基于Copula量化解析结构模型的复杂系统模块分类

doi:10.13229/j.cnki.jdxbgxb20210008

Abstract

Abstract:

Considering the influence of faults between units of complex system， the relationship between the faults among the units is analyzed. Relevant parameters of associated units are obtained through Copula Numerical Interpretative Structural Modeling （CNISM）， and the fault association matrix among units is established to determine the initial clustering module. Using the degree of aggregation and coupling of modules as numerical quantization indexes， the objective function of the complex system unit fault clustering mathematical model is constructed. The Grouping Genetic Algorithm （GGA） is used to optimize the target function and determine the optimal clustering module. Finally， a certain machining center system is classified according to the above logic.

Key words: machining center, Copula numerical interpretative structural modeling, module classification, complex system, degree of aggregation, coupling

CLC Number:

TG659

Yu-bin ZHENG,Jie SONG,Jin-tong LIU,Li-ming MU,Zhe-hui CHEN,Jun ZHENG. Complex system module classification based on Copula numerical interpretative structural modeling[J].Journal of Jilin University(Engineering and Technology Edition), 2022, 52(6): 1281-1291.

Figures/Tables 11

Fig.1

Table 1

Table 2

Subsystem fault distribution function and its linear correlation coefficient"

子系统	故障分布函数	相关系数
数控系统（ $S 1$ ）	$F 1 (t) = 1 - e x p [- (t ? / 1147.65 18) 0.972]$	0.9021
进给系统（ $S 2$ ）	$F 2 (t) = 1 - e x p [- (t ? / 762.562 1) 0.7949]$	0.9647
液压系统（ $S 3$ ）	$F 3 (t) = 1 - e x p [- (t ? / 357.2172) 0.7365]$	0.9495
气压系统（ $S 4$ ）	$F 4 (t) = 1 - e x p [- (t ? / 1075.4109) 0.8648]$	0.9817
排屑系统（ $S 5$ ）	$F 5 (t) = 1 - e x p [- (t ? / 991.4704) 1.7389]$	0.9696
润滑系统（ $S 6$ ）	$F 6 (t) = 1 - e x p [- (t ? / 1014.4202) 0.8739]$	0.9664
刀库系统（ $S 7$ ）	$F 7 (t) = 1 - e x p [- (t ? / 1017.7001) 1.0054]$	0.9621
防护系统（ $S 8$ ）	$F 8 (t) = 1 - e x p [- (t ? / 1745.0702) 0.4951]$	0.9989
主轴系统（ $S 9$ ）	$F 9 (t) = 1 - e x p [- (t ? / 1377.2212) 0.9244]$	0.9673
电气系统（ $S 10$ ）	$F 10 (t) = 1 - e x p [- (t ? / 878.1532) 2.0632]$	0.9208
冷却系统（ $S 11$ ）	$F 11 (t) = 1 - e x p [- (t ? / 1314.6229) 0.7198]$	0.9005

Table 2

Table 3

Machine tool fault associated factors and their weights"

关联交互	主要结构功能部件		辅助部件
子系统	$S 2$ $S 7$ $S 9$	$S 1$ $S 10$	$S 3$ $S 4$ $S 5$ $S 6$ $S 8$ $S 11$
关联因素	机械	电子	辅助
故障次数	54	17	35
故障频率	0.5094	0.1604	0.3302
权重值	0.5094	0.1604	0.3302

Table 3

Table 4

Table 5

Initial cluster module quantization index and objective function results"

$ε$	K	$J$	$E$	$φ$
0	4	0.1201	0.0132	0.5534
0.2	3	0.0709	0.0131	0.5289
0.4（0.6）	2	0.0413	0.0227	0.5093

Table 5

Table 6

Matlab optimized the results of 10 times"

优化次数	$J$	$E$	$φ$
1	0.3589	0.0132	0.6729
2	0.3103	0.0149	0.6477
3	0.3136	0.0143	0.6497
4	0.3162	0.0167	0.6498
5	0.3074	0.0176	0.6449
6	0.3589	0.0132	0.6729
7	0.3484	0.0145	0.6669
8	0.3146	0.0159	0.6494
9	0.3306	0.0139	0.6584
10	0.3339	0.0157	0.6591

Table 6

Fig.2

Fig.3

Table7

Reliability under different conditions"

可靠度	时间/h
可靠度	10	50	100	200	300	400	500
$R s y s t e$	0.943	0.823	0.722	0.579	0.477	0.399	0.338
$R o p t_g r o u p$	0.915	0.782	0.664	0.482	0.342	0.234	0.155
$R i n d e p$	0.758	0.402	0.210	0.065	0.022	0.007	0.002
$R o r d_g r o u p 1$	0.905	0.740	0.597	0.396	0.262	0.171	0.109
$R o r d_g r o u p 2$	0.951	0.790	0.632	0.406	0.259	0.163	0.101
$R o r d_g r o u p 3$	0.956	0.805	0.651	0.427	0.278	0.178	0.113

Table7

Fig.4

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关系类型	关系描述	等级
无	无关联	0
较弱	基本独立	0.2
一般	关联微弱	0.4
适中	存在一定的关联	0.6
较强	关联较强	0.8
极强	不可分	1

Complex system module classification based on Copula numerical interpretative structural modeling

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