Active-learning Based Kriging Methods For Kinematic Reliability Analysis Of Mechanisms

The process of quantifying the influence of uncertain factors in the engineering practice on the trajectory of the mechanism and estimating the failure probability based on the error threshold is defined as kinematic reliability analysis of the mechanism.In order to evaluate the kinematic trajectory of the mechanism as a whole,the continuous trajectory is usually discretized into a series of mechanism positions,and the system reliability analysis is directly performed on the maximum error of these positions.Since the operation of causing the function irregularity is performed when the extremum function is obtained,it is difficult to solve the extremum statistic.Therefore,it is necessary to develop a more accurate and efficient reliability algorithm to deal with such reliability model based on extremum function.This paper focuses on Active-learning based Kriging methods for kinematic reliability analysis of mechanisms,and the main research contents are as follows:(1)By establishing the mathematical model and parameter analysis of the maximum for the kinematic error of the mechanism,the numerical method based on the classical Kriging theory is proposed to compared with the first order reliability method(FORM),saddle point approximation(SPA)method and stochastic simulation method.Combined with the example of rack and pinion steering mechanism in automobile,determining the optimal Kriging modeling strategy,and obtaining an effective approach for kinematic reliability analysis of mechanisms in this paper.(2)Based on the principle of expectation improvement in the active learning Kriging method,a new learning function(REIF)is proposed in combination with the folded normal distribution,then the joint probability density function of the input random variable is further introduced to modulate the Kriging learning process(REIF2).Combined with the accuracy and efficiency comparison in numerical examples,the optimizing performance of the new learning function for the active learning Kriging training sample sequence is verified.(3)In order to further reduce the number of candidate samples in the active learning process,this paper proposed the adaptive uniform candidate samples by introducing the adaptive adjustment strategy of sampling region in the literature and combining it with the uniform sample and importance sampling theory,it solves the huge computational burden in traditional active learning algorithm.By comparing the CPU time in numerical examples,it is proved that the adaptive uniform candidate samples can greatly improve the computational efficiency of the active learning Kriging algorithm.(4)Starting from the task requirements of the Delta-type parallel robot to perform the pick-and-place operation,the motion path and trajectory of the robot are programed.Combined with the requirements of kinematic and positioning accuracy of Delta-type robots,the results for system kinematic reliability analysis of the common active learning Kriging algorithm in the current literature are compared.The computational accuracy and efficiency of the proposed active learning algorithm are verified.