基于灰色关联协同效应权重配置的费用预测模型

doi:10.12305/j.issn.1001-506X.2024.04.19

摘要/Abstract

摘要：

费用预测是复杂装备成本管理的核心内容。在同类型复杂装备仅有少量样本信息的情况下, 为提高估算预测精度, 解决贫信息下费用影响要素筛选困难、要素间由于协同效应导致的权重分配不合理、费用预测误差较大等问题, 提出了一种基于灰色关联协同效应贡献度分配的要素权重配置方法。首先通过灰色关联度分析筛选相似样本及费用关键影响要素; 然后, 依据各要素在协同效应下对灰色关联度提高的贡献程度大小, 参考Shapley值思想计算各要素的灰色比较关联重要性, 以此确定权重; 最后, 构建相应的异阶参数灰色分数阶预测模型, 对目标装备进行费用预测。通过与已有文献中的方法进行对比, 结果表明所提方法有较高的预测精度且具有一定的适用性, 能够挖掘小样本下费用影响要素间的潜在信息, 更可以合理地分配要素权重, 提高费用预测精度。

关键词: 复杂装备费用, 协同效应, Shapley值, 灰色关联分析, 灰色分数阶GM(0, N)模型

Abstract:

Cost estimation is the core content of complex equipment cost management. In the case that only a small amount of sample information is available for the same type of complex equipment, in order to improve the estimation and prediction accuracy, and to solve the problems of difficult screening of cost-influencing elements under poor information, unreasonable weight distribution among elements due to synergistic effects, and large cost prediction errors, a method for allocating element weights based on the contribution of grey relational synergistic effects is proposed. Firstly, similar samples and key cost influencing elements are screened by grey relational analysis. Secondly, based on the contribution of each element to the improvement of grey relational grade under the synergistic effect, the grey comparative relational importance of each element with reference to the idea of Shapley value is calculated, and thus the weights are determined. Finally, the corresponding heterogeneous order parameter grey fractional order prediction model is constructed for cost prediction of target equipment. By comparing with the existing methods in the literatures, the comparison results show that the proposed method has a high prediction accuracy and certain applicability, indicating that the proposed method can explore the potential information among the cost-influencing elements in a small amount of sample, assign the element weights more reasonably and improve the accuracy of cost prediction.

Key words: complex equipment costs, synergistic effect, Shapley value, grey relational analysis, grey fractional order GM (0, N) model

中图分类号:

N941.5

赵潞, 方志耕, 于亮, 张亚东, 邱玺睿, 华晨晨. 基于灰色关联协同效应权重配置的费用预测模型[J]. 系统工程与电子技术, 2024, 46(4): 1309-1319.

Lu ZHAO, Zhigeng FANG, Liang YU, Yadong ZHANG, Xirui QIU, Chenchen HUA. Cost prediction model based on grey relational synergistic effect weight allocation[J]. Systems Engineering and Electronics, 2024, 46(4): 1309-1319.

图/表 14

表1

表2

表3

表4

表5

表6

表7

表8

表9

表10

表11

表12

表13

表14

参考文献 28

1	李成, 吴斌. 面向大型复杂装备制造的企业级集成质量系统[J]. 系统工程, 2012, 30 (6): 117- 121. doi: 10.3969/j.issn.1001-2362.2012.06.057
	LI C , WU B . Integrated quality system for large-scale complex equipment manufacturing[J]. Systems Engineering, 2012, 30 (6): 117- 121. doi: 10.3969/j.issn.1001-2362.2012.06.057
2	GUO X J , LIU S F , YANG Y J , et al. Grey self-memory combined model for complex equipment cost estimation[J]. Journal of Gery System, 2017, 29 (1): 78- 91.
3	LIU S B , YIN C W , CAO D Z . Weapon equipment management cost prediction based on forgetting factor recursive GM (1, 1) model[J]. Grey Systems: Theory and Application, 2020, 10 (1): 38- 45.
4	CHEN Y H , HU P , ZHANG D . Predication of life cycle cost of equipment base on unbiased grey Markov models[J]. MATEC Web of Conferences, 2020, 309 (1): 05005.
5	王骏, 罗鹏程, 周经伦, 等. 军用飞机出厂费用估算方法研究进展综述[J]. 系统工程与电子技术, 2017, 39 (9): 2012- 2021.
	WANG J , LUO P C , ZHOU J L , et al. Survey on military aircraft fly-away cost estimation methons[J]. Systems Engineering and Electronics, 2017, 39 (9): 2012- 2021.
6	王景玫, 郭鹏. 基于TRL和SVM的航天型号研制成本预测研究[J]. 航空制造技术, 2015, (Z2): 97- 102.
	WANG J M , GUO P . Research on aerospace product development cost prediction based on TRL and SVM[J]. Aeronautical Manufacturing Technology, 2015, (Z2): 97- 102.
7	ZHANG Y J , CAO K , LIANG K , et al. A serialized civil aircraft R&D cost estimation model considering commonality based on BP algorithm[J]. Chinese Journal of Aeronautics, 2022, 35 (4): 253- 265. doi: 10.1016/j.cja.2021.04.013
8	蔡伟宁, 方卫国. 飞机研制费用的组合预测方法[J]. 系统工程与电子技术, 2014, 36 (8): 1573- 1579.
	CAI W N , FANG W G . Combination forecasting methon for development cost of aircraft[J]. Systems Engineering and Electronics, 2014, 36 (8): 1573- 1579.
9	JIANG H , HU Y C , LIN J Y , et al. Analyzing China's OFDI using a novel multivariate grey prediction model with Fourier series[J]. International Journal of Intelligent Computing and Cybernetics, 2019, 12 (3): 352- 371. doi: 10.1108/IJICC-07-2018-0095
10	袁泉, 曾祥艳. 基于新息优先累积法的GM(0, N)模型及其应用[J]. 统计与决策, 2018, 34 (12): 79- 81.
	YUAN Q , ZENG X Y . GM(0, N) model based on the new information-first accumulation method and its application[J]. Statistics & Decision, 2018, 34 (12): 79- 81.
11	吴利丰, 刘思峰, 方世力, 等. 相似信息优先的复杂装备费用测算模型[J]. 系统工程与电子技术, 2014, 36 (10): 2024- 2028.
	WU L F , LIU S F , FANG S L , et al. Complicated equipment cost estimation model with similarity information priority[J]. Systems Engineering and Electronics, 2014, 36 (10): 2024- 2028.
12	吴利丰, 于亮, 文朝霞. 预测复杂装备研制费用的GM(0, N)模型[J]. 中国管理科学, 2019, 27 (7): 203- 207.
	WU L F , YU L , WEN Z X . GM(0, N) model for its application on forecasting the development cost of complicated equipment[J]. Chinese Journal of Management Science, 2019, 27 (7): 203- 207.
13	TIAN M , CAO Y , XIE N M , et al. IN-GM (0, N) cost forecasting model of commercial aircraft based on interval grey numbers[J]. Kybernetes, 2012, 41 (7/8): 886- 896. doi: 10.1108/03684921211257739
14	CHEN H Z , FAN K F , FANG Z G . Research on complex product cost estimation based on the N-GM (0, N) model[J]. Grey Systems: Theory and Application, 2013, 3 (1): 46- 59. doi: 10.1108/20439371311293697
15	CHEN X N , HUANG J , YI M X , et al. Prediction of the development cost of commercial aviation aircraft[J]. Aircraft Engineering and Aerospace Technology, 2019, 91 (4): 567- 574. doi: 10.1108/AEAT-09-2018-0248
16	CHEN X N , HUANG J , YI M X . Cost estimation for general aviation aircrafts using regression models and variable importance in projection analysis[J]. Journal of Cleaner Production, 2020, 256, 120648- 120672. doi: 10.1016/j.jclepro.2020.120648
17	魏东涛, 刘晓东, 丁刚, 等. 基于熵理论的复杂装备费用测算模型[J]. 北京航空航天大学学报, 2022, 48 (5): 816- 823.
	WEI D T , LIU X D , DING G , et al. Complex equipment cost estimation model based on entropy theory[J]. Journal of Beijing University of Aeronautics and Astronautics, 2022, 48 (5): 816- 823.
18	刘凤华, 谢乃明. 小样本、贫信息下民用飞机费用估算模型及算法[J]. 系统仿真学报, 2014, 26 (3): 687- 691.
	LIU F H , XIE N M . Civilian aircraft cost estimation model and algorithm based on small sample and poor information[J]. Journal of System Simulation, 2014, 26 (3): 687- 691.
19	YIN S M, XIE N M, HU C Z. Development cost estimation of civil aircraft based on combination model of GM (1, N) and MLP neural network[C]//Proc. of the IEEE International Conference on Grey Systems and Intelligent Services, 2015: 312-317.
20	XIE N M , YIN S M , HU C Z . Estimating a civil aircraft's development cost with a GM (1, N) model and an MLP neural network[J]. Grey Systems: Theory and Application, 2017, 7 (1): 2- 18. doi: 10.1108/GS-11-2016-0049
21	CHEN X N , HUANG J , YI M X . Development cost prediction of general aviation aircraft projects with parametric modeling[J]. Chinese Journal of Aeronautics, 2019, 32 (6): 1465- 1471. doi: 10.1016/j.cja.2019.03.024
22	LEE J F , LEE H S , PARK M , et al. Early-stage cost estimation model for power generation project with limited historical data[J]. Engineering Construction and Architectural Management, 2022, 29 (7): 2599- 2614. doi: 10.1108/ECAM-04-2020-0261
23	吴利丰, 刘思峰, 姚立根. 基于分数阶累加的离散灰色模型[J]. 系统工程理论与实践, 2014, 34 (7): 1822- 1827.
	WU L F , LIU S F , YAO L G . Discrete grey model based on fractional order accumulate[J]. System Engineering Theory and Practice, 2014, 34 (7): 1822- 1827.
24	孟伟. 基于分数阶拓展算子的灰色预测模型[D]. 南京: 南京航空航天大学, 2015.
	MENG W. Grey prediction modeling based on fractional order operators[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2015.
25	吴利丰. 分数阶灰色预测模型及其应用研究[D]. 南京: 南京航空航天大学, 2015.
	WU L F. Fractional order grey forecasting models and their application[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2015.
26	罗佑新. 分数阶累加多变量灰色模型FMGM(1, n)及应用[J]. 中南大学学报(自然科学版), 2017, 48 (10): 2686- 2690.
	LUO Y X . Multivariable grey model FMGM(1, n) with fractional order accumulation and its application[J]. Journal of Central South University (Science and Technology), 2017, 48 (10): 2686- 2690.
27	方世力. 基于灰信息的运载火箭方案优选与研制费用估算模型研究[D]. 南京: 南京航空航天大学, 2016.
	FANG S L. Selection model and cost estimation model construction of launch vehicle development scheme under the perspective of grey information[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2016.
28	刘思峰. 灰色系统理论及其应用[M]. 9版北京: 科学出版社, 2021: 75- 77.
	LIU S F . Grey system theory and its applicationgs[M]. 9th ed Beijing: Science Press, 2021: 75- 77.

s	2	{2, 3}	{2, 4}	…	{2, 3, …, m}
v(s)
v(s\i)
v(s)－v(s\i)
\|s\|
w(\|s\|)
w(\|s\|)[v(s)－v(s\i)]

机型	成本费用/百万元	最大起飞重量/t	巡航速度/(km/h)	发动机最大推力/t	最大升限/英尺	最大载油量/L	机身长度/英尺
1	32.0	65.09	0.79	26.3	11 280	17 800	102
2	65.2	85.13	0.78	27.3	12 500	29 660	138
3	200.2	395.00	0.84	63.3	11 680	216 840	211
4	174.6	230.00	0.84	77.2	12 500	117 340	208
5	122.2	163.00	0.85	53.1	13 000	120 000	186
6	144.7	257.00	0.82	72.0	12 800	139 100	192
7	261.9	560.00	0.85	70.0	13 100	310 000	239
8	61.5	73.50	0.78	27.0	12 000	29 680	123
9	172.4	257.00	0.82	34.0	12 800	139 100	208

机型	成本费用/百万元	最大起飞重量/t	巡航速度/(km/h)	发动机最大推力/t	最大升限/英尺	最大载油量/L	机身长度/英尺
1	0.223 8	0.284 7	0.964 9	0.505 5	0.912 8	0.145 2	0.583 3
2	0.456 0	0.372 4	0.952 7	0.524 7	1.011 5	0.242 0	0.789 1
3	1.400 3	1.728 0	1.026 0	1.216 7	0.945 2	1.769 4	1.206 6
4	1.221 2	1.006 2	1.026 0	1.483 9	1.011 5	0.957 5	1.189 4
5	0.854 7	0.713 1	1.038 2	1.020 7	1.052 0	0.979 2	1.063 6
6	1.012 1	1.124 3	1.001 5	1.384 0	1.035 8	1.135 0	1.097 9
7	1.831 8	2.449 8	1.038 2	1.345 5	1.060 1	2.529 5	1.366 7
8	61.500 0	0.321 5	0.952 7	0.519 0	0.971 1	0.242 2	0.703 4

机型	成本费用/百万元	最大起飞重量/t	巡航速度/(km/h)	发动机最大推力/t	最大升限/英尺	最大载油量/L	机身长度/英尺	灰色关联度
7	261.9	560.00	0.85	70.0	13 100	310 000	239	0.625 8
3	200.2	395.00	0.84	63.3	11 680	216 840	211	0.685 0
6	144.7	257.00	0.82	72.0	12 800	139 100	192	0.727 9
4	174.6	230.00	0.84	77.2	12 500	117 340	208	0.731 8
5	122.2	163.00	0.85	53.1	13 000	120 000	186	0.778 8
1	32.0	65.09	0.79	26.3	11 280	17 800	102	0.954 2
2	65.2	85.13	0.78	27.3	12 500	29 660	138	0.974 7

机型	成本费用/百万元	最大起飞重量/t	巡航速度/(km/h)	发动机最大推力/t	最大升限/英尺	最大载油量/L	机身长度/英尺
7	1.831 8	2.233 3	1.031 2	1.259 0	1.055 7	2.282 4	1.311 1
3	1.400 3	1.575 3	1.019 1	1.138 5	0.941 3	1.596 5	1.157 5
6	1.012 1	1.024 9	0.994 8	1.295 0	1.031 5	1.024 1	1.053 3
4	1.221 2	0.917 3	1.019 1	1.388 5	1.007 4	0.863 9	1.141 1
5	0.854 7	0.650 1	1.031 2	0.955 0	1.047 7	0.883 5	1.020 4
1	0.223 8	0.259 6	0.958 4	0.473 0	0.909 0	0.131 1	0.559 6
2	0.456 0	0.339 5	0.946 3	0.491 0	1.007 4	0.218 4	0.757 1