A reliability design optimization method for separating impact components of a breakaway connector

Abstract

A reliability design optimization method suitable for separating impact components of a shedding connector belongs to the technical field of engineering optimization. In order to solve the problems that traditional reliability optimization design is highly dependent on physical test, and the test cycle is long and the cost is high, the present application proposes a spatial self-adaptive sampling strategy for Kriging surrogate model, which combines model prediction uncertainty and gradient information, dynamically identifies active constraints, thereby effectively reducing misclassification and redundant sampling; in view of the different response characteristics of the objective function and the constraint function, an anisotropic sampling space is constructed for each function, guiding the sample to focus on the area with higher optimization potential; based on the maximum chord deviation criterion, the sampling points are placed in the nonlinear significant area, so as to improve the accuracy of the local surrogate model and accelerate the convergence speed, thereby realizing reliability design optimization.

Description

Technical Field

[0001] This invention belongs to the field of engineering optimization technology and relates to a reliability design method for impact-affected components of a detached connector. Background Technology

[0002] Separable and break-off connectors are a type of connection device widely used in aerospace, automation, and electrical systems, integrating an electromagnetic disconnection mechanism. Specifically, when the connector is in the mating state and a rated voltage is applied across its coil, the electromagnetic force generated by the coil attracts the armature, thereby unlocking the disconnection mechanism and achieving rapid disconnection of the electrical connection. To shorten the disconnection response time, the disconnection mechanism typically needs to generate a large disconnection thrust and requires the internal moving parts to have the smallest possible mass to reduce inertia. To achieve this, high-stiffness springs are often incorporated inside the connector, resulting in some force-transmitting parts being subjected to transient high impact loads during operation. Therefore, achieving lightweight construction of key components while meeting strength and stiffness requirements is crucial for improving connector performance.

[0003] Existing component design methods are mostly based on safety margins, relying solely on empirical coefficients or single margins to ensure structural reliability. They fail to explicitly consider the impact of multiple uncertainties such as manufacturing processes, material properties, and load conditions, leading to overly conservative design results or inaccurate reliability assessments. Furthermore, traditional reliability optimization design often heavily relies on physical testing, resulting in long testing cycles and high costs, making it difficult to meet the needs of rapid iterative engineering design. When using finite element simulation for optimization design, commonly used methods such as orthogonal experiments and global uniform sampling require extensive calculations in high-dimensional sample spaces. This results in numerous finite element simulations, high computational time costs, and low sampling efficiency in critical areas such as failure constraints, making it difficult to balance computational accuracy and efficiency. Existing optimization algorithms also generally suffer from insufficient global search capabilities, susceptibility to local optima, and poor convergence stability in complex nonlinear problems, further restricting the engineering application of reliability optimization design for impact-exposed components of detached connectors. Summary of the Invention

[0004] This invention addresses the problems of traditional reliability optimization design, which heavily relies on physical testing, resulting in long testing cycles and high costs, as well as the issues of current component design methods, which involve numerous finite element simulations and high computational time costs.

[0005] A reliability design optimization method for impact-exposed components of a detachable connector is proposed. First, a 3D model of the detachable connector is established based on drawings to determine key dimensional parameters and their value ranges; these key dimensional parameters constitute a design parameter vector. Then, design optimization is performed, including:

[0006] Step 4: Determine the distribution type of each design variable;

[0007] Step 5: Use the Latin hypercube sampling technique to randomly generate sampling points within the range of each optimization parameter value as the initial sampling point set;

[0008] Step 6: Determine the mathematical model based on reliability optimization design as follows:

[0009] (1)

[0010] in, A vector composed of design parameters. This represents the optimal value of the design parameters obtained in the k-th iteration. Therefore The vector of random variables with mean X, and the components of X follow the distribution type determined in step 4; It is the Kriging surrogate model with the objective function equation; Representing the kriging surrogate model for the i-th constraint equation, the failure event is denoted as... <0; N is the number of constraint equations; and They are respectively The lower and upper bounds; Let be the translation vector of the feasible region for the i-th constraint in the (k+1)-th iteration. The MPTP point corresponding to the i-th constraint obtained in the k-th iteration is the design parameter vector most likely to fail under a given reliability, and is called the minimum functional target point.

[0011] The asymmetric learning factor particle swarm optimization algorithm is used to solve the mathematical model based on reliability optimization design to determine the design variables and achieve design optimization.

[0012] Furthermore, the process of establishing a 3D model of the detachable connector based on the drawings and determining the key dimensional parameters and their value ranges includes:

[0013] Step 1: Create a 3D model of the detachable connector based on the drawings:

[0014] Step 2: Select the target component to be optimized as the design object and determine the set of design parameters;

[0015] Step 3: Based on the set of design parameters, pre-screen key dimension parameters and their value ranges, and the key dimension parameters constitute the design parameter vector.

[0016] Furthermore, based on the design parameter set, the specific process of pre-screening key dimensional parameters and their value ranges includes:

[0017] Step 301: Construct several sets of simulation conditions using orthogonal experimental design method to characterize the combined changes of design parameters within a reasonable range;

[0018] Step 302: Perform finite element analysis on each group of orthogonal test conditions to obtain the output performance index response values ​​under different parameter combinations;

[0019] Step 303: Perform statistical and sensitivity analysis on the simulation results, qualitatively or quantitatively rank the degree of influence of each design parameter on the performance index, and identify the influence threshold of each parameter.

[0020] Step 304: Determine the key dimensional parameters based on the target performance indicators to form a design parameter vector.

[0021] Furthermore, the process of determining the distribution type of each design variable includes:

[0022] Step 401: Treat the nominal values ​​of each key dimension on the drawing as the expected values ​​of the corresponding design variables; in the actual production process, sample from multiple batches of products, measure each key dimension, and obtain the sample dataset of each design variable.

[0023] Step 402: Perform statistical analysis on the sample data of each design variable to fit the distribution model. Determine the optimal distribution type that each design variable follows, i.e., the determined distribution type, through goodness-of-fit tests or related statistical tests.

[0024] Furthermore, the process of solving the mathematical model based on reliability optimization design to determine the design variables includes:

[0025] Step 8: Convert the design parameter vector A candidate solution is used as the position vector of the i-th particle, and the optimal design parameters are solved using the asymmetric learning factor particle swarm optimization algorithm; the optimal design parameters obtained in this iteration are denoted as... This is also known as the deterministic optimal solution;

[0026] Step 9: Convert the deterministic optimal solution By mapping to the standard normal space U;

[0027] Step 10: Solve for the minimum functional objective point for each constraint in the standard normal space U. point;

[0028] Step 11: Find the minimum functional objective point for each constraint in the U-space. Inverse transformation mapped to design space yields ;

[0029] Step 12: Optimize the design parameters based on this round of optimization. Minimum functional target point Obtain the offset vectors corresponding to each constraint function. ;

[0030] Step 13: Evaluate the accuracy of the objective function at the optimal design point. If the accuracy requirement is met, then the accuracy requirement is not met. The objective function is the Kriging surrogate model accuracy threshold.

[0031] Step 14: If step 13 meets the accuracy requirements, proceed directly to step 16; otherwise, according to... Obtain the partial derivatives of the objective function kriging surrogate model with respect to each dimension of the optimal design point; where, This represents the vector corresponding to the partial derivatives of each dimension at the optimal design point. The components are the partial derivatives of the objective function Kriging surrogate model with respect to each dimension of the optimal design point. Reference or ; , They are respectively and about Jacobian matrix, This represents the regression basis function vector corresponding to the Kriging surrogate model. This is a vector relating to each sample point; For regression coefficients, The correlation coefficient;

[0032] Step 15: Transform the optimal design point to the standard normal space, and generate the local sampling space according to formula (7);

[0033] (7)

[0034] (8)

[0035] (9)

[0036] in, For the local sampling space corresponding to the sample point, This is the mathematical definition of the local sampling space; and As a regulating factor; Gradient adaptive scaling factor; represent The absolute value of the j-th component, ; Let be the sampling radius in the j-th dimension; This represents the maximum value of the given target reliability index in the RBDO problem; As a global regulatory factor; This represents the mean squared error of the Krijing model's predictions. This represents the minimum value among the components of the vector. This represents the maximum value of each component of the vector. The mean square error of the prediction at the optimal design point;

[0037] Step 16, if ,but For active constraints, otherwise Inactive constraint; ,in Represents the 2-norm of a vector; Representing variables dimensionality; For tolerance, intermediate variables Used to adjust tolerance ; For control coefficients; Kriging surrogate model representing constraint functions exist The mean square error of the prediction at that location; For the i-th constraint function in the previous (k-1)th iteration, the MPTP point is initialized to the point obtained in the current iteration. The kriging proxy model is used for the i-th function in the k-th loop. The gradient of the constraint at the point of maximum possible failure;

[0038] Step 17, if If it is an active constraint, then evaluate at the minimum functional objective point. If the accuracy requirement is met, then the accuracy requirement is not met. The Kriging surrogate model accuracy threshold is used as the constraint function.

[0039] Step 18: If step 17 does not meet the accuracy requirements, calculate the partial derivatives of the constraint function in each dimension at the minimum functional objective point;

[0040] (12)

[0041] in, This represents the mean squared error of the Kriging surrogate model's prediction at point x. for The gradient with respect to x; represents the process variance; F represents the regression matrix, whose rows are composed of the regression basis function vectors at the sample points; R represents the correlation matrix between the sample points. This represents the correlation vector between the new point x and each sample point;

[0042] Step 19: Transform the minimum functional target point to the standard normal space, and generate the local sampling space according to equation (13);

[0043] (13)

[0044] (14)

[0045] (15)

[0046] in, Kriging surrogate model representing the k-th cycle constraint function Predicted gradient function The absolute value of the j-th component; , Gradient adaptive scaling factor; The sampling radius in the j-th dimension; The reliability index corresponding to each constraint;

[0047] Step 20: If step 17 meets the accuracy requirements, or the constraint function... If the constraint is inactive, then determine whether the next constraint is an active constraint.

[0048] Step 21: After all constraint function tests are completed, in the local sampling space... and The Latin hypercube sampling technique is used to generate local optimization candidate sample points for the objective function and constraint functions. ;

[0049] Step 22: Transform candidate sample points into the design space; use the maximum chord length deviation method to select the optimal addition point in each local sampling space;

[0050] Step 23: Using the true objective function and the actual constraint equations Obtain the true values ​​at the optimal candidate samples and add them to the objective function and the sample set of each active constraint function kriging model, respectively.

[0051] Step 24: Calculate the offset vector according to Step 12, and then substitute the calculated offset into the mathematical model of reliability optimization design to update the constraint equation Kriging surrogate model.

[0052] Step 25: Increment the iteration count by 1, and use the asymmetric learning factor particle swarm optimization algorithm to solve for the optimal design point;

[0053] Step 26: Determine whether the optimal design point has converged. If it has converged, end the process and output the optimal design point. If it has not converged and the maximum number of iterations has not been reached, return to step 9 to perform a reliability assessment and solve for the minimum functional objective point.

[0054] Furthermore, the mathematical model for the asymmetric learning factor particle swarm optimization algorithm in step 8 is as follows:

[0055] (2)

[0056] (3)

[0057] in, For the first The position vector of the i-th particle in the next iteration, i.e., the design parameter vector. A candidate solution; For the first The velocity vector of the i-th particle in the next iteration; w is the inertia weight coefficient, which adjusts the influence of the velocity vector in the previous iteration on the velocity vector in the current iteration; Is it up to the The optimal position that the i-th particle has passed through up to the nth iteration; To reach the first The optimal positions reached by all particles up to the nth iteration; r1 and r2 are random numbers uniformly distributed in the interval (0, 1); d is the current iteration number; The maximum number of iterations is preset. , Learning factor , The preset initial value; , They are respectively , The preset final value; the parameter vector is designed during the solution process. That is Particles, the optimal particles obtained in the final calculation The numerical value represents the optimal design parameters obtained in this optimization. .

[0058] Furthermore, the offset vectors corresponding to each constraint function described in step 12 .

[0059] Furthermore, step 22 involves selecting the optimal addition point in each local sampling space using the maximum chord length deviation method, as follows:

[0060] (16)

[0061] (17)

[0062] (18)

[0063] Where D is Mahalanobis distance between the sample point set and existing points in the sample point set The mean Mahalanobis distance between all existing points in the set of all sample points; F represents the objective function surrogate model or the constraint function surrogate model; To calculate the step size, a value is typically taken as... ; , , , All are intermediate variables.

[0064] Furthermore, the criterion for determining whether the optimal design point has converged in step 26 is as follows: , The threshold for convergence accuracy at the optimal design point is used to determine convergence; convergence is achieved if the condition is met, otherwise convergence is not achieved.

[0065] Furthermore, in step 26, if convergence is not achieved and the number of iterations exceeds the maximum number of iterations limit, then the result is returned as non-convergence.

[0066] Beneficial effects:

[0067] This invention improves global search capability and convergence stability through an asymmetric learning factor particle swarm optimization algorithm, making it easier to obtain globally optimal or near-globally optimal reliability design schemes. Furthermore, by employing a sequential local sampling strategy to centrally and densely sample at key locations, this invention enhances the prediction accuracy of the surrogate model in sensitive areas such as failure constraints. Compared to traditional global uniform sampling, it further reduces the cost of surrogate model construction while maintaining accuracy. This invention not only effectively addresses the problems of traditional reliability optimization design's heavy reliance on physical testing, resulting in long testing cycles and high costs, and the issues of current component design methods involving numerous finite element simulations and high computational time costs, but also solves the problem of low sampling efficiency in key areas such as failure constraints in existing technologies, making it difficult to balance computational accuracy and efficiency.

[0068] This invention can significantly reduce the number of finite element simulations and physical tests, shorten the reliability design cycle, and reduce the time and money costs of design, while ensuring that the impacted components of the detached connector meet the predetermined failure probability index. It provides a more accurate, reliable, and efficient low-cost means for reliability optimization design of impacted components of detached connectors in engineering applications. Attached Figure Description

[0069] Figure 1 This is a distribution diagram of the sampling points in Example 1.

[0070] Figure 2 This is a diagram of the force transmission structure of the connector. Detailed Implementation Specific implementation method one:

[0072] This embodiment describes a reliability design optimization method for impact-affected components of a detached connector, comprising:

[0073] Step 1: Create a 3D model of the detachable connector based on the drawings:

[0074] (1) Establish a high-precision three-dimensional digital model of the detachable connector: Based on the design drawings, use three-dimensional modeling software to construct a three-dimensional model containing key components of the detachable locking mechanism. The key components include force transmission ring, force transmission sleeve, coil, spring, steel ball, pull rod and protective sleeve. The assembly is completed according to the assembly relationship to restore the details of the cooperation between the components.

[0075] (2) Finite element simulation analysis of electromagnetic unlocking process: Import the three-dimensional model of step (1) into the finite element simulation software ANSYS WORKBENCH, define material properties, set contact relationship, constraint conditions and spring parameters, perform transient simulation after meshing, and obtain equivalent stress data of force transmission ring during electromagnetic unlocking process.

[0076] (3) Experimental verification of simulation results: Build an experimental platform, trigger the connector electromagnetic unlocking with a 24V DC power supply, use a laser vibrometer to measure the speed of the pull rod, and use a high-speed camera to measure the displacement of the force transmission ring during the unlocking process. Compare the measured results with the simulation results of step (2). It is necessary to ensure that the relative error between the model simulation value and the actual test value is not greater than 10%. If it is greater, the model needs to be fine-tuned by referring to the finite element modeling method until it meets the requirements.

[0077] Step 2, Parametric connector model:

[0078] Step 201: Based on the structural function and actual application requirements of the connector, select the target component to be optimized as the design object; on this basis, determine the design parameter set by combining prior engineering experience. The design parameter set includes geometric dimension parameters, material parameters and constraint-related parameters. The design parameters should be controllable parameter types in the actual production process. The above parameter types include, but are not limited to, the aforementioned categories.

[0079] In step 201, the principle for selecting design parameters is: under the premise of meeting engineering feasibility, select as many dimensions or physical quantities as possible that may affect performance indicators, so as to cover all key factors affecting requirements and reduce the risk of omitting important parameters.

[0080] Step 202: Based on the design requirements and performance concerns, select performance index parameters from the finite element analysis results as objective function values ​​or constraint function values. The performance indexes include, but are not limited to, fatigue life, maximum equivalent stress, maximum displacement, natural frequency, and peak contact pressure. In the simulation platform (e.g., ANSYS Workbench), set the above performance indexes as output parameters.

[0081] Step 203: During the 3D modeling and finite element preprocessing, the design parameters are set one by one to adjustable "driving parameters". The parameter switch is turned on at the corresponding dimension annotation, and the parameter mark "P" is displayed on the interface, thereby completing the parameter setting of the connector finite element model.

[0082] Step 3: Pre-screen key dimension parameters and their value ranges:

[0083] Based on the parameterized connector model in step 2, a pre-analysis is performed using finite element simulation to screen key dimensional parameters that significantly affect performance indicators. That is, step 2 selects a series of design parameters, and step 3 uses a pre-experiment to select the design parameters most relevant to performance, which will then be used as variables for subsequent optimization. The specific process includes:

[0084] Step 301: Based on the finite element model with parameterized settings completed in Step 2, determine the value range of each parameter according to the preset design parameter level, and construct several sets of simulation conditions using orthogonal experimental design method to characterize the combined changes of design parameters within a reasonable range.

[0085] Step 302: Perform finite element analysis on each group of orthogonal test conditions to obtain the output performance index response values ​​under different parameter combinations, including but not limited to maximum equivalent stress, maximum displacement, natural frequency, peak contact pressure, etc.

[0086] Step 303: Perform statistical and sensitivity analysis on the simulation results. For example, use range analysis, variance analysis or other parameter sensitivity evaluation methods to qualitatively or quantitatively rank the degree of influence of each design parameter on the performance index, and identify the influence threshold of each parameter.

[0087] Step 304: Based on the project timeline requirements and the available computing resources / simulation time budget, retain only a few key dimensional parameters that significantly affect the target performance indicators to form a design parameter vector, providing variables for subsequent optimization design.

[0088] Step 4: Confirm the distribution type of each design variable:

[0089] Step 401: Treat the nominal values ​​of each key dimension on the drawings as the expected values ​​of the corresponding design variables; in the actual production process, sample from multiple batches of products, measure each key dimension, and obtain a sample dataset of each design variable. Where conditions permit, the sample size should be increased as much as possible; where conditions are limited, several candidate distribution types can be hypothesized based on engineering experience, and relevant industry standards should be consulted. The sampling size should not be less than the maximum of the minimum sample size required for each candidate distribution type to determine its distribution affiliation.

[0090] Step 402: Perform statistical analysis on the sample data of each design variable, attempt to fit several common engineering distribution models, such as normal distribution, log-normal distribution, uniform distribution or other applicable probability distributions, and determine the optimal distribution type that each design variable follows through goodness-of-fit tests or related statistical tests.

[0091] Step 5: Use the Latin hypercube sampling technique to randomly generate sampling points within the range of values ​​of each optimization parameter as the initial sampling point set. The initial sampling scale is usually 3 to 15 times the number of design variables.

[0092] Step 6: Construct an initial objective function based on the initial sample point set to obtain the mathematical model for reliability optimization design as follows:

[0093] (1)

[0094] in, A vector composed of design parameters. This represents the optimal value of the design parameters obtained in the k-th iteration. Therefore The vector of random variables with mean X, and the components of X follow the optimal distribution type determined in step 4; It is a Kriging surrogate model with an objective function equation, typically including a certain performance metric or cost of the product, or both; for applications This represents the true objective function, which can be obtained from finite element simulation or physical experiments in practical engineering. Representing the kriging surrogate model for the i-th constraint equation, the failure event is denoted as... <0; for applications This represents the actual constraint equations, which can be obtained from finite element simulation or physical experiments in practical engineering; N is the number of constraint equations. and They are respectively The lower and upper bounds; Let be the translation vector of the feasible region for the i-th constraint in the (k+1)-th iteration. Let MPTP point be the MPTP point corresponding to the i-th constraint obtained in the k-th iteration. MPTP point refers to the design parameter vector most likely to fail under a given reliability, and is called the minimum functional target point.

[0095] Then solve this problem through the following steps.

[0096] Step 8: Solve for the optimal design parameters using the asymmetric learning factor particle swarm optimization algorithm. The mathematical model of the asymmetric learning factor particle swarm optimization algorithm is as follows:

[0097] (2)

[0098] (3)

[0099] in, For the first The position vector of the i-th particle in the next iteration, i.e., the design parameter vector. A candidate solution; For the first The velocity vector of the i-th particle in the next iteration; w is the inertia weight coefficient, which adjusts the influence of the velocity vector in the previous iteration on the velocity vector in the current iteration; Is it up to the The optimal position that the i-th particle has passed through up to the nth iteration; To reach the first The optimal positions reached by all particles up to the nth iteration; r1 and r2 are random numbers uniformly distributed in the interval (0, 1); d is the current iteration number; The maximum number of iterations is preset. , Learning factor , The preset initial value; , They are respectively , The preset final value. The parameter vector is designed during the solution process. That is Particles, the optimal particles obtained in the final calculation The numerical value represents the optimal design parameters obtained in this optimization. .

[0100] Let the optimal design parameters obtained from this round of iterative calculations be denoted as... This is also known as the deterministic optimal solution.

[0101] Step 9: Convert the deterministic optimal solution Map to the standard normal space (U space) using the method shown in Table 1.

[0102] Table 1

[0103]

[0104] In Table 1, X represents a physical space random variable, and U represents a standard normal space random variable N(0,1). In practical processing, it is necessary to transform it to the standard normal distribution according to the "X→U transformation formula" before processing.

[0105] Standard normal distribution: μ—mean, σ—standard deviation.

[0106] Log-normal distribution: ln(·) — natural logarithm, exp(·) — exponential function.

[0107] Relevant parameters of the Weibull distribution: λ—Weibull scale parameter, k—Weibull shape parameter, Γ(·)—gamma function.

[0108] Parameters related to the Gumbel distribution: ν—Gumbel location parameter, α—Gumbel scale parameter, γ—Euler constant.

[0109] Parameters related to uniform distribution: a, b—upper and lower bounds of uniform distribution.

[0110] Step 10: Solve for the following equation in the standard normal space U, which is the minimum functional objective point for each constraint. point.

[0111] (4)

[0112] Where U is the design variable in the U-space. Represents the 2-norm of a vector; For each constraint, there is a corresponding reliability index. Essentially, the reliability index is a quantile of a normal distribution. The reliability index represents the product's reliability, meaning the probability of the product failing during stable operation is no greater than [a certain value]. For example, a reliability index of 3 means that the probability of failure cannot be greater than the normal distribution quantile of -3.

[0113] Step 11: Find the minimum functional objective point for each constraint in the U-space. Inverse transformation mapped to design space yields Let T denote any function that maps X to the standard normal space U (as shown in Table 1), then Its inverse transform, through Convert U to X.

[0114] Step 12: Optimize the design parameters based on this round of optimization. Minimum functional target point Calculate the offset vectors corresponding to each constraint function.

[0115] (5)

[0116] Step 13: Evaluate the accuracy of the objective function at the optimal design point. , This is the accuracy threshold for the Kriging surrogate model, typically set to 1%.

[0117] Step 14: If the accuracy requirements are met in step 13, proceed directly to step 16; otherwise, if the accuracy requirements are not met ( According to equation (6), the partial derivatives of the objective function kriging surrogate model with respect to each dimension of the optimal design point are obtained.

[0118] (6)

[0119] in, This represents the vector corresponding to the partial derivatives of each dimension at the optimal design point. The components are the partial derivatives of the objective function Kriging surrogate model with respect to each dimension of the optimal design point. Reference or ; , They are respectively and about Jacobian matrix, This represents the regression basis function vector corresponding to the Kriging surrogate model. This is a vector relating to each sample point; For regression coefficients, The correlation coefficient.

[0120] Step 15: Transform the optimal design point to the standard normal space, and generate the local sampling space according to formula (7);

[0121] (7)

[0122] (8)

[0123] (9)

[0124] in, For the local sampling space corresponding to the sample point, (x in bold) is the mathematical definition of the local sampling space; and As a regulating factor, Usually, 1.2 is taken. The value is usually 0.3; Gradient adaptive scaling factor; The kriging surrogate model represents the objective function of the k-th iteration. Predicted gradient function The absolute value of the j-th component, ; Let be the sampling radius in the j-th dimension; This represents the maximum value of the given target reliability index in the RBDO problem; As a global control factor, the basic radius of the sampling region is adjusted based on historical iteration data, and is taken in the first iteration. =1; This represents the prediction mean square error (error vector) of the Krijing model. This represents the minimum value among the components of the vector. This represents the maximum value of each component of the vector. This represents the mean square error of the prediction at the optimal design point.

[0125] Step 16: Use the following formula to check if the constraint is an active constraint:

[0126] (10)

[0127] (11)

[0128] in, Represents the 2-norm of a vector; Representing variables dimensionality; For tolerance, intermediate variables Used to adjust tolerance ; As a control factor, it is set to 2 in this embodiment; Kriging surrogate model representing constraint functions exist The mean square error of the prediction at that location; The MPTP point is the maximum possible failure point corresponding to the i-th constraint function in the previous (k-1)th iteration. In the first iteration, the MPTP point is initialized to the point obtained in the current iteration. The kriging proxy model is used for the i-th function in the k-th loop. The gradient is the constraint at the point of maximum possible failure, and its value is obtained similarly from step 14.

[0129] Step 17, if If it is an active constraint, then evaluate at the minimum functional objective point. , The Kriging surrogate model accuracy threshold is used as the constraint function, typically set to 1%.

[0130] Step 18: If the accuracy requirements are not met, i.e. Then calculate the partial derivatives of the constraint function in each dimension at the minimum functional objective point;

[0131] (12)

[0132] in, This represents the mean squared error of the Kriging surrogate model's prediction at point x. for The gradient with respect to x; The process variance (variance parameter of the Kriging surrogate model) is represented by F; F represents the regression matrix, whose rows are represented by the regression basis function vectors at the sample points. Composition; R represents the correlation matrix between sample points; This represents the correlation vector between the new point x and each sample point;

[0133] Step 19: Transform the minimum functional target point to the standard normal space, and generate the local sampling space according to equation (13);

[0134] (13)

[0135] (14)

[0136] (15)

[0137] in, Kriging surrogate model representing the k-th cycle constraint function Predicted gradient function The absolute value of the j-th component; , Gradient adaptive scaling factor; The sampling radius in the j-th dimension; The reliability index corresponding to each constraint.

[0138] Step 20: If the accuracy requirements are met, i.e. or constraint function If a constraint is inactive, then determine whether the next constraint is an active constraint.

[0139] Step 21: After all constraint function tests are completed, in the local sampling space... and The Latin hypercube sampling technique is used to generate local optimization candidate sample points for the objective function and constraint functions. .

[0140] Step 22: Transfer candidate sample points to the design space.

[0141] The optimal insertion point is selected in each local sampling space using the Maximum Chordal Deviation (MCD) method:

[0142] (16)

[0143] (17)

[0144] (18)

[0145] Where D is Mahalanobis distance between the sample point set and existing points in the sample point set The mean Mahalanobis distance between all existing points in the set of all sample points; F represents the objective function surrogate model or the constraint function surrogate model; To calculate the step size, a value is typically taken as... ; , , , All are intermediate variables.

[0146] Step 23: Using the true objective function and the actual constraint equations (Numerical values ​​obtained from finite element simulation or physical experiments) Obtain the true values ​​at the optimal candidate samples and add them to the sample sets of the objective function and each active constraint function kriging model, respectively.

[0147] Step 24: Calculate the offset vector according to Step 12, and then substitute the calculated offset into Formula (1) to update the constraints. ;

[0148] Step 25: Increment the iteration count by 1, and use the asymmetric learning factor particle swarm optimization algorithm to solve for the optimal design point;

[0149] Step 26: Determine if the optimal design point has converged. , The optimal design point convergence accuracy threshold is generally selected as follows: If convergence is achieved, the process ends, and the optimal design point is output.

[0150] Step 27: If the algorithm does not converge and the maximum number of iterations has not been reached, return to step 9 to perform a reliability assessment and solve for the minimum functional objective point.

[0151] Step 28: If the number of iterations exceeds the maximum number of iterations limit, return "not converged".

[0152] The performance of the present invention is verified through the following two embodiments.

[0153] Example 1:

[0154] This embodiment includes two random variables that follow a normal distribution. , And three constraint equations. The design variables are random variables. , mean , The initial design point is the midpoint of the range of design variable values. The target reliability index for each constraint function is 3, meaning the failure probability of the system at each constraint condition must not exceed 0.13%. The descent direction of the objective function points towards the origin, meaning the minimum value of the objective function lies in the region of the design space close to the origin. A reliability design optimization model based on sequential optimization and reliability assessment framework:

[0155]

[0156]

[0157]

[0158]

[0159]

[0160]

[0161]

[0162]

[0163] The distribution of sampling points is as follows Figure 1 As shown, the yellow, red, and blue markers correspond to three different constraint functions. The solid lines represent the actual constraint function curves, while the dashed lines are approximate curves obtained from the Kriging surrogate model. Figure 1 As can be seen, some initial constraint functions were correctly identified as inactive constraints and therefore excluded during the model update process. Most of the newly added sampling points are distributed on both sides of the limit state constraints, especially concentrated near the MPTP point, where accurate characterization of the constraints is crucial. This example generates two new sampling points for the objective function based on the shared initial dataset; in addition, six and four new sampling points are generated for constraints 1 and 2, respectively, demonstrating the adaptive capability of the proposed update strategy in selectively refining the surrogate model.

[0164] Table 2 shows the minimum values ​​of the objective function obtained by the six methods. and optimal parameter design parameters . This represents the actual number of times the target function was called; This represents the number of times the actual constraint function is called; This represents the reliability index corresponding to the i-th constraint function. The reliability index is obtained by randomly generating sampling points centered on the optimal design point using the MCS method. Table 2 also shows the maximum relative error between various reliability methods and Anal.SORA reliability. The method proposed in this invention minimizes the calls to the true objective function and constraint functions, ensuring a very small relative error. Although the relative error is greater than that of the LHS-kriging method, the strategy proposed in this invention calls the objective function and constraint functions only about one-tenth of the number of times the LHS-kriging method does so. Compared to the high computational cost, the computational error is negligible.

[0165] Table 2

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[0167] Example 2:

[0168] Optimization of lightweight and reliability design for impact-affected components of the detached connector:

[0169] Figure 2 This is a diagram of the connector's force transmission structure, such as... Figure 2 As shown, the force transmission ring, as the core force-bearing component in this separation mechanism, plays a crucial role in the connector engagement and unlocking process. The thrust generated by the separation spring is transmitted to the force transmission ring through the sleeve, thereby driving the subsequent mechanism to complete the unlocking action. Since it bears the main force transmission function, the structural performance of the force transmission ring has a significant impact on the reliability and response speed of the entire separation process. Optimizing the structural parameters of this component to minimize mass while meeting performance requirements is a typical reliability-based design optimization (RBDO) problem. In this study, the mass of the load transfer ring is selected as the objective function. A reliability-based optimization model was established. The following performance requirements are considered as constraints:

[0170] 1. The maximum equivalent stress of the force transmission ring under impact load. Not exceeding the yield strength of the material ;

[0171] 2. Under the deformation caused by impact load, interference between adjacent components must be avoided to prevent jamming. This indicates the maximum deformation of the force transmission ring. 3. Fatigue life Must exceed the given limit The outer diameter of the force transmission ring. Outer diameter of the stress step Ring thickness The width of the stress step and Fixed step width Based on the measurement data of batch parts, the distribution type is determined using the design parameters, and the mathematical model for this reliability design optimization is as follows:

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[0184] Tables 3 and 4 systematically compare the optimization performance and computational efficiency of different sampling strategies in RBDO.

[0185] Table 3

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[0187] Table 4

[0188]

[0189] Table 3 shows the minimum objective function value. Optimal design parameters and reliability indicators These reliability metrics are generated near the optimal design parameters. A number of Monte Carlo samples are used to evaluate the probability of failure events. Table 3 summarizes the computational cost, including the number of objective function evaluations. Number of constraint function evaluations and total number of function calls The latter corresponds to the number of finite element transient impact simulations required in the optimization process. Results show that although the LHS-Kriging and CBS methods have higher computational costs, they achieve similar optimization results. Although CBS produces the smallest... However, its first constraint has the lowest reliability index, thus not fully meeting the reliability requirements. Besides CBS, the proposed method not only achieves near-optimal results... Moreover, it is the only one that can consistently meet the reliability conditions under all constraints. The method, as shown in Table 3, requires only 376 objective function evaluations and 1928 total function calls, representing reductions of 71% and 63% respectively compared to LHS-Kriging. Furthermore, by employing an active constraint identification strategy, this method successfully identified... With inactive constraints, 115 fewer evaluations are required compared to LUOC-SORA. Overall, the proposed method significantly reduces computational costs while maintaining optimization accuracy and reliability, demonstrating its effectiveness in engineering RBDO applications.

[0190] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A reliability design optimization method for impact-affected components of a detached connector, characterized in that, First, a 3D model of the detachable connector is created based on the drawings to determine the key dimensional parameters and their value ranges. These key dimensional parameters constitute the design parameter vector. Then, design optimization is performed, including: Step 4: Determine the distribution type of each design variable; Step 5: Use the Latin hypercube sampling technique to randomly generate sampling points within the range of each optimization parameter value as the initial sampling point set; Step 6: Determine the mathematical model based on reliability optimization design as follows: （1） in, A vector composed of design parameters. This represents the optimal value of the design parameters obtained in the k-th iteration. Therefore The vector of random variables with mean X, and the components of X follow the distribution type determined in step 4; It is the Kriging surrogate model with the objective function equation; Representing the kriging surrogate model for the i-th constraint equation, the failure event is denoted as... <0; N is the number of constraint equations; and They are respectively The lower and upper bounds; Let be the translation vector of the feasible region for the i-th constraint in the (k+1)-th iteration. The MPTP point corresponding to the i-th constraint obtained in the k-th iteration is the design parameter vector most likely to fail under a given reliability, and is called the minimum functional target point. The asymmetric learning factor particle swarm optimization algorithm is used to solve the mathematical model based on reliability optimization design to determine the design variables and achieve design optimization.

2. The reliability design optimization method for impact-affected components of a detached connector according to claim 1, characterized in that, The process of creating a 3D model of the detachable connector based on the drawings and determining the key dimensional parameters and their value ranges includes: Step 1: Create a 3D model of the detachable connector based on the drawings: Step 2: Select the target component to be optimized as the design object and determine the set of design parameters; Step 3: Based on the set of design parameters, pre-screen key dimension parameters and their value ranges, and the key dimension parameters constitute the design parameter vector.

3. The reliability design optimization method for impact-affected components of a detached connector according to claim 2, characterized in that, The specific process of pre-screening key dimensional parameters and their value ranges based on the design parameter set includes: Step 301: Construct several sets of simulation conditions using orthogonal experimental design method to characterize the combined changes of design parameters within a reasonable range; Step 302: Perform finite element analysis on each group of orthogonal test conditions to obtain the output performance index response values ​​under different parameter combinations; Step 303: Perform statistical and sensitivity analysis on the simulation results, qualitatively or quantitatively rank the degree of influence of each design parameter on the performance index, and identify the influence threshold of each parameter. Step 304: Determine the key dimensional parameters based on the target performance indicators to form a design parameter vector.

4. The reliability design optimization method for impact-affected components of a detached connector according to claim 1, characterized in that, The process of determining the distribution type of each design variable includes: Step 401: Treat the nominal values ​​of each key dimension on the drawing as the expected values ​​of the corresponding design variables; in the actual production process, sample from multiple batches of products, measure each key dimension, and obtain the sample dataset of each design variable. Step 402: Perform statistical analysis on the sample data of each design variable to fit the distribution model. Determine the optimal distribution type that each design variable follows, i.e., the determined distribution type, through goodness-of-fit tests or related statistical tests.

5. A reliability design optimization method for impact-affected components of a detached connector according to any one of claims 1 to 4, characterized in that, The process of solving the mathematical model based on reliability optimization design and determining the design variables includes: Step 8: Convert the design parameter vector A candidate solution is used as the position vector of the i-th particle, and the optimal design parameters are solved using the asymmetric learning factor particle swarm optimization algorithm; the optimal design parameters obtained in this iteration are denoted as... This is also known as the deterministic optimal solution; Step 9: Convert the deterministic optimal solution By mapping to the standard normal space U; Step 10: Solve for the minimum functional objective point for each constraint in the standard normal space U. point; Step 11: Find the minimum functional objective point for each constraint in the U-space. Inverse transformation mapped to design space yields ; Step 12: Optimize the design parameters based on this round of optimization. Minimum functional target point Obtain the offset vectors corresponding to each constraint function. ; Step 13: Evaluate the accuracy of the objective function at the optimal design point. If the accuracy requirement is met, then the accuracy requirement is not met. The objective function is the Kriging surrogate model accuracy threshold. Step 14: If step 13 meets the accuracy requirements, proceed directly to step 16; otherwise, according to... Obtain the partial derivatives of the objective function kriging surrogate model with respect to each dimension of the optimal design point; where, This represents the vector corresponding to the partial derivatives of each dimension at the optimal design point. The components are the partial derivatives of the objective function Kriging surrogate model with respect to each dimension of the optimal design point. Reference or ; , They are respectively and about Jacobian matrix, This represents the regression basis function vector corresponding to the Kriging surrogate model. This is a vector relating to each sample point; For regression coefficients, The correlation coefficient; Step 15: Transform the optimal design point to the standard normal space, and generate the local sampling space according to formula (7); （7） （8） （9） in, For the local sampling space corresponding to the sample point, This is the mathematical definition of the local sampling space; and As a regulating factor; Gradient adaptive scaling factor; represent The absolute value of the j-th component, ; Let be the sampling radius in the j-th dimension; This represents the maximum value of the given target reliability index in the RBDO problem; As a global regulatory factor; This represents the mean squared error of the Krijing model's predictions. This represents the minimum value among the components of the vector. This represents the maximum value of each component of the vector. The mean square error of the prediction at the optimal design point; Step 16, if ,but For active constraints, otherwise Inactive constraint; ,in Represents the 2-norm of a vector; Representing variables dimensionality; For tolerance, intermediate variables Used to adjust tolerance ; For control coefficients; Kriging surrogate model representing constraint functions exist The mean square error of the prediction at that location; For the i-th constraint function in the previous (k-1)th iteration, the MPTP point is initialized to the point obtained in the current iteration. The kriging proxy model is used for the i-th function in the k-th loop. The gradient of the constraint at the point of maximum possible failure; Step 17, if If it is an active constraint, then evaluate at the minimum functional objective point. If the accuracy requirement is met, then the accuracy requirement is not met. The Kriging surrogate model accuracy threshold is used as the constraint function. Step 18: If step 17 does not meet the accuracy requirements, calculate the partial derivatives of the constraint function in each dimension at the minimum functional objective point; （12） in, This represents the mean squared error of the Kriging surrogate model's prediction at point x. for The gradient with respect to x; represents the process variance; F represents the regression matrix, whose rows are composed of the regression basis function vectors at the sample points; R represents the correlation matrix between the sample points. This represents the correlation vector between the new point x and each sample point; Step 19: Transform the minimum functional target point to the standard normal space, and generate the local sampling space according to equation (13); （13） （14） （15） in, Kriging surrogate model representing the k-th cycle constraint function Predicted gradient function The absolute value of the j-th component; , Gradient adaptive scaling factor; The sampling radius in the j-th dimension; The reliability index corresponding to each constraint; Step 20: If step 17 meets the accuracy requirements, or the constraint function... If the constraint is inactive, then determine whether the next constraint is an active constraint. Step 21: After all constraint function tests are completed, in the local sampling space... and The Latin hypercube sampling technique is used to generate local optimization candidate sample points for the objective function and constraint functions. ; Step 22: Transform candidate sample points into the design space; use the maximum chord length deviation method to select the optimal addition point in each local sampling space; Step 23: Using the true objective function and the actual constraint equations Obtain the true values ​​at the optimal candidate samples and add them to the objective function and the sample set of each active constraint function kriging model, respectively. Step 24: Calculate the offset vector according to Step 12, and then substitute the calculated offset into the mathematical model of reliability optimization design to update the constraint equation kriging surrogate model. Step 25: Increment the iteration count by 1, and use the asymmetric learning factor particle swarm optimization algorithm to solve for the optimal design point; Step 26: Determine whether the optimal design point has converged. If it has converged, end the process and output the optimal design point. If it has not converged and the maximum number of iterations has not been reached, return to step 9 to perform a reliability assessment and solve for the minimum functional objective point.

6. A reliability design optimization method for impact-affected components of a detached connector according to claim 5, characterized in that, The mathematical model for the asymmetric learning factor particle swarm optimization algorithm in step 8 is as follows: （2） （3） in, For the first The position vector of the i-th particle in the next iteration, i.e., the design parameter vector. A candidate solution; For the first The velocity vector of the i-th particle in the next iteration; w is the inertia weight coefficient, which adjusts the influence of the velocity vector in the previous iteration on the velocity vector in the current iteration; Is it up to the The optimal position that the i-th particle has passed through up to the nth iteration; To reach the first The optimal positions reached by all particles up to the nth iteration; r1 and r2 are random numbers uniformly distributed in the interval (0, 1); d is the current iteration number; The maximum number of iterations is preset. , Learning factor , The preset initial value; , They are respectively , The preset final value; the parameter vector is designed during the solution process. That is Particles, the optimal particles obtained in the final calculation The numerical value represents the optimal design parameters obtained in this optimization. .

7. A reliability design optimization method for impact-affected components of a detached connector according to claim 5, characterized in that, The offset vectors corresponding to each constraint function mentioned in step 12 .

8. A reliability design optimization method for impact-affected components of a detached connector according to claim 5, characterized in that, Step 22 describes the selection of the optimal addition point in each local sampling space using the maximum chord length deviation method, as follows: （16） （17） （18） Where D is Mahalanobis distance between the sample point set and existing points in the sample point set The mean Mahalanobis distance between all existing points in the set of all sample points; F represents the objective function surrogate model or the constraint function surrogate model; To calculate the step size, a value is typically taken as... ; , , , All of these are intermediate variables.

9. A reliability design optimization method for impact-affected components of a detached connector according to claim 5, characterized in that, Step 26: The criterion for determining whether the optimal design point has converged is: , The threshold for convergence accuracy at the optimal design point is used to determine convergence; convergence is achieved if the condition is met, otherwise convergence is not achieved.

10. A reliability design optimization method for impact-affected components of a detached connector according to claim 9, characterized in that, If the process fails to converge in step 26 and the number of iterations exceeds the maximum number of iterations, then return "not convergent".

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