Adaptive kriging based reliability analysis method for planar parallel mechanism system

Abstract

This invention provides an adaptive kriging-based reliability analysis method for planar parallel mechanism systems, relating to the field of reliability analysis for planar parallel mechanism systems. The method includes: establishing a dynamic model, determining the distribution type of random variables, and establishing corresponding wear function functions; sampling and generating initial sample points and their corresponding function functions as an initial training set; predicting the predicted values ​​and variances of the overall sample based on the initial kriging model, estimating the uncertainty bound and the current failure probability, and determining whether the stopping criterion is met; selecting updated samples according to the optimal point selection principle, performing dynamic simulation on the updated samples to obtain the corresponding real responses, adding them to the initial training set, retraining the kriging model, and repeating this process until all sample points are used to terminate the iteration. This invention continuously filters out samples with the largest differences, selecting the optimal samples without sacrificing prediction accuracy, avoiding tedious calculations of large amounts of data, and improving computational efficiency.

Description

Technical Field

[0001] This invention relates to the field of reliability analysis technology for planar parallel mechanism systems, and specifically to a method for reliability analysis of planar parallel mechanism systems using adaptive kriging. Background Technology

[0002] A planar parallel mechanism is a closed-loop mechanism consisting of a moving platform and a fixed platform connected in a plane by at least two independent kinematic chains. It boasts advantages such as compact structure, high rigidity, high precision, and fast movement speed, and is widely used in high-speed, light-load positioning and operation scenarios. As the core execution unit of high-precision automated equipment, the reliability of the planar parallel mechanism directly determines the lifespan and performance stability of the entire equipment.

[0003] Currently, there are few reliability analysis methods for wear systems of planar parallel mechanisms. Furthermore, due to the intertwining of multiple sources of uncertainty, it is difficult to accurately quantify the wear evolution process. The nonlinearity of the modeling process is high, making it difficult to balance computational efficiency and accuracy. There is a lack of a unified framework for system-level reliability modeling. In addition, the experimental verification cycle is long and the equipment requirements are high. As a result, reliability analysis is very difficult and cannot meet the actual industrial needs.

[0004] For example, the U learning function in the traditional AK-SYS does not consider the probability density function of random variables, resulting in low computational efficiency, which can no longer meet the urgent needs of modern industry for real-time assessment and predictive maintenance of equipment status. Summary of the Invention

[0005] To address the shortcomings of the prior art, the present invention aims to provide an adaptive kriging method for reliability analysis of planar parallel mechanism systems, which can balance computational efficiency and engineering applicability, thereby solving the problem of balancing computational efficiency and accuracy in existing reliability analysis methods for wear systems of planar parallel mechanisms.

[0006] Specifically, on the one hand, the present invention provides a reliability analysis method for an adaptive kriging planar parallel mechanism system, which includes the following steps: S1: Establish a dynamic model of the planar parallel mechanism considering irregular wear of kinematic pairs; S2: Determine the distribution type of the random variables of the mechanism system parameters and establish the corresponding function of the kinematic pair with respect to the wear depth; S3: Initial sample points are generated using the Latin hypercube sampling method. ; S4: Initial sample points through different kinematic pairs Its corresponding function value Use this as the initial training set to train the corresponding initial kriging model; S5: Generate the Monte Carlo population sample based on the joint distribution of the input random variables. ; S6: Based on the initial kriging model of each kinematic pair in S4, predict the predicted value of the overall sample P in S5. With prediction variance And estimate the uncertainty bound Compared with the current failure probability ; S7: Uncertainty bound estimated in conjunction with S6 Compared with the current failure probability Determine whether the stopping criterion is met. If it is met, terminate the iteration and output the system failure probability. If it is not met, proceed to the next step. S8: Select updated samples according to the optimal point selection principle. Specifically, it includes the following steps: S81: Select the minimum predicted response value among the different failure modes corresponding to each sample point in the overall sample P. and its corresponding prediction variance ; S82: Classify each sample point in the total sample P and determine whether the prediction is correct: determine the sample size of each sample point. Does it meet the requirements? If the conditions are met, the group is classified as a prediction error group. S83: For each sample point in the prediction error group, the KB strategy is applied sequentially. While keeping the hyperparameters unchanged, the kriging model of the corresponding failure mode is updated. The updated kriging model replaces the initial kriging model in S6, and S6 to S82 are re-executed to obtain the updated prediction error group. The sample with the largest difference is selected as the update sample. ; S9: Update the sample Perform dynamic simulation to obtain the corresponding real response. The sample will be updated. Its corresponding actual response Add it to the initial training set, retrain the kriging model, and return to execute S6 until all sample points are exhausted and the iteration terminates.

[0007] Furthermore, in S1, the methods for establishing a dynamic model of the planar parallel mechanism considering irregular wear of the kinematic pairs include: S11: The dynamic model of the planar parallel mechanism is established using the Lagrange multiplier method; S12: Based on the dynamic model of the planar parallel mechanism in S11, a dynamic model of the planar parallel mechanism with gaps is established by reducing the corresponding constraints by reducing the Lagrange multipliers; S13: Based on the dynamic model of the planar parallel mechanism with gap established in S12, a wear prediction model for the kinematic pair is established by using the Lankarani-Nikravesh contact force model and combining it with the Archard wear prediction model.

[0008] Furthermore, the random variables of system parameters in S2 include the geometric dimensions of the drive rod and connecting rod, the Young's modulus and Poisson's ratio of the bearings and bushings, and the coefficient of friction.

[0009] Furthermore, the distribution types of the random variables of the system parameters in S2 include uniform distribution, normal distribution, and Poisson distribution.

[0010] Furthermore: the kinematic pair type in S2 is a revolute pair consisting of a shaft and a bushing.

[0011] Furthermore, S3 also includes: conducting irregular wear dynamics simulation experiments on the initial sample points to obtain the true function values ​​of the corresponding kinematic pairs. .

[0012] Furthermore: In S7, the stopping criterion is: ; Among them, the threshold parameter Set as If the condition is met three times, it is considered convergent. This is the upper bound of the failure probability. This is the lower bound of the failure probability. This represents the failure probability.

[0013] Preferably, the number of kinematic pairs is three.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention trains kriging models corresponding to various failure modes, outputs multiple predicted values ​​after inputting samples, selects the group of predicted errors from samples that do not meet the stopping criterion, and selects the sample with the largest difference as the best update sample. Its corresponding actual response By adding samples to the initial training set and retraining the kriging model, the above screening steps are repeated to continuously select the samples with the largest differences until the iteration is complete. This method can effectively select the best samples without losing prediction accuracy, thereby avoiding the tedious calculation process of large amounts of data, improving computational efficiency, and saving the cost of reliability analysis.

[0015] This invention applies the iterative optimization method for the Kriging model to planar parallel mechanism systems. Addressing the issues of complex models, numerous uncertainties, and high computational demands, it provides a novel approach and methodology for reliability analysis of planar parallel mechanism systems through continuous screening, optimization, and iteration, achieving a balance between computational efficiency and accuracy. Attached Figure Description

[0016] Figure 1 This is an overall flowchart of the system reliability analysis method based on the improved adaptive kriging planar parallel mechanism in the embodiments of the present invention; Figure 2 This is a diagram of the 3RRR planar parallel mechanism in an embodiment of the present invention; Figure 3 The figures are curves showing the change in failure probability of the 3RRR planar parallel mechanism with the number of iterations, calculated by AK-MCS in the embodiments and by the reliability analysis method disclosed in this invention. Detailed Implementation

[0017] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.

[0018] Example 1 like Figure 1 As shown, this invention provides a reliability analysis method for an adaptive kriging planar parallel mechanism system, comprising the following steps: S1: Establish a dynamic model of the planar parallel mechanism considering irregular wear of the kinematic pairs, which specifically includes: S11: The dynamic model of the planar parallel mechanism is established using the Lagrange multiplier method.

[0019] S12: Based on the dynamic model of the planar parallel mechanism in S11, a dynamic model of the planar parallel mechanism with gaps is established by reducing the corresponding constraints by reducing the Lagrange multipliers.

[0020] S13: Based on the dynamic model of the planar parallel mechanism with gap established in S12, a wear prediction model for the kinematic pair is established by using the Lankarani-Nikravesh contact force model and the improved Coulomb friction model, combined with the Archard wear prediction model.

[0021] S2: Determine the distribution type of the random variables of the mechanism system parameters, and establish the corresponding function of the kinematic pair with respect to the wear depth. The random variables of the system parameters include the geometric dimensions of the drive rod and connecting rod, the Young's modulus and Poisson's ratio of the bearing and bushing, and the coefficient of friction.

[0022] like Figure 2 The diagram shown is a schematic of the 3RRR planar parallel mechanism in an embodiment of the present invention.

[0023] The distribution types are shown in Table 1. The wear kinematic pairs considered are the three kinematic pairs connected to the moving platform. , , It operates with 3 kinematic pairs containing clearance. The wear depth per cycle is used as a reliability evaluation index for the mechanism. The wear depth at which the mechanism fails is set as... The function of the 3RRR parallel mechanism with respect to wear depth is established as follows: , , .

[0024] Table 1: Distribution Types and Parameters of System Random Variables S3: In the kinematic pair , , Initial sample points were generated using hypercubic Latin sampling (LHS). , where k=1, 2, 3.

[0025] S4: Irregular wear dynamics simulation experiment for 3RRR planar parallel mechanism, using initial sample points of the three kinematic pairs. Its corresponding function value The initial kriging model is trained using this initial training set.

[0026] S5: Generate the Monte Carlo population sample based on the joint distribution of the input random variables. .

[0027] S6: Based on the initial kriging model of each kinematic pair in S4, predict the predicted value of the overall sample P in S5. With prediction variance And estimate the uncertainty bound Compared with the current failure probability .

[0028] S7: Uncertainty bound estimated in conjunction with S6 Compared with the current failure probability Determine if the stopping criterion is met; if so, terminate the iteration and output the system failure probability. If the conditions are not met, proceed to the next step.

[0029] The stopping criterion is as follows: ; Among them, parameters Set as If the condition is met three times, it is considered convergent. This is the upper bound of the failure probability. This is the lower bound of the failure probability. This represents the failure probability.

[0030] S8: Select updated samples according to the optimal point selection principle. Specifically, it includes the following steps: S81: Select the minimum predicted response value among the different failure modes corresponding to each sample point in the overall sample P. and its corresponding prediction variance .

[0031] S82: Calculate the number of samples with a high probability of prediction error: Classify each sample point in the total sample P and determine whether the prediction is correct: Determine the sample size of each sample point. Does it meet the requirements? If the conditions are met, the group is classified as a prediction error group.

[0032] S83: For each sample point in the prediction error group, the KB strategy is applied sequentially. While ensuring that the hyperparameters of the kriging model of the corresponding kinematic pair remain unchanged, the kriging model of the corresponding failure mode is updated. The updated kriging model replaces the initial kriging model in S6, and S6 to S82 are executed again to obtain the updated prediction error group. The sample with the largest difference is selected as the update sample. .

[0033] S9: Update the sample Perform dynamic simulation to obtain the corresponding real response. The sample will be updated. Its corresponding actual response Added to the initial training set to form a new overall sample set. The kriging model is retrained using the new overall sample training set, and then returned to execute S6 to re-predict the new overall sample. Predicted value With prediction variance Continue iterating until all sample points are exhausted, at which point the iteration ends.

[0034] Comparative Example 1 To verify the effectiveness of the system reliability analysis method for the planar parallel mechanism based on the improved adaptive kriging in the technical solution of this invention, the MCS method and the AK-MCS method were used as comparison methods to analyze the reliability of the 3-RRR planar parallel mechanism.

[0035] like Figure 3 As shown, Figure 3The curves showing the change in failure probability of the 3RRR planar parallel mechanism with the number of iterations are calculated using AK-MCS and the method of this invention, respectively. Figure 3 As can be seen, with the increase of iterations, AK-SYS slowly converges to the true failure probability, while the IAK-SYS method proposed in this invention converges to the true failure probability quickly. Therefore, under the same stopping criterion, the number of function calls of IAK-SYS is less than that of AK-SYS.

[0036] Therefore, the method of the present invention converges to the true failure probability more quickly while ensuring computational accuracy, thus improving the efficiency of reliability analysis of wear systems and demonstrating its advantages in the field of system reliability analysis. Furthermore, this embodiment also provides a comparison of the failure probability prediction and computational efficiency of three methods, as shown in Table 2.

[0037] Table 2 shows that the failure probability of the 3RRR mechanism under trajectory 2 is 0.03248, which is lower than that under trajectory 1. The wear failure probability of the 3RRR mechanism calculated by the IAK-SYS method is similar to the results obtained by the MCS and AK-SYS methods. Regarding the number of function calls, compared with AK-SYS and MCS, IAK-SYS only requires 104 function calls, effectively reducing computational costs. In terms of accuracy, IAK-SYS has an error of only 0.74%, demonstrating higher accuracy.

[0038] In summary, the adaptive kriging method for reliability analysis of planar parallel mechanism systems provided by this invention can select updated samples by combining the optimal point selection principle without sacrificing prediction accuracy. By continuously filtering out the samples with the largest differences, the optimal samples are effectively selected, thereby avoiding the tedious calculation process of large amounts of data, improving computational efficiency, and saving the cost of reliability analysis. It provides a brand-new method and approach for reliability analysis of planar parallel mechanism systems, achieving a balance between computational efficiency and accuracy, and is suitable for widespread use.

[0039] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A reliability analysis method for an adaptive kriging planar parallel mechanism system, characterized in that, Includes the following steps: S1: Establish a dynamic model of the planar parallel mechanism considering irregular wear of kinematic pairs; S2: Determine the distribution type of the random variables of the mechanism system parameters and establish the corresponding function of the kinematic pair with respect to the wear depth; S3: Initial sample points are generated using the Latin hypercube sampling method. ; S4: Initial sample points through different kinematic pairs Its corresponding function value Use this as the initial training set to train the corresponding initial kriging model; S5: Generate the Monte Carlo population sample based on the joint distribution of the input random variables. ; S6: Based on the initial kriging model of each kinematic pair in S4, predict the predicted value of the overall sample P in S5. With prediction variance And estimate the uncertainty bound Compared with the current failure probability ; S7: Uncertainty bound estimated in conjunction with S6 Compared with the current failure probability Determine whether the stopping criterion is met. If it is met, terminate the iteration and output the system failure probability. If it is not met, proceed to the next step. S8: Select updated samples according to the optimal point selection principle. Specifically, it includes the following steps: S81: Select the minimum predicted response value among the different failure modes corresponding to each sample point in the overall sample P. and its corresponding prediction variance ; S82: Classify each sample point in the total sample P and determine whether the prediction is correct: determine the sample size of each sample point. Does it meet the requirements? If the conditions are met, the group is classified as a prediction error group. S83: For each sample point in the prediction error group, the KB strategy is applied sequentially. While keeping the hyperparameters unchanged, the kriging model of the corresponding failure mode is updated. The updated kriging model replaces the initial kriging model in S6, and S6 to S82 are re-executed to obtain the updated prediction error group. The sample with the largest difference is selected as the update sample. ; S9: Update the sample Perform dynamic simulation to obtain the corresponding real response. The sample will be updated. Its corresponding actual response Add it to the initial training set, retrain the kriging model, and return to execute S6 until all sample points are exhausted and the iteration terminates.

2. The method for reliability analysis of a planar parallel mechanism system with adaptive kriging as described in claim 1, characterized in that: In S1, the methods for establishing a dynamic model of a planar parallel mechanism considering irregular wear of kinematic pairs include: S11: The dynamic model of the planar parallel mechanism is established using the Lagrange multiplier method; S12: Based on the dynamic model of the planar parallel mechanism in S11, a dynamic model of the planar parallel mechanism with gaps is established by reducing the corresponding constraints by reducing the Lagrange multipliers; S13: Based on the dynamic model of the planar parallel mechanism with gap established in S12, a wear prediction model for the kinematic pair is established by using the Lankarani-Nikravesh contact force model and combining it with the Archard wear prediction model.

3. The method for reliability analysis of a planar parallel mechanism system with adaptive kriging as described in claim 1, characterized in that: The random variables of system parameters in S2 include the geometric dimensions of the drive rod and connecting rod, the Young's modulus and Poisson's ratio of the bearings and bushings, and the coefficient of friction.

4. The method for reliability analysis of a planar parallel mechanism system with adaptive kriging as described in claim 1, characterized in that: The random variables of system parameters in S2 include uniform distribution, normal distribution, and Poisson distribution.

5. The method for reliability analysis of a planar parallel mechanism system with adaptive kriging as described in claim 1, characterized in that: In S2, the kinematic pair type is a revolute pair consisting of a shaft and a bushing.

6. The method for reliability analysis of a planar parallel mechanism system with adaptive kriging as described in claim 1, characterized in that: S3 It also includes: conducting irregular wear dynamics simulation experiments on initial sample points to obtain the true function values ​​of the corresponding kinematic pairs. .

7. The method for reliability analysis of a planar parallel mechanism system with adaptive kriging as described in claim 1, characterized in that: In S7, the stopping criterion is: ； Among them, threshold parameter Set as If the condition is met three times, the expression is considered convergent. This is the upper bound of the failure probability. This is the lower bound of the failure probability. This represents the failure probability.

8. The method for reliability analysis of a planar parallel mechanism system with adaptive kriging as described in any one of claims 1-7, characterized in that: There are three kinematic pairs.

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