基于相似性加权的复杂系统费用测算模型

常菊; 刘晓东; 何荧

doi:10.13700/j.bh.1001-5965.2023.0840

基于相似性加权的复杂系统费用测算模型

doi: 10.13700/j.bh.1001-5965.2023.0840

常菊^{1, 2},
刘晓东^1, ,,
何荧²

1.
空军工程大学装备管理与无人机工程学院，西安 710051
2.
江南机电设计研究所，贵阳 550009

详细信息

通讯作者:
E-mail：xdliu6609@qq.com

中图分类号: V267
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- 被引次数: 0
出版历程
- 收稿日期: 2023-12-29
- 录用日期: 2024-03-06
- 网络出版日期: 2024-04-10
- 整期出版日期: 2026-03-31

Complex equipment cost estimation model based on similarity weight

CHANG Ju^{1, 2},
LIU Xiaodong^{1
, ,},
HE Ying²

1.
College of Equipment Management and UAV Engineering，Air Force Engineering University，Xi’an 710051，China
2.
Jiangnan Mechanical and Electrical Design Institute，Guiyang 550009，China

More Information

Corresponding author: E-mail：xdliu6609@qq.com

摘要

摘要:
为进一步提高航天器等大型复杂系统的费用测算精度，将大型复杂系统看作一定参数集合的系统分布，定义待测系统与样本的Jensen-Shannon(JS)散度、灰色关联度及综合相似度，根据综合相似度计算样本权重大小，构建复杂系统费用测算的加权回归模型。当样本量较少不满足最小二乘法建模条件时，选择综合相似度最大的样本作为基准样本，构建费用的驱动效应矩阵，根据矩阵中参数与费用的JS散度大小，按序选取散度较大的参数作为测算模型的自变量。针对样本量大于和不大于参数量2种情况实例计算结果。结果表明：基于JS散度和灰色关联度融合的相似性加权回归测算模型具有较高的预测精度和稳定性。
- 复杂系统 /
- JS散度 /
- 灰色关联度 /
- 综合相似度 /
- 驱动因子 /
- 精确度 /
- 费用测算
Abstract:
In order to further improve the accuracy of cost estimation for large and complex equipment, such as spacecraft and weapon systems, the large and complex equipment is regarded as a system distribution of a certain parameter set. Define the Jensen-Shannon (JS) divergence, grey correlation, and comprehensive similarity between the tested equipment and the equipment samples, and calculate the sample weight based on the similarity to construct a weighted regression model for cost estimation of complex equipment. To create the cost driving impact matrix, the sample with the highest complete similarity is chosen as the benchmark sample when the sample size does not satisfy the requirements of the least squares modeling. Based on the JS divergence between the parameters and the cost in the matrix, the parameters with larger divergence are selected as the independent variables for the prediction model. By comparing two scenarios in which the sample size is larger and smaller than the parameter size, the comparative analysis demonstrates the excellent prediction accuracy and stability of the similarity weighted regression calculation model based on the combination of JS divergence and grey correlation degree.
- complex equipment /
- JS divergence /
- grey correlation /
- comprehensive similarity /
- driving factor /
- accuracy /
- cost estimation

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表 1 机载电子设备费用样本

Table 1. Sample of airborne electronic equipment costs

飞机型号	首飞时间$ {x}_{1}/\text{a} $	质量$ {x}_{2}/\text{kg} $	体积$ {x}_{3}/{\mathrm{m}}^{3} $	功率$ {x}_{4}/\text{kW} $	实际平均费用 $ c $/10³美元
A-6E	70	624.25	0.5691	6.4	1069
A-7D	68	508.25	0.7101	10.5	669
F-4D	65	790.41	0.8430	8.2	582
A-10A	72	265.14	0.2394	3.1	315
E-4E	67	566.14	0.6773	5.3	662
F-4J	66	1021.05	0.9824	19.4	1329
F-15A	72	717.32	0.8331	22.5	2488
F-111A	64	805.40	0.8774	5.6	1267
F-111D	68	1068.72	0.9102	12.5	2392
F-111F	71	933.88	1.0611	8.9	1577
FB-111A	70	1136.36	1.3432	7.9	1965
F-14A	70	998.35	1.0628	29.4	2383
A-7E	68	653.76	0.8413	8.3	828
F-111E	69	987.00	1.1054	8.9	1564

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表 2 3个待预测机载电子设备综合相似度和权重

Table 2. Comprehensive similarity and weight of three predicted airborne electronic devices

飞机型号	相似度			权重
飞机型号	与F-14A对比	与A-7E对比	与F-111E对比	与F-14A对比	与A-7E对比	与F-111E对比
A-6E	0.77	0.85	0.80	0.09	0.10	0.09
A-7D	0.76	0.90	0.81	0.09	0.10	0.09
F-4D	0.75	0.88	0.82	0.09	0.10	0.09
A-10A	0.52	0.55	0.53	0.06	0.06	0.06
E-4E	0.73	0.87	0.78	0.09	0.10	0.09
F-4J	0.85	0.75	0.81	0.10	0.08	0.09
F-15A	0.82	0.81	0.74	0.10	0.09	0.08
F-111A	0.70	0.78	0.76	0.08	0.09	0.09
F-111D	0.83	0.86	0.87	0.10	0.10	0.10
F-111F	0.86	0.82	0.92	0.10	0.09	0.11
FB-111A	0.82	0.79	0.88	0.10	0.09	0.10

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表 3 4种预测方法的结果比较

Table 3. Result comparison of four prediction methods 万元

飞机型号	实际费用	回归预测费用^[17]	支持向量机预测^[17]	基于熵理论预测^[17]	本文方法预测
F-14A	2383	2182	2465	2695.8	2558.80
A-7E	828	708	1114	922.4	911.49
F-111E	1564	753	1867	1701.8	1682.80

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表 4 4种预测方法的预测误差比较

Table 4. Comparison of prediction errors among four prediction methods

飞机型号	回归预测误差/%^[17]	支持向量机预测误差/%^[17]	基于熵理论预测误差/%^[17]	本文方法预测误差/%
F-14A	8.43	3.44	13.13	7.37
A-7E	14.49	34.54	11.40	10.08
F-111E	51.85	19.37	8.81	7.60

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表 5 运输机性能数据与费用

Table 5. Performance data and cost of transport aircraft

飞机型号	最大起飞质量 $ {x}_{1}/\text{kg} $	机身长 $ {x}_{2}/\text{m} $	机高 $ {x}_{3}/\text{m} $	起飞距离 $ {x}_{4}/\text{m} $	满油航程 $ {x}_{5}/\text{km} $	最大平飞速度 $ {x}_{6}/(\text{m}\cdot {\text{s}}^{{-1}}) $	空重 $ {x}_{7}/\text{kg} $	载油量 $ {x}_{8}/\text{kg} $	费用 $ c $/万元
A	13494	23.500	8.43	867	4262	425.0	6597	5683	6666.70
B	6849	14.390	4.57	987	3701	746.0	3655	2640	3524.30
C	9979	16.900	5.12	1581	4679	874.0	5357	3350	6569.90
D	5670	13.340	4.57	536	3641	536.0	3656	1653	5586.23
E	63503	39.750	9.30	1859	6764	925.0	33183	21273	27768.80
F	22000	29.870	6.75	1200	2870	907.0	34360	5500	17575.20
G	21500	27.170	7.65	1050	2000	580.0	12200	5000	18137.60
H	70310	29.790	11.66	1091	7876	602.0	36300	36300	50476.00
I	21000	24.615	7.30	1300	3100	819.2	11700	6000	14250.00

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表 6 6种预测方法的比较

Table 6. Comparison of six prediction methods

飞机型号	实际费用/万元	不同预测方法预测费用/万元
飞机型号	实际费用/万元	偏最小二乘回归^[18]	相似信息优先原理^[6]	逐步多元回归预测^[19]	极大熵^[19]	基于熵理论^[17]	本文预测方法
I	14250	10510	15262	13680	14530.27	14016	14028.3

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