基于复合函数的复杂机械系统分层响应面建模与可靠性分析

Hierarchical Response Surface Modeling and Reliability Analysis of Complex Mechanical System Based on Composite Function

针对复杂机械系统可靠性问题,提出一种基于复合函数的分层响应面法(HRSM)。根据系统结构组成的层次和物理关系,建立基本变量到各零部件的响应函数,作为中间层节点;针对基本变量及中间层响应综合作用的系统性能,拟合其极限状态的响应面模型,作为顶层节点;采用一次2阶矩法及蒙特卡洛仿真法求解系统失效概率。以某双轴驱动机构为例,从误差逐级传递的角度,成功应用HRSM对其运动精度可靠性问题进行了建模分析。经对比可知,该方法输出的最大失效概率与蒙特卡洛仿真抽样结果基本一致,且不随样本点系数波动,充分验证了HRSM的稳健性和有效性。

A hierarchical response surface method（ HRSM） based on composite functions is proposed for the reliability assessment of complex mechanical systems. According to the structure and composition of the system and the physical relationship,the proposed method is used to establish the basic variables and the response functions of the parts as the middle-level nodes. For the system performance affected by some basic variables and the above middle-level response functions,HRSM is used to construct the response surface model of the limit state as the top-level node. The first-order second-moment method and Monte Carlo method are used for solving the system failure probability. Taking a two-axis-position mechanism as an example,HRSM is successfully applied to model and analyze the motion accuracy reliability on the basis of error propagation. The maximum failure probability of HRSM is almost the same as the output of Monte Carlo simulation,and does not fluctuate with the sample coefficient,which fully verifies the validity and robustness of HRSM.