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基于背景值和结构相容性改进的多维灰色预测模型

缪燕子 王志铭 李守军 代伟

缪燕子, 王志铭, 李守军, 代伟. 基于背景值和结构相容性改进的多维灰色预测模型. 自动化学报, 2020, x(x): 1−12 doi: 10.16383/j.aas.c200780
引用本文: 缪燕子, 王志铭, 李守军, 代伟. 基于背景值和结构相容性改进的多维灰色预测模型. 自动化学报, 2020, x(x): 1−12 doi: 10.16383/j.aas.c200780
Miao Yao-Zi, Wang Zhi-Ming, Li Shou-Jun, Dai Wei. Improved multi-dimensional grey prediction model based on background value and structural compatibility. Acta Automatica Sinica, 2020, x(x): 1−12 doi: 10.16383/j.aas.c200780
Citation: Miao Yao-Zi, Wang Zhi-Ming, Li Shou-Jun, Dai Wei. Improved multi-dimensional grey prediction model based on background value and structural compatibility. Acta Automatica Sinica, 2020, x(x): 1−12 doi: 10.16383/j.aas.c200780

基于背景值和结构相容性改进的多维灰色预测模型

doi: 10.16383/j.aas.c200780
基金项目: 国家重点研发计划重点专项(2018YFC0808100), 国家自然科学基金(61976218, 61973306), 江苏省高等学校自然科学研究项目(19KJB440002), 江苏省自然科学基金(BK20200086), 中央高校基本科研业务费专项资金资助(2020ZDPY0303)资助
详细信息
    作者简介:

    缪燕子:中国矿业大学信息与控制工程学院教授, 主要研究方向为多传感器信息融合、机器人智能感知与控制. 本文通信作者. E-mail: myz@cumt.edu.cn

    王志铭:中国矿业大学信息与控制工程学院硕士研究生, 2019年获中国矿业大学电气工程及其自动化学士学位, 主要研究方向为预测控制、煤矿安全. E-mail: 04151249@cumt.edu.cn

    李守军:宿迁学院机电工程学院副教授, 主要研究方向为工业自动化、人工智能与灰色系统理论. Email: lishoujunbox@126.com

    代伟:中国矿业大学信息与控制工程学院教授, 主要研究方向为复杂工业过程建模、运行优化与控制. Email: weidai@cumt.edu.cn

Improved Multi-dimensional Grey Prediction Model Based on Background Value and Structural Compatibility

Funds: Supported by the Key Project of National Key Research and Development Project (2018YFC0808100), National Natural Science Foundation of China(61976218, 61973306), Natural Science Research Project of Higher Education Institutions in Jiangsu Province (19KJB440002), Natural Science Foundation of Jiangsu Provinces(BK20200086), Fundamental Research Fund for the Central Universities(2020ZDPY0303)
  • 摘要: 现有的多变量灰色预测模型的背景值估计误差及模型结构单一是导致该模型预测性能不稳定的重要因素, 致使该模型在实际预测领域中应用并不广泛. 本文通过分析背景值函数的几何意义, 结合积分几何面积公式, 提出一种改进的背景值优化方法, 使预测模型在背景值系数的选取上更加灵活.在此基础上, 模型中加入灰色作用量, 提出一种新的多维灰色预测模型IBSGM(1,N). 通过对模型参数的改变分析, 新模型理论上可达到与传统单变量和多变量灰色预测模型的兼容性. 为检验新模型的性能, 本文进行了三个案例对比分析, 实验结果表明, 与现有的GM(1,1)和GM(1,N)预测模型相比较, 所提出的IBSGM(1,N)模型在背景值参数估计上误差明显减小, 结构相容性更强, 泛化性能更好, 具有更高的预测精度.
  • 图  1  背景值几何示意图1

    Fig.  1  Schematic diagram 1 of the background value

    图  2  背景值几何示意图2

    Fig.  2  Schematic diagram 2 of the background value

    图  3  例1中四种模型的模拟预测结果曲线图

    Fig.  3  Curves of simulated prediction results of the four models in Example 1

    图  4  例2中四种模型的模拟预测结果曲线图

    Fig.  4  Curves of simulation prediction results of the four models in Example 2

    图  5  例3中四种模型的模拟预测结果曲线图

    Fig.  5  Curves of simulation prediction results of the four models in Example 3

    表  1  寸草塔煤矿日均瓦斯浓度及影响因素

    Table  1  Daily average gas concentration and influencing factors in Cuncaota Coal Mine

    序号X1(0)X2(0)X3(0)X4(0)
    10.340.3421.70.34
    20.340.2918.10.36
    30.260.2925.30.31
    40.260.4121.40.33
    50.230.5125.30.28
    60.220.3722.30.29
    70.210.3823.20.23
    80.170.4122.50.35
    90.170.3624.10.19
    100.160.4822.90.25
    下载: 导出CSV

    表  2  IBSGM(1,N)与GM(1,N)模型预测模拟值误差对比

    Table  2  Comparison of prediction and simulation errors between IBSGM(1,N) and GM(1,N) model

    实际值0.340.340.260.260.230.220.210.170.170.16平均误差
    GM(1,N)0.340.2590.3640.3670.1880.2690.1350.3470.0540.1130.38
    IBSGM(1,N)0.340.330.270.250.2470.2190.2040.1730.160.1650.0337
    下载: 导出CSV

    表  3  一种热处理钢在400℉至1100℉的抗拉强度及布氏硬度

    Table  3  The tensile strength and Brinell hardness of a heat-treated steel from 400°F to 1100°F

    序号X1(0)X2(0)X3(0)
    1897514400
    2897495500
    3890444600
    4876401700
    5848352800
    6814293900
    77792691000
    87382351100
    下载: 导出CSV

    表  4  IBSGM(1,N)模型的参数值

    Table  4  Parameter values of IBSGM(1,N) model

    $ a $$ {b}_{1} $$ {b}_{2} $$ \gamma $$ \lambda $
    0.17110.29740.0247728.17820
    下载: 导出CSV

    表  5  四种模型下预测结果和误差对比

    Table  5  Comparison of prediction results and errors under the four models

    序号原始数据IBSGM(1,N)模型OGM(1,N)模型GM(1,N)模型GM(1,1)模型
    模拟值相对误差模拟值相对误差模拟值相对误差模拟值相对误差
    18978970897089708970
    2897897.0130.0015%896.7820.0243%791.44611.7674%911.5441.6214%
    3890890.4210.0473%890.8820.0991%1013.10313.8317%886.2650.4197%
    4876874.7070.1476%874.5890.1611%919.9235.0140%861.6871.6340%
    5848849.2830.1513%848.9210.1086%854.5670.7744%837.7901.2040%
    6814813.5710.0527%813.7970.0250%797.1612.0686%914.5560.0683%
    7779779.0050.0007%778.9520.0062%798.8702.5507%791.9671.6646%
    平均拟合误差0.0573%0.0606%5.1438%0.9446%
    预测结果预测值相对误差预测值相对误差预测值相对误差预测值相对误差
    8738735.2630.3709%742.1470.5619%787.4256.6972%770.0044.3366%
    下载: 导出CSV

    表  6  我国无线通信用户数量和相关因素

    Table  6  Number of wireless communication users and related factors in my country

    序号X1(0)X2(0)X3(0)X4(0)X5(0)
    18453.313985.699241.6563.549817825.6
    214522.221926.3109655.2703.576925566.3
    320600.527400.3120322.7773.0128656.8
    426995.333698.4135822.8869.399835082.5
    533482.439684.3159878.31262.99842346.9
    639340.648241.7184937.41371.63147196.1
    746105.861032216314.41442.34350279.9
    854730.685496.1265810.31709.22151034.6
    964124.5114531.4314045.41690.71950863.2
    1074721.4144084.7340902.81684.90349265.6
    1185900.3150284.9401.2021641.46446537.3
    下载: 导出CSV

    表  7  IBSGM(1,N)模型的参数值

    Table  7  Parameter values of IBSGM(1,N) model

    $ a $$ {b}_{1} $$ {b}_{2} $$ {b}_{3} $$ {b}_{4} $$ \gamma $$ \lambda $
    0.50830.2095−0.00670.78830.2811−533.7480
    下载: 导出CSV

    表  8  四种模型下预测结果和误差对比

    Table  8  Comparison of prediction results and errors under the four models

    序号原始数据IBSGM(1,N)模型OBGM(1,N)模型GM(1,N)模型GM(1,1)模型
    模拟值相对误差模拟值相对误差模拟值相对误差模拟值相对误差
    18453.38453.308453.308453.308453.30
    214522.214487.370.24%14522.13013547.076.71%18836.5929.71%
    320600.520703.430.49%20767.870.81%26762.8329.91%22465.689.05%
    426995.326927.630.25%27021.50.10%36603.2135.59%26793.960.75%
    533482.433346.360.41%33260.960.66%44119.8731.77%31956.144.56%
    639340.639540.970.51%39664.410.82%50502.8328.37%38112.873.12%
    746105.846149.150.09%46512.320.88%57002.6623.63%45455.771.41%
    891054730.654533.320.36%54578.750.28%66192.8120.94%54213.370.95%
    64124.564228.940.16%64095.540.05%77398.6920.70%64658.220.83%
    74721.474706.120.02%74999.450.37%88385.6018.29%77115.403.20%
    平均拟合误差0.25%0.4%21.59%5.36%
    预测结果预测值相对误差预测值相对误差预测值相对误差预测值相对误差
    1185900.386179.620.32%85586.720.37%95722.4011.43%91972.607.07%
    下载: 导出CSV

    表  9  2003-2011年浙江省经济总产值与固定资产投资额

    Table  9  2003-2011 Zhejiang Province's total economic output value and fixed asset investment

    序号X1(0)X2(0)
    19705.024180.38
    211648.75384.38
    313417.76138.39
    415718.476964.28
    518753.737704.9
    621462.698550.71
    722990.359906.46
    827722.3111451.98
    932318.8514077.25
    下载: 导出CSV

    表  10  IBSGM(1,N)模型的参数值

    Table  10  Parameter values of IBSGM(1,N) model

    $ a $$ {b}_{1} $$ \gamma $$ \lambda $
    0.00480.32688.63751
    下载: 导出CSV

    表  11  四种模型下预测结果和误差对比

    Table  11  Comparison of prediction results and errors under the four models

    序号原始数据IBSGM(1,N)模型时滞GM(1,N)模型GM(1,N)模型GM(1,1)模型
    模拟值相对误差模拟值相对误差模拟值相对误差模拟值相对误差
    19705.029705.0209705.0209705.0209705.020
    211648.711660.780.10%9554.9617.97%9991.7420.43%11562.080.74%
    313417.713602.451.38%12461.417.13%16856.4533.23%13911.743.68%
    415718.4715802.970.54%15718.470.00%18698.0610.94%15882.741.05%
    518753.7318230.982.79%20665.3110.19%19884.382.99%18133.003.31%
    621462.6920922.412.52%20773.853.21%21595.318.91%20702.073.54%
    722990.3524049.574.61%25883.5612.58%25006.368.77%23892.543.92%
    827722.3127659.110.23%27355.391.32%28491.672.78%27293.701.55%
    平均拟合误差1.52%6.55%11.01%2.22%
    预测结果预测值相对误差预测值相对误差预测值相对误差预测值相对误差
    932318.8532104.520.66%31523.812.46%34864.87.88%31179.033.53%
    下载: 导出CSV
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  • 收稿日期:  2020-09-21
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