机械装配过程的偏差传递网络建模与误差溯源

祝鹏,余建波,郑小云,王永松,孙习武

Variation propagation network-based modeling and error tracing in mechanical assembling process

Peng ZHU,Jian-bo YU,Xiao-yun ZHENG,Yong-song WANG,Xi-wu SUN

表 1 偏差传递网络的网络特性及计算方法

Tab.1 Network characteristics of variation propagation network and calculation methods

网络特性 定义 计算方法 复杂网络 赋权偏差传递网络 节点出（强）度 节点误差对邻居节点的影响效应 ${\rm{ES}}_i^{{\rm{out}}} = \displaystyle\sum\limits_{j \in {N_i}} {{a_{ij}}} $ ${\rm{ES}}_i^{{\rm{out}}} = \displaystyle\sum\limits_{j \in {N_i}} {{a_{ij}}{\omega _{ij}}} $ 节点入（强）度 节点受邻居节点误差的影响效应 ${\rm{AS}}_i^{\rm{in}} = \displaystyle\sum\limits_{j \in {N_i}} {{a_{ji}}} $ ${\rm{AS}}_i^{\rm{in}} = \displaystyle\sum\limits_{j \in {N_i}} {{a_{ji}}{\omega _{ji}}} $ 节点（强）度 节点在网络中的重要性 ${S_{{i}}} = {\rm{AS}}_i^{\rm{in}} + {\rm{ES}}_i^{\rm{out}}$ ${S_{{i}}} = {\rm{AS}}_i^{\rm{in}} + {\rm{ES}}_i^{\rm{out}}$ 聚集系数 节点间的误差传递效应 ${c_i}{\rm{ = }}\displaystyle\frac{{\displaystyle\sum\limits_{r = 1}^{{k}} {\displaystyle\sum\limits_{s = 1}^k {d\left( {{n_r},{n_s}} \right)} } }}{{k\left( {k - 1} \right)}}$ $c_{_B}^\omega {\rm{ = }}\displaystyle\frac{1}{{{s_i}\left( {{k_i} - 1} \right)}}\sum\limits_{j,k} {\frac{{{\omega _{_{ij}}} + {\omega _{ik}}}}{2}{a_{ij}}{a_{jk}}{a_{ki}}} $ 平均聚集系数 网络节点的聚集程度 $C = \displaystyle\sum\limits_{i = 1}^N {{c_i}} /N$ $C =\displaystyle\sum\limits_{i = 1}^N {c_{_B}^\omega } /N$ 平均最短路径 任意两节点间最短路径的平均值 $L = \displaystyle\sum\limits_{i,j \in {\bf N},i \ne j}^N {{d_{ij}}} /M$ $L = \displaystyle\frac{2}{{N(N - 1)}}\displaystyle\sum\limits_{i > j} {\frac{{{\omega _{ik}}{\omega _{kj}}}}{{{\omega _{ik}} + {\omega _{ik}}}}} $ 介数 节点在网络传播中的重要性 $B = \displaystyle\sum\limits_{j,l,j \ne l \ne i}^n {{{{N_{jl}}(i)}}/{{{N_{jl}}}}} $