamic stiffness characteristics and vibration isolation performance in various directions; a parallel inertial capacitance vibration isolator, which uses the averaging method to investigate the isolator's dynamic amplitude-frequency response and vibration isolation performance; an improved incremental harmonic balance method to investigate the nonlinear vibration characteristics of a quasi-zero stiffness Gauss-Stewart vibration isolation platform and the structural configuration to reduce the coupling effect between degrees of freedom; and a multidimensional vibration isolation system based on parallel mechanisms and dampers, which uses the Lagrange equation and geometric relationships to construct a multidimensional vibration isolation dynamic model and studies the influence of frequency domain vibration isolation capability and uncertainty factors on vibration isolation performance under random excitation.

[0004] The aforementioned studies provide a reference for the analysis of the dynamic characteristics, vibration reduction performance, and structural optimization design of multi-link isolators, and the research theory has matured. However, most studies rarely consider the mechanism of isolator reliability optimization design based on the uncertainties of isolator parameters and excitation loads. Factors such as isolator structure, dimensional parameters, and excitation parameters affect the dynamic behavior of multi-link isolators, and consequently, their vibration isolation performance. Due to inherent uncertainties in manufacturing errors, assembly processes, and structural perception, the impact of these uncertainties on vibration isolation performance cannot be ignored. These uncertainties lead to uncertainties in the dynamic response or vibration transmissibility of the isolator, thus affecting the reliability of vibration isolation performance. Therefore, it is necessary to conduct research on the reliability optimization design of multi-link isolators considering the influence of uncertainties in structural, dimensional, and excitation factors. Summary of the Invention

[0005] The purpose of this invention is to provide a reliability optimization design method for multi-link shock isolators under impact excitation, so as to solve the problem in the prior art that factors such as the structure, size parameters and excitation parameters of the shock isolator affect the dynamic behavior of the multi-link shock isolator, and thus affect the vibration isolation performance of the shock isolator.

[0006] A reliability optimization design method for a multi-link shock absorber under impact excitation includes:

[0007] S1. Define generalized coordinates, establish the dynamic control equations of the multi-link shock absorber based on the small deformation assumption, calculate the generalized mass matrix of the multi-link shock absorber according to the coordinate changes, calculate the generalized stiffness matrix and generalized damping matrix of the multi-link shock absorber using the screw theory, and solve the dynamic control equations of the multi-link shock absorber under excitation using the fourth-order Runge-Kutta numerical method.

[0008] S2. Establish the limit state function of the multi-link shock absorber. Using the multi-link shock absorber parameters that affect the limit state function value as input variables, analyze the global sensitivity index based on the failure probability of each input variable using the two-layer Mond Carlo simulation method. Set the sensitivity parameters based on the estimated value of the global sensitivity index.

[0009] S3. Using the sensitivity parameter as a random variable, calculate the estimated value of the failure probability of the vibration isolation performance of the multi-link damper using the Mond Carlo simulation method. Based on the estimated value of the failure probability and the distribution parameters of the random variable, construct a Kriging surrogate model of the failure probability function. Using the trained Kriging surrogate model of the failure probability function, obtain the estimated value of the failure probability function.

[0010] S4. Establish the displacement response constraint function, the initial vibration isolation frequency constraint function, and the vibration isolation performance failure probability constraint function. Establish the boundary function of the input variables. Combine the three constraint functions and the boundary function to obtain the normalized objective function for the reliability optimization design of the multi-link vibration isolator.

[0011] S5. Using a metaheuristic algorithm, solve the normalized objective function to obtain the optimal design parameter configuration for high-frequency acceleration transmissivity under various constraints.

[0012] S1 includes S1.1, which uses the translational and rotational coordinates of the upper plane of the multi-link depressor relative to the lower plane as generalized coordinates, and establishes the dynamic control equations of the multi-link depressor based on the small deformation assumption:

[0013] ;

[0014] ;

[0015] In the formula, For generalized coordinates, For time, The first derivative, It is the second derivative. For the generalized mass matrix, For the generalized damping matrix, For generalized stiffness matrix, The magnitude of the acceleration impact excitation applied to the lower platform, The frequency at which the excitation is applied, for Axial coordinates, for Axial coordinates, for Axial coordinates, To bypass Axis rotation angle, To bypass Axis rotation angle, To bypass Axis rotation angle;

[0016] S1 includes S1.2, which establishes the transformation matrix of the lower platform relative to the upper platform based on coordinate changes. :

[0017] ;

[0018] In the formula, For the next platform, To get on the platform;

[0019] The generalized mass matrix is:

[0020] ;

[0021] ;

[0022] In the formula, To ensure the quality of the platform, Let be the inertial tensor of the upper plane of the multi-link shock absorber based on the lower plane coordinate system. Let be the inertia tensor matrix of the lower plane; This is the transpose symbol.

[0023] S1 includes S1.3. Based on the spiral theory, the force of the anti-collision linkage is along the direction of the linkage, and each component force satisfies:

[0024] ;

[0025] In the formula, The external excitation force acting on the separator is a spiral. The force of the shock-absorbing link, The element force along the rod direction is based on the lower plane coordinate system. Let the number of anti-collision linkages be denoted as follows: For the index of the anti-impact linkage, , For the first The force of the shock absorber link, For the first The element force along the rod direction of the root isolation link is based on the lower plane coordinate system;

[0026] Will Rewritten as the equilibrium equations in matrix form:

[0027] ;

[0028] In the formula, For the Jacobian matrix:

[0029] ;

[0030] ;

[0031] ;

[0032] In the formula, For the first The vector of the upper platform hinge point of the root link relative to the lower plane coordinate system. For the first The vector of the lower platform hinge point of the root link relative to the lower plane coordinate system. For the first The vector of the hinge point of the upper platform of the root link in the upper plane coordinate system. For the first The unit direction vector of the root link. For the first The torque vector generated by the unit force applied by the root link relative to the center of mass of the upper platform. It is the absolute value;

[0033] Based on the duality between motion transmission and force transmission, let... For the velocity Jacobian matrix, for transpose:

[0034] ;

[0035] ;

[0036] In the formula, This is a diagonal matrix representing the initial stiffness coefficients of the anti-collision linkage. It is a diagonal matrix formed by the initial damping coefficients of the shock-absorbing link.

[0037] S1 includes S1.4, solving the dynamic control equations under multi-link shock absorber excitation using the fourth-order Runge-Kutta numerical method, including transforming the dynamic control equations under multi-link shock absorber excitation load into state equations:

[0038] ;

[0039] In the formula, This is the link damping coefficient. This is the stiffness coefficient of the connecting rod. The state equation is... for The state variable at time t, ,satisfy:

[0040] ;

[0041] ;

[0042] In the formula, State variable 1 represents displacement; State variable 2 represents velocity;

[0043] set up For any time step, the index is used. , Calculated to The iteration format is:

[0044] ;

[0045] In the formula, , , , This represents the slope vector during iterations at different time points. For the first The time of the step, For the first The state variables of the step, For the first The state variables of the step, The step size.

[0046] S2 includes S2.1, using the transient displacement response amplitude of the upper plane of the multi-link shock absorber under impact excitation environment as an evaluation index of the shock absorber's vibration isolation performance, and establishing the limit state function of the multi-link shock absorber under impact environment based on whether the evaluation index exceeds the limited displacement response threshold:

[0047] ;

[0048] ;

[0049] In the formula, Let be the limit state function. The input variables that affect the value of the limit state function. For the first One input variable, ; The limit for the displacement response of the multi-link shock absorber. For the upper platform Translational displacement along the axial direction as a function of time. The amplitude of the transient displacement response of the multi-link shock absorber under impact excitation;

[0050] S2 includes, S2.2, according to The joint probability density function and the hyper-Latin cube sampling method are used to generate... Training sample set of input random variables :

[0051] ;

[0052] In the formula, For the first A sample of input random variables, ;

[0053] according to Estimate the probability of vibration isolation performance failure of multi-link shock absorbers under impact excitation. :

[0054] ;

[0055] In the formula, This is an estimated value for the failure probability of vibration isolation performance. For indicator functions, when hour, ;when hour, .

[0056] S2 includes, S2.3, according to The probability density function and the hyper-Latin cube sampling method generate information about... of One training sample set:

[0057] ;

[0058] In the formula, for Specific sample values, For the first A specific sample value, ;

[0059] definition Other input variables are:

[0060] ;

[0061] according to The joint probability density function and the hyper-Latin cube sampling method generate information about... of One training sample set:

[0062] ;

[0063] In the formula, From The first one drawn from the distribution One sample vector;

[0064] based on Estimate the multi-link damper in Probability of condition failure at:

[0065] ;

[0066] The global sensitivity index for the failure probability of the vibration isolation performance of a multi-link shock absorber under impact excitation is:

[0067] ;

[0068] In the formula, for The global sensitivity index is estimated based on the failure probability of the vibration isolation performance of the multi-link isolator; parameters exceeding the influence threshold are extracted based on the global sensitivity index estimate and set as sensitivity parameters.

[0069] S3 includes, S3.1, random variables involved in the failure probability function of the multi-link damper's vibration isolation performance, with the sensitivity parameter as the random variable, and the distribution parameter of the random variable is given by... Randomly generated in the distribution parameter space indivual training samples :

[0070] ;

[0071] from Random selection Sample , As initial training samples for constructing the Kriging surrogate model of the failure probability function of the vibration isolation performance of multi-link isolators, The initial distribution parameters of the Kriging surrogate model for the failure probability function are the number of samples.

[0072] S3 includes S3.2, which uses the Mond Carlo simulation method to calculate... Estimate the failure probability of the multi-link shock absorber vibration isolation performance at the location ;

[0073] Construct training samples ,based on Constructing a Kriging surrogate model with a failure probability function Calculate based on the Kriging surrogate model of the failure probability function Predicted failure probability and standard deviation for each sample point , ;

[0074] S3 includes S3.3, which introduces a learning function. :

[0075] ;

[0076] In the formula, To learn from the learning function The sample point with the largest predicted standard deviation was selected from the sample points. In order to be in Standard deviation of the Kriging agent model;

[0077] Expand the training sample set to ;

[0078] Establish the stopping criterion for the learning function:

[0079] ;

[0080] In the formula, This is the error threshold for the failure probability estimate;

[0081] Based on the trained failure probability function, the Kriging surrogate model obtains an estimate of the failure probability function. .

[0082] S4 includes applying an impact acceleration excitation vertically to the lower platform of the multi-link isolator, calculating the corresponding vertical relative displacement response of the upper and lower platforms using the fourth-order Runge-Kutta method, setting a limit displacement threshold for the transient displacement response amplitude, and establishing a displacement response constraint function:

[0083] ;

[0084] In the formula, The amplitude of the transient displacement response in the vertical direction. To limit the displacement threshold;

[0085] Using the initial vibration isolation frequency in the acceleration response as the initial vibration isolation frequency index, a threshold value for the initial vibration isolation frequency is set, and an initial vibration isolation frequency constraint function is established:

[0086] ;

[0087] In the formula, The threshold value for the initial vibration isolation frequency; The initial vibration isolation frequency of the multi-link shock absorber under impact excitation:

[0088] ;

[0089] In the formula, For acceleration transmissivity; In search of The maximum value of the independent variable for which the internal conditions are true;

[0090] Using the transient displacement response amplitude as an evaluation index for whether the vibration isolation performance has failed, a threshold for the probability of vibration isolation performance failure is set, and a constraint function for the probability of vibration isolation performance failure is established:

[0091] ;

[0092] In the formula, This is a threshold value set for the probability of vibration isolation performance failure. The failure probability of the vibration isolation performance is estimated by the Kriging surrogate model based on the failure probability function. These are sensitive variables that affect the failure probability of vibration isolation performance;

[0093] Establish the boundary function for the input variables:

[0094] ;

[0095] In the formula, The lower bound of the input variable. This represents the upper boundary of the input variable;

[0096] Using a penalty function , and Normalization to regularization objective function:

[0097] ;

[0098] In the formula, The normalized objective function for reliability optimization design of multi-link shock absorbers. The high-frequency average transmissivity of a multi-link shock absorber under impact excitation. For the first The penalty factor for each constraint function. , This is the penalty factor for the failure probability constraint.

[0099] S5 includes, in S5.1, the metaheuristic algorithm is a particle swarm optimization algorithm. First, particle initialization is performed, randomly initializing a group of particles. Each particle represents a set of design parameters. Initial position and velocity are randomly assigned to each particle. Simultaneously, algorithm parameters are set, including inertia weights. Individual learning factors Social learning factors ;

[0100] S5 includes S5.2, which uses the normalized objective function of the multi-link shock absorber reliability optimization design as the fitness function to calculate the corresponding fitness function value for each particle.

[0101] S5 includes S5.3, for each generation of particle swarm, calculating the current fitness function value and the historical best fitness function value of each particle; if the current fitness function value is less than the historical best fitness function value, updating the individual's best position.

[0102] Find the particle with the best fitness function value among all particles, compare it with the best fitness value of random neighboring particles, and update the best neighboring position if the particle's fitness function value is less than the best fitness value of random neighboring particles.

[0103] The location update calculation formula is:

[0104] ;

[0105] In the formula, For particles The updated location For particles Current location; For particles Updated speed:

[0106] ;

[0107] In the formula, and for Random numbers within a range For particles The individual's optimal position For particles The best location in the neighborhood;

[0108] S5 includes S5.4, setting a maximum iteration threshold. When the maximum iteration count is reached, the optimal design parameter configuration for the high-frequency acceleration transmissibility under each constraint condition is obtained. And the corresponding fitness function value.

[0109] Compared with the prior art, the present invention has the following beneficial effects: By analyzing the multi-link vibration isolator under impact excitation, the present invention achieves a reduction in the vibration transmission rate of the vibration isolation device, an improvement in the performance robustness of the vibration isolation device, and a obtaining of the optimal design parameters for vibration isolation performance under the constraints of considering the performance reliability and dynamic behavior of the vibration isolation device. Attached Figure Description

[0110] Figure 1 This is a flowchart of the technology of this invention;

[0111] Figure 2 This is a schematic diagram of a multi-link shock absorber structure;

[0112] Figure 3 It is a simplified model of a multi-link shock absorber;

[0113] Figure 4 This is a graph showing the relative displacement amplitude-frequency response of a multi-link shock absorber under impact excitation.

[0114] Figure 5 It is a graph of acceleration transmissivity under impact excitation of a multi-link shock absorber;

[0115] Figure 6 The average quality coefficient of different platforms Schematic diagram illustrating the impact on the failure probability of vibration isolation performance;

[0116] Figure 7 It is the average stiffness of different connecting rods Schematic diagram illustrating the impact on the failure probability of vibration isolation performance;

[0117] Figure 8 The average damping of different connecting rods Schematic diagram illustrating the impact on the failure probability of vibration isolation performance;

[0118] Figure 9 It is the average value of the hinge point and the origin of the coordinate system on different lower platforms. Schematic diagram illustrating the impact on the failure probability of vibration isolation performance;

[0119] Figure 10 It is the average angle between the hinge point of the same platform and the coordinate axis. Schematic diagram illustrating the impact on the failure probability of vibration isolation performance;

[0120] Figure 11 It is the average vertical distance between different upper and lower platforms. Schematic diagram illustrating the impact on the failure probability of vibration isolation performance;

[0121] Figure 12 It is the average value of different acceleration excitation amplitudes Schematic diagram illustrating the impact on the failure probability of vibration isolation performance;

[0122] Figure 13 It is the average value of different incentive cycles. Schematic diagram illustrating the impact on the failure probability of vibration isolation performance;

[0123] Figure 14 This is an iterative curve of the reliability optimization design of the multi-link shock absorber obtained from 10 independent runs;

[0124] Figure 15 This is a schematic diagram showing the objective function value and iteration convergence number of the multi-link shock absorber obtained from 10 independent runs;

[0125] Figure 16 This is a comparison chart of the results of optimized and unoptimized designs for the reliability of multi-link shock absorbers;

[0126] In the diagram, 1-upper platform; 2-lower platform; 3-lower hinge seat; 4-fastener; 5-impact barrier link; 6-upper hinge seat. Detailed Implementation

[0127] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0128] A reliability optimization design method for a multi-link shock absorber under impact excitation includes:

[0129] S1. Define generalized coordinates, establish the dynamic control equations of the multi-link shock absorber based on the small deformation assumption, calculate the generalized mass matrix of the multi-link shock absorber according to the coordinate changes, calculate the generalized stiffness matrix and generalized damping matrix of the multi-link shock absorber using the screw theory, and solve the dynamic control equations of the multi-link shock absorber under excitation using the fourth-order Runge-Kutta numerical method.

[0130] S2. Establish the limit state function of the multi-link shock absorber. Using the multi-link shock absorber parameters that affect the limit state function value as input variables, analyze the global sensitivity index based on the failure probability of each input variable using the two-layer Mond Carlo simulation method. Set the sensitivity parameters based on the estimated value of the global sensitivity index.

[0131] S3. Using the sensitivity parameter as a random variable, calculate the estimated value of the failure probability of the vibration isolation performance of the multi-link damper using the Mond Carlo simulation method. Based on the estimated value of the failure probability and the distribution parameters of the random variable, construct a Kriging surrogate model of the failure probability function. Using the trained Kriging surrogate model of the failure probability function, obtain the estimated value of the failure probability function.

[0132] S4. Establish the displacement response constraint function, the initial vibration isolation frequency constraint function, and the vibration isolation performance failure probability constraint function. Establish the boundary function of the input variables. Combine the three constraint functions and the boundary function to obtain the normalized objective function for the reliability optimization design of the multi-link vibration isolator.

[0133] S5. Using a metaheuristic algorithm, solve the normalized objective function to obtain the optimal design parameter configuration for high-frequency acceleration transmissivity under various constraints.

[0134] S1 includes S1.1, which uses the translational and rotational coordinates of the upper plane of the multi-link depressor relative to the lower plane as generalized coordinates, and establishes the dynamic control equations of the multi-link depressor based on the small deformation assumption:

[0135] ;

[0136] ;

[0137] In the formula, For generalized coordinates, For time, The first derivative, It is the second derivative. For the generalized mass matrix, For the generalized damping matrix, For generalized stiffness matrix, The magnitude of the acceleration impact excitation applied to the lower platform, The frequency at which the excitation is applied, for Axial coordinates, for Axial coordinates, for Axial coordinates, To bypass Axis rotation angle, To bypass Axis rotation angle, To bypass Axis rotation angle;

[0138] S1 includes S1.2, which establishes the transformation matrix of the lower platform relative to the upper platform based on coordinate changes. :

[0139] ;

[0140] In the formula, For the next platform, To get on the platform;

[0141] The generalized mass matrix is:

[0142] ;

[0143] ;

[0144] In the formula, To ensure the quality of the platform, Let be the inertial tensor of the upper plane of the multi-link shock absorber based on the lower plane coordinate system. Let be the inertia tensor matrix of the lower plane; This is the transpose symbol.

[0145] S1 includes S1.3. Based on the spiral theory, the force of the anti-collision linkage is along the direction of the linkage, and each component force satisfies:

[0146] ;

[0147] In the formula, The external excitation force acting on the separator is a spiral. The force of the shock-absorbing link, The element force along the rod direction is based on the lower plane coordinate system. Let the number of anti-collision linkages be denoted as follows: For the index of the anti-impact linkage, , For the first The force of the shock absorber link, For the first The element force along the rod direction of the root isolation link is based on the lower plane coordinate system;

[0148] Will Rewritten as the equilibrium equations in matrix form:

[0149] ;

[0150] In the formula, For the Jacobian matrix:

[0151] ;

[0152] ;

[0153] ;

[0154] In the formula, For the first The vector of the upper platform hinge point of the root link relative to the lower plane coordinate system. For the first The vector of the lower platform hinge point of the root link relative to the lower plane coordinate system. For the first The vector of the hinge point of the upper platform of the root link in the upper plane coordinate system. For the first The unit direction vector of the root link. For the first The torque vector generated by the unit force applied by the root link relative to the center of mass of the upper platform. It is the absolute value;

[0155] Based on the duality between motion transmission and force transmission, let... For the velocity Jacobian matrix, for transpose:

[0156] ;

[0157] ;

[0158] In the formula, This is a diagonal matrix representing the initial stiffness coefficients of the anti-collision linkage. It is a diagonal matrix formed by the initial damping coefficients of the shock-absorbing link.

[0159] S1 includes S1.4, solving the dynamic control equations under multi-link shock absorber excitation using the fourth-order Runge-Kutta numerical method, including transforming the dynamic control equations under multi-link shock absorber excitation load into state equations:

[0160] ;

[0161] In the formula, This is the link damping coefficient. This is the stiffness coefficient of the connecting rod. The state equation is... for The state variable at time t, ,satisfy:

[0162] ;

[0163] ;

[0164] In the formula, State variable 1 represents displacement; State variable 2 represents velocity;

[0165] set up For any time step, the index is used. , Calculated to The iteration format is:

[0166] ;

[0167] In the formula, , , , This represents the slope vector during iterations at different time points. For the first The time of the step, For the first The state variables of the step, For the first The state variables of the step, The step size.

[0168] S2 includes S2.1, using the transient displacement response amplitude of the upper plane of the multi-link shock absorber under impact excitation environment as an evaluation index of the shock absorber's vibration isolation performance, and establishing the limit state function of the multi-link shock absorber under impact environment based on whether the evaluation index exceeds the limited displacement response threshold:

[0169] ;

[0170] ;

[0171] In the formula, Let be the limit state function. The input variables that affect the value of the limit state function. For the first One input variable, ; The limit for the displacement response of the multi-link shock absorber. For the upper platform Translational displacement along the axial direction as a function of time. The amplitude of the transient displacement response of the multi-link shock absorber under impact excitation;

[0172] S2 includes, S2.2, according to The joint probability density function and the hyper-Latin cube sampling method are used to generate... Training sample set of input random variables :

[0173] ;

[0174] In the formula, For the first A sample of input random variables, ;

[0175] according to Estimate the probability of vibration isolation performance failure of multi-link shock absorbers under impact excitation. :

[0176] ;

[0177] In the formula, This is an estimated value for the failure probability of vibration isolation performance. For indicator functions, when hour, ;when hour, .

[0178] S2 includes, S2.3, according to The probability density function and the hyper-Latin cube sampling method generate information about... of One training sample set:

[0179] ;

[0180] In the formula, for Specific sample values, For the first A specific sample value, ;

[0181] definition Other input variables are:

[0182] ;

[0183] according to The joint probability density function and the hyper-Latin cube sampling method generate information about... of One training sample set:

[0184] ;

[0185] In the formula, From The first one drawn from the distribution One sample vector;

[0186] based on Estimate the multi-link damper in Probability of condition failure at:

[0187] ;

[0188] The global sensitivity index for the failure probability of the vibration isolation performance of a multi-link shock absorber under impact excitation is:

[0189] ;

[0190] In the formula, for The global sensitivity index is estimated based on the failure probability of the vibration isolation performance of the multi-link isolator; parameters exceeding the influence threshold are extracted based on the global sensitivity index estimate and set as sensitivity parameters.

[0191] S3 includes, S3.1, random variables involved in the failure probability function of the multi-link damper's vibration isolation performance, with the sensitivity parameter as the random variable, and the distribution parameter of the random variable is given by... Randomly generated in the distribution parameter space indivual training samples :

[0192] ;

[0193] from Random selection Sample , As initial training samples for constructing the Kriging surrogate model of the failure probability function of the vibration isolation performance of multi-link isolators, The initial distribution parameters of the Kriging surrogate model for the failure probability function are the number of samples.

[0194] S3 includes S3.2, which uses the Mond Carlo simulation method to calculate... Estimate the failure probability of the multi-link shock absorber vibration isolation performance at the location ;

[0195] Construct training samples ,based on Constructing a Kriging surrogate model with a failure probability function Calculate based on the Kriging surrogate model of the failure probability function Predicted failure probability and standard deviation for each sample point , ;

[0196] S3 includes S3.3, which introduces a learning function. :

[0197] ;

[0198] In the formula, To learn from the learning function The sample point with the largest predicted standard deviation was selected from the sample points. In order to be in Standard deviation of the Kriging agent model;

[0199] Expand the training sample set to ;

[0200] Establish the stopping criterion for the learning function:

[0201] ;

[0202] In the formula, This is the error threshold for the failure probability estimate;

[0203] Based on the trained failure probability function, the Kriging surrogate model obtains an estimate of the failure probability function. .

[0204] S4 includes applying an impact acceleration excitation vertically to the lower platform of the multi-link isolator, calculating the corresponding vertical relative displacement response of the upper and lower platforms using the fourth-order Runge-Kutta method, setting a limit displacement threshold for the transient displacement response amplitude, and establishing a displacement response constraint function:

[0205] ;

[0206] In the formula, The amplitude of the transient displacement response in the vertical direction. To limit the displacement threshold;

[0207] Using the initial vibration isolation frequency in the acceleration response as the initial vibration isolation frequency index, a threshold value for the initial vibration isolation frequency is set, and an initial vibration isolation frequency constraint function is established:

[0208] ;

[0209] In the formula, The threshold value for the initial vibration isolation frequency; The initial vibration isolation frequency of the multi-link shock absorber under impact excitation:

[0210] ;

[0211] In the formula, For acceleration transmissivity; In search of The maximum value of the independent variable for which the internal conditions are true;

[0212] Using the transient displacement response amplitude as an evaluation index for whether the vibration isolation performance has failed, a threshold for the probability of vibration isolation performance failure is set, and a constraint function for the probability of vibration isolation performance failure is established:

[0213] ;

[0214] In the formula, This is a threshold value set for the probability of vibration isolation performance failure. The failure probability of the vibration isolation performance is estimated by the Kriging surrogate model based on the failure probability function. These are sensitive variables that affect the failure probability of vibration isolation performance;

[0215] Establish the boundary function for the input variables:

[0216] ;

[0217] In the formula, The lower bound of the input variable. This represents the upper boundary of the input variable;

[0218] Using a penalty function , and Normalization to regularization objective function:

[0219] ;

[0220] In the formula, The normalized objective function for reliability optimization design of multi-link shock absorbers. The high-frequency average transmissivity of a multi-link shock absorber under impact excitation. For the first The penalty factor for each constraint function. , This is the penalty factor for the failure probability constraint.

[0221] S5 includes, in S5.1, the metaheuristic algorithm is a particle swarm optimization algorithm. First, particle initialization is performed, randomly initializing a group of particles. Each particle represents a set of design parameters. Initial position and velocity are randomly assigned to each particle. Simultaneously, algorithm parameters are set, including inertia weights. Individual learning factors Social learning factors ;

[0222] S5 includes S5.2, which uses the normalized objective function of the multi-link shock absorber reliability optimization design as the fitness function to calculate the corresponding fitness function value for each particle.

[0223] S5 includes S5.3, for each generation of particle swarm, calculating the current fitness function value and the historical best fitness function value of each particle; if the current fitness function value is less than the historical best fitness function value, updating the individual's best position.

[0224] Find the particle with the best fitness function value among all particles, compare it with the best fitness value of random neighboring particles, and update the best neighboring position if the particle's fitness function value is less than the best fitness value of random neighboring particles.

[0225] The location update calculation formula is:

[0226] ;

[0227] In the formula, For particles The updated location For particles Current location; For particles Updated speed:

[0228] ;

[0229] In the formula, and for Random numbers within a range For particles The individual's optimal position For particles The best location in the neighborhood;

[0230] S5 includes S5.4, setting a maximum iteration threshold. When the maximum iteration count is reached, the optimal design parameter configuration for the high-frequency acceleration transmissibility under each constraint condition is obtained. And the corresponding fitness function value.

[0231] The following explanation, in conjunction with the accompanying drawings, will provide further details. Figure 1 As shown, the steps of this invention include: taking a multi-link shock absorber as the research object, establishing the dynamic control equations of the multi-link shock absorber under impact excitation, and solving its dynamic behavior using the fourth-order Runge-Kutta method; based on the two-layer Mond Carlo simulation method, solving the global sensitivity index values ​​of the parameters affecting the dynamic behavior of the multi-link shock absorber, and extracting the parameters with relatively large influence (influence threshold of 0.01) as sensitivity parameters; using the self-learning Kriging method, establishing a surrogate model of the failure probability function of the vibration isolation performance of the multi-link shock absorber considering the uncertainty of the sensitivity parameters, and estimating the failure probability of the vibration isolation performance under different distribution parameters; taking the parameters affecting the dynamic behavior as input variables, with failure probability, displacement response, and initial vibration isolation frequency as constraints, and vibration transmissibility as the objective function, establishing a normalized reliability optimization design objective function using the penalty function method; and using a metaheuristic algorithm (particle swarm optimization algorithm) to solve the normalized reliability optimization design objective function, obtaining the optimal design parameter configuration that satisfies the minimum vibration transmissibility under each constraint function.

[0232] Multi-link shock absorber solid model as follows Figure 2As shown, the system includes an upper platform 1, a lower platform 2, a lower hinge seat 3, fasteners 4, anti-collision connecting rods 5, and an upper hinge seat 6. The lower hinge seats 3 are equidistantly arranged on the upper edge of the lower platform 2 and are fixed to the lower platform 2 by fasteners 4. The upper hinge seats 6 are equidistantly arranged on the lower edge of the upper platform 1 and are fixed to the upper platform 1 by fasteners 4. The anti-collision connecting rods 5 are arranged in pairs and are distributed evenly on the lower platform 2 with the same deflection angle. They are hinged to the lower platform 2 by the lower hinge seats 3. The top of each anti-collision connecting rod 5 is hinged to the upper platform 1 by the upper hinge seat 6.

[0233] Simplified model of multi-link shock absorber as follows Figure 3 As shown, To get on the platform, For the next platform, The shortest distance between the upper and lower platforms. This is the stiffness coefficient of the connecting rod. This is the link damping coefficient. The radius of the platform. Let the radius of the lower platform be [the radius of the lower platform]. Establish a coordinate system with the center of the coordinate system as the origin. for Axis coordinates for Axis coordinates for Axis coordinates; Establish a coordinate system with the center of the coordinate system as the origin. for Axis coordinates for Axis coordinates for Axis coordinates; The angle between the lower platform hinge point and the coordinate axis. For the first The vector of the upper platform hinge point of the root link relative to the lower plane coordinate system. For the first The vector of the lower platform hinge point of the root link relative to the lower plane coordinate system.

[0234] The dynamic amplitude-frequency response curve of the multi-link depressor was obtained using the fourth-order Runge-Kutta method, as shown in the figure below. Figure 4 As shown, the amplitude-frequency response first increases with increasing frequency until it reaches the resonant frequency, and then decreases with increasing frequency, demonstrating the excellent vibration isolation performance of the multi-link shock absorber. The acceleration transmissibility curve of the multi-link shock absorber under impact excitation, obtained using the fourth-order Runge-Kutta method, is shown in the figure below. Figure 5 As shown in the curve, the results indicate that the transmissivity value decreases rapidly with increasing frequency, demonstrating the excellent vibration isolation performance of the multi-link isolator.

[0235] The failure probability curves of multi-link dampers under different distribution parameters, calculated based on the Kriging surrogate model with the failure probability function, are shown in the figure below. Figure 6 , Figure 7 , Figure 8 , Figure 9 , Figure 10 , Figure 11 , Figure 12 and Figure 13 As shown, Figure 6 This reflects the average quality coefficient of different platforms. The impact on the failure probability of vibration isolation performance, as As the size increases, the probability of failure also increases. Figure 7 It reflects the average stiffness of different connecting rods The impact on the failure probability of vibration isolation performance, as As the value increases, the probability of failure decreases accordingly; Figure 8 It reflects the average damping of different connecting rods The impact on the failure probability of vibration isolation performance, as As the value increases, the probability of failure decreases accordingly; Figure 9 This reflects the average value of the hinge point and the origin of the coordinate system on different lower platforms. The impact on the failure probability of vibration isolation performance, as As the value increases, the probability of failure decreases accordingly; Figure 10 This reflects the average angle between the hinge point of the lower platform and the coordinate axis. The impact on the failure probability of vibration isolation performance, as As the value increases, the probability of failure decreases accordingly; Figure 11 This reflects the average vertical distance between different upper and lower platforms. The impact on the failure probability of vibration isolation performance, as As the size increases, the probability of failure also increases. Figure 12 It reflects the average amplitude of different acceleration excitations. The impact on the failure probability of vibration isolation performance, as As the value increases, the probability of failure also increases. The increase was relatively small at that time. The increase in the hourly rate surged; Figure 13 It reflects the average value of different incentive cycles. The impact on the failure probability of vibration isolation performance, when At that time, with As the number increases, the probability of failure increases sharply. At that time, with As the number of cases increases, the failure probability gradually converges to 1.

[0236] The parameters that affect the limit state function value are input variables. The specific definitions and statistical information of the parameters are shown in Table 1.

[0237] Table 1. Parameter definitions and statistical information of multi-link dampers

[0238] .

[0239] Based on the limit state function of the multi-link vibration isolator and the statistical information of the parameters shown in Table 1, the global sensitivity index values ​​of all parameters affecting the vibration isolation performance evaluation index are obtained, as shown in Table 2:

[0240] Table 2. Global sensitivity index of multi-link shock absorbers based on failure probability of vibration isolation performance

[0241] .

[0242] In the design process of multi-link dampers, factors such as assembly and manufacturing processes, dimensional tolerances, and installation methods cause input variables to fluctuate within a certain range, which needs to be determined. The upper and lower boundaries are defined to ensure that the optimization results meet the requirements of practical engineering applications. The boundary function that the input variables follow is expressed as:

[0243] ;

[0244] Based on the distribution statistics of the design parameters listed in Table 1, the upper and lower boundary values ​​of the input variables are determined according to the 3 sigma principle. The specific boundary ranges of the input variables are shown in Table 3.

[0245] Table 3. Boundary values ​​of input variables for reliability optimization design of multi-link shock absorbers

[0246] .

[0247] In addition, other parameter settings in the reliability optimization design are shown in Table 4:

[0248] Table 4. Parameter settings in the reliability optimization design process of multi-link shock absorbers

[0249] .

[0250] A limitation of metaheuristic optimization algorithms is that they cannot guarantee obtaining the optimal solution in a single run. While the probability of obtaining the optimal solution increases with the maximum number of iterations and the initial number of particles, efficiency may decrease. Therefore, this invention selects the average of the optimization solutions from 10 independent runs, achieving a balance between accuracy and efficiency. The specific parameter settings for the particle swarm optimization algorithm are shown in Table 5.

[0251] Table 5. Parameter settings in the particle swarm optimization algorithm

[0252] ;

[0253] The iterative curves obtained by the reliability optimization design method for multi-link shock absorbers after 10 iterations are as follows: Figure 14 As shown, the results indicate that as the number of iterations increases, the fitness function value gradually decreases until the iteration completion criterion is met. The curve shows that when the number of iterations is greater than 45, the fitness function value basically stabilizes and no longer fluctuates significantly, indicating that the iteration is complete.

[0254] Furthermore, the optimal objective function value obtained after 10 iterations and the corresponding number of convergence iterations are as follows: Figure 15 As shown, the average value of the optimal objective function obtained after 10 iterations is 0.0129, and the maximum relative deviation of the optimal objective function obtained after 10 iterations is 6.47%, which can meet the requirements of engineering applications. In addition, the number of convergence iterations after 10 iterations is within 50, indicating the rationality of the particle swarm algorithm parameter settings.

[0255] Furthermore, to demonstrate the effectiveness of the reliability optimization design method for multi-link depressors, the original parameters of the unoptimized multi-link depressor were used as design parameters, and the corresponding constraint function values ​​and objective function values ​​were calculated. Simultaneously, using the optimal design parameters obtained from the reliability optimization design search, the corresponding constraint function values ​​and objective function values ​​were calculated, and the results are as follows. Figure 16 As shown in Table 6:

[0256] Table 6. Optimal design parameters and results after reliability optimization design

[0257] ;

[0258] Compared to unoptimized multi-link dampers, the reliability optimization design method can consider the uncertainties of design parameters, significantly reducing the failure probability of the multi-link damper's vibration isolation performance. Simultaneously, it ensures that the displacement response amplitude and acceleration isolation initiation frequency are below defined thresholds, and reduces the average high-frequency acceleration transmissibility of the damper. These results demonstrate the effectiveness and superiority of the multi-link damper reliability optimization design method.

[0259] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for reliability optimization design of a multi-link dash absorber under impact excitation, characterized in that, The application relates to a reliability optimization design method for a multi-link shock isolator. S1, defining generalized coordinates, establishing a dynamic control equation of the multi-link shock isolator based on a small deformation assumption, calculating a generalized mass matrix of the multi-link shock isolator according to coordinate changes, calculating a generalized stiffness matrix and a generalized damping matrix of the multi-link shock isolator by using a screw theory, and solving the dynamic control equation of the multi-link shock isolator under excitation by using a fourth-order Runge-Kutta numerical method; S2, establishing a limit state function of the multi-link shock isolator, taking parameters of the multi-link shock isolator affecting a limit state function value as input variables, analyzing global sensitivity indexes of the input variables based on failure probability by using a double-layer Monte Carlo simulation method, and setting a sensitivity parameter according to an estimated value of the global sensitivity index; S3, taking the sensitivity parameter as a random variable, calculating an estimated value of a failure probability of the vibration isolation performance of the multi-link shock isolator by using the Monte Carlo simulation method, constructing a Kriging surrogate model of the failure probability function based on the estimated value of the failure probability and distribution parameters of the random variable, and obtaining the estimated value of the failure probability function by using the trained Kriging surrogate model of the failure probability function; S4, establishing a displacement response constraint function, a starting vibration isolation frequency constraint function and a vibration isolation performance failure probability constraint function, establishing a boundary function of the input variable, and combining the three constraint functions and the boundary function to obtain a normalized objective function of the reliability optimization design of the multi-link shock isolator; S5, solving the normalized objective function by using a meta-heuristic algorithm to obtain an optimal design parameter configuration of the high-frequency acceleration transmissibility under the constraint conditions.

2. The reliability optimization design method of a multi-link shock absorber under impact excitation according to claim 1, characterized in that, S1 includes S1.1, taking the translational and rotational coordinates of the upper plane of the multi-link shock isolator relative to the lower plane as generalized coordinates, and establishing a dynamic control equation of the multi-link shock isolator based on a small deformation assumption: ； ； wherein, is a generalized coordinate, is time, is a first order derivative, is a second order derivative, is a generalized mass matrix, is a generalized damping matrix, is a generalized stiffness matrix, is an acceleration shock excitation amplitude applied to the lower platform, is a frequency at which the excitation is applied, is an axial direction coordinate, is an axial direction coordinate, is an axial direction coordinate, is a rotation angle about an axial direction, is a rotation angle about an axial direction, is a rotation angle about an axial direction; S1 comprises, S1.2, establishing a transformation matrix of the lower platform relative to the upper platform based on the coordinate changes : ； In the formula, is a lower platform, is an upper platform; The generalized mass matrix is: ； ； wherein is the upper platform mass, is the inertia tensor of the upper platform of the multi-link shock absorber based on the lower platform coordinate system, is the inertia tensor matrix of the lower platform; is the transpose symbol.

3. The reliability optimization design method of a multi-link dash absorber under impact excitation according to claim 2, characterized in that, S1 includes S1.3, based on the screw theory, the force of the shock isolator link is along the direction of the link, and each component force satisfies: ； wherein is the external excitation force acting on the isolator, is the force of the isolator link, is the element force in the direction of the link based on the lower plane coordinate system, is the number of isolator links, set is the index of the isolator link, , is the force of the th isolator link, is the element force in the direction of the link based on the lower plane coordinate system of the th isolator link; The Rewrite as a matrix representation of the balance equation: ； wherein is the force Jacobian matrix: ； ； ； In the formula, For the first The vector of the upper platform hinge point of the root link relative to the lower plane coordinate system. For the first The vector of the lower platform hinge point of the root link relative to the lower plane coordinate system. For the first The vector of the hinge point of the upper platform of the root link in the upper plane coordinate system. For the first The unit direction vector of the root link. For the first The torque vector generated by the unit force applied by the root link relative to the center of mass of the upper platform. It is the absolute value; Based on the duality between motion transmission and force transmission, let be the velocity Jacobian matrix, be the transpose of ； ； wherein is a diagonal matrix of the initial stiffness coefficients of the isolated control arm, is a diagonal matrix of the initial damping coefficients of the isolated control arm.

4. The reliability optimization design method of a multi-link dash absorber under impact excitation according to claim 3, characterized in that, S1 includes S1.4, the fourth-order Runge-Kutta numerical method is used to solve the dynamic control equation of the multi-link shock isolator under excitation, including converting the dynamic control equation of the multi-link shock isolator under the excitation load into a state equation: ； wherein is a connecting rod damping coefficient, is a connecting rod stiffness coefficient, is a state equation, is the state variable at the time instant t, satisfies: ； ； wherein is state variable 1, representing displacement; is state variable 2, representing velocity; Let be the index of the time step, for any time step , The iterative format to compute is: ； wherein , , , is the slope vector at iteration time, is the time of the th step, is the state variable at the th step, is the state variable at the th step, is the step size.

5. The reliability optimization design method of a multi-link dash absorber under impact excitation according to claim 4, characterized in that, S2 includes S2.1, taking the displacement transient response amplitude of the upper plane under the impact excitation environment of the multi-link shock isolator as an evaluation index of the vibration isolation performance of the shock isolator, and establishing a limit state function of the multi-link shock isolator under the impact environment according to whether the evaluation index exceeds a limited displacement response threshold value: ； ； wherein is a limit state function, is an input variable influencing the value of the limit state function, is the input variable, ; is a defined displacement response threshold value for the multi-link bumper, is a function of the time variation of the translational displacement of the upper platform along the axis, is the amplitude of the transient displacement response of the multi-link bumper under impact excitation; S2 comprises, S2.2, generating a training sample set of input random variables according to the joint probability density function and the hyper-latin hypercube sampling method :​ ； In the formula, is the first input random variable sample, ; According to Estimation of the probability of failure of the performance of a multi-link isolator under impact excitation : ； In the formula, is the estimated value of the isolation performance failure probability, is an indicator function, when , ; when , .

6. The reliability optimization design method of a multi-link dash absorber under impact excitation according to claim 5, characterized in that, S2 comprises, S2.3, generating the probability density function and hyper- Latin hypercube sampling method according to training sample sets:​​ ； wherein is a particular sample value, is the particular sample value, ; Definitions The input variables are, in addition to the above: ； According to the joint probability density function and the hyper-latin hypercube sampling method, generate the training sample set of samples:​ ； wherein is the i-th sample vector drawn from the distribution of the i-th sample vector drawn from the distribution of Based on Estimating the probability of conditional failure of a multi-link bump stop at a location ； The global sensitivity index of the isolation performance failure probability of the multi-link isolator under impact excitation is: ； In the formula, is Based on the global sensitivity index estimate value of the failure probability of the multi-link shock absorber isolation performance; based on the global sensitivity index estimate value, extract parameters exceeding the influence threshold, and set them as sensitivity parameters.

7. The method according to claim 6, wherein S3 comprises, S3.1, setting the distribution parameters of the random variables involved in the sensitivity parameter as the failure probability function of the multi-link shock isolator vibration isolation performance, assuming that the distribution parameters of the random variables are randomly generated in the distribution parameter space training samples :​ ； ​​​​​​ S3 comprises, S3.2, calculating, using a Monte Carlo simulation method, the estimate of the failure probability of the multi-link shock isolator vibration isolation performance at the location ;​ constructing training samples , based on constructing a kriging surrogate model of the failure probability function , calculating the failure probability prediction value and the standard deviation corresponding to the sample point according to the kriging surrogate model of the failure probability function , ;​ S3 comprises, S3.3, introducing a learning function : ； In the formula, is the sample point with the maximum prediction standard deviation selected from according to the learning function, is the sample point with the maximum prediction standard deviation selected from is the standard deviation of the Kriging surrogate model at The training sample set is extended to ; A stop criterion of the learning function is established: ； In the formula, is an error threshold for the failure probability estimate value; Based on the kriging surrogate model of the failure probability function after training, an estimated value of the failure probability function is obtained .

8. The method according to claim 7, wherein, S4 includes vertically applying an impact acceleration excitation to the lower platform of the multi-link shock isolator, calculating the relative displacement response of the corresponding vertical upper and lower platforms by using the fourth-order Runge-Kutta method, setting a limited displacement threshold value of the transient displacement response amplitude, and establishing a displacement response constraint function: ； wherein is the vertical transient displacement response amplitude, is the defined displacement threshold; Taking the vibration isolation starting frequency in the acceleration response as a starting vibration isolation frequency index, setting a limited threshold value of the starting vibration isolation frequency, and establishing a starting vibration isolation frequency constraint function: ； wherein is a defined threshold value for the starting isolation frequency; is the starting isolation frequency for the acceleration of the multi-link shock isolator under impact excitation: ； wherein is the acceleration transmissibility; is to find the maximum value of the argument for which the inner condition holds; Taking the transient displacement response amplitude as an evaluation index of whether the vibration isolation performance fails, setting a limited threshold value of the vibration isolation performance failure probability, and establishing a vibration isolation performance failure probability constraint function: ； wherein is a defined threshold for the failure probability of the isolation performance, is the failure probability of the isolation performance estimated based on the Kriging surrogate model of the failure probability function, is a sensitive variable that influences the failure probability of the isolation performance; The input variable boundary function is established: ； wherein is the lower boundary of the input variable, is the upper boundary of the input variable; The penalty function is normalized to a regularized objective function using , and ​ ； wherein is a normalized objective function for multi-link shock absorber reliability optimization design, is a high-frequency average transmissibility of multi-link shock absorber under impact excitation, is a penalty factor of the th constraint function, , is a penalty factor of the failure probability constraint.

9. The reliability optimization design method of a multi-link dash absorber under impact excitation according to claim 8, characterized in that, S5 includes that the meta-heuristic algorithm is a particle swarm optimization algorithm, first particle initialization, a group of particles are randomly initialized, each particle represents a set of design parameters, randomly assigns an initial position and velocity to each particle, and sets algorithm parameters, including inertia weight , individual learning factor , and social learning factor ; S5 includes, S5.2, the normalized objective function of the multi-link shock absorber reliability optimization design is the fitness function, the corresponding fitness function value of each particle is calculated.

10. The method of claim 9, wherein, S5 includes, S5.3, for each generation of particle group, the current fitness function value of each particle is calculated and the historical best fitness function value, such as the current fitness function value is less than the historical best fitness function value, the individual best position is updated; Find the particle with the best fitness function value in all particles, and compare it with the best fitness value of the random neighborhood particles, if the fitness function value of the particle is less than the best fitness value of the random neighborhood particles, the neighborhood best position is updated; The position updating calculation formula is: ； wherein is a particle updated position, is a particle current position; is a particle updated velocity: ； wherein and is a random number in the range is the individual best position of a particle is the best position in the neighborhood of a particle is the individual best position of a particle is the best position in the neighborhood of a particle S5 includes, S5.4, setting a maximum iteration number threshold, when the maximum iteration number is reached, obtaining the optimal design parameter configuration of the high-frequency acceleration transmissibility under each constraint condition and the corresponding fitness function value.

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