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残差修正灰色模型及其在珩磨尺寸预报中的应用

李奇军 牛永江 宁会峰

李奇军, 牛永江, 宁会峰. 残差修正灰色模型及其在珩磨尺寸预报中的应用[J]. 机械科学与技术, 2019, 38(5): 761-766. doi: 10.13433/j.cnki.1003-8728.20180210
引用本文: 李奇军, 牛永江, 宁会峰. 残差修正灰色模型及其在珩磨尺寸预报中的应用[J]. 机械科学与技术, 2019, 38(5): 761-766. doi: 10.13433/j.cnki.1003-8728.20180210
Li Qijun, Niu Yongjiang, Ning Huifeng. Grey Model for Residual Modification and its Application in Honing Size Prediction[J]. Mechanical Science and Technology for Aerospace Engineering, 2019, 38(5): 761-766. doi: 10.13433/j.cnki.1003-8728.20180210
Citation: Li Qijun, Niu Yongjiang, Ning Huifeng. Grey Model for Residual Modification and its Application in Honing Size Prediction[J]. Mechanical Science and Technology for Aerospace Engineering, 2019, 38(5): 761-766. doi: 10.13433/j.cnki.1003-8728.20180210

残差修正灰色模型及其在珩磨尺寸预报中的应用

doi: 10.13433/j.cnki.1003-8728.20180210
基金项目: 

甘肃省高校科研项目 2017A-076

国家自然科学基金项目 51565033

详细信息
    作者简介:

    李奇军(1988-), 讲师, 硕士, 研究方向为珩磨加工理论与技术, liqj-88@163.com

  • 中图分类号: TH161

Grey Model for Residual Modification and its Application in Honing Size Prediction

  • 摘要: 针对一阶一变量灰色模型(Grey model with first order and one variable,GM(1,1))预测精度低、稳健性差的问题,提出了一种改进的GM(1,1)模型。通过背景值优化和参数累积估计,重新推导了GM(1,1)模型的预测公式,并引入残差修正系数和加权马尔科夫链对预测值进行两次残差修正,以提高预测精度。对柱塞套内圆珩磨尺寸的预测结果表明,该模型在原始数据波动条件下的预测精度最高,能弥补其它GM(1,1)模型的不足并实现对珩磨尺寸的预报。
  • 图  1  实测值与预测值对比图

    表  1  预测结果对比表

    序号 实测值/μm GM(1, 1)预测值/μm ε1(i) AGM(1, 1)预测值/μm e+(0)(i)预测值/μm GAGM(1, 1)预测值/μm ε2(i) 状态 MGAGM(1, 1)预测值/μm ε3(i)
    1 19.42 19.420 0 0 19.420 0 0 19.420 0 0 3 - -
    2 20.82 22.397 1 -0.075 7 22.536 9 1.521 2 21.015 7 -0.009 4 3 - -
    3 19.54 21.182 4 -0.084 1 21.288 8 1.385 0 19.903 8 -0.018 6 3 - -
    4 21.98 20.033 6 0.088 6 20.109 9 1.261 0 21.370 9 0.027 7 4 - -
    5 19.64 18.947 1 0.035 3 18.996 2 1.148 1 20.144 3 -0.025 7 2 - -
    6 18.52 17.919 5 0.032 4 17.944 3 1.045 4 18.989 7 -0.025 4 2 - -
    7 17.04 16.947 7 0.005 4 16.950 5 0.951 8 17.902 3 -0.050 6 1 - -
    8 17.56 16.028 5 0.087 2 16.011 9 0.866 6 16.878 5 0.038 8 4 - -
    9 15.54 15.159 2 0.024 5 15.125 2 0.789 0 15.914 2 -0.024 1 2 - -
    10 14.12 14.337 1 -0.015 4 14.287 6 0.718 4 13.569 2 0.039 0 4 - -
    11 14.54 13.559 5 0.067 4 13.496 3 0.654 0 14.150 3 0.026 8 4 - -
    12 12.70 12.824 1 -0.009 8 12.748 9 0.595 5 12.153 4 0.043 0 4 - -
    13 10.50 12.128 6 -0.155 1 12.042 9 0.542 2 11.500 7 -0.095 3 1 - -
    14 11.26 11.470 9 -0.018 7 11.376 0 0.493 6 10.882 4 0.033 5 4 - -
    15 9.74 10.848 7 -0.113 8 10.746 0 0.449 4 10.296 6 -0.057 1 1 - -
    16 10.64 10.260 4 0.035 7 10.150 9 0.409 2 9.741 7 0.084 4 4 10.095 0 0.051 2
    17 9.46 9.703 9 -0.025 8 9.588 8 0.372 6 9.216 2 0.025 8 1 8.573 2 0.093 7
    18 8.28 9.177 6 -0.108 4 9.057 8 0.339 2 8.718 6 -0.053 0 4 9.034 8 -0.091 2
    19 7.53 8.679 9 -0.152 7 8.556 2 0.308 9 8.247 3 -0.095 3 1 7.671 9 -0.018 8
    20 7.12 8.209 2 -0.153 0 8.082 4 0.281 2 7.801 2 -0.095 7 4 8.084 1 -0.135 4
    21 6.62 7.763 9 -0.172 8 7.634 8 0.256 0 7.378 8 -0.114 6 1 6.864 0 -0.036 9
    22 6.08 7.342 9 -0.2077 7.212 0 0.233 1 6.978 9 -0.147 8 4 7.232 0 -0.189 5
    23 5.73 6.9446 -0.2120 6.812 6 0.212 2 6.600 4 -0.151 9 1 6.139 9 -0.071 5
    24 5.36 6.5680 -0.2254 6.435 3 0.193 2 6.242 1 -0.164 6 4 6.468 5 -0.206 8
    下载: 导出CSV

    表  2  状态划分表

    状态 E2 E2 E3 E4
    相对误差范围/% [-10, -5] [-5, -2] [-2, 2] [2, 5]
    下载: 导出CSV

    表  3  rkωk

    步长 1 2 3 4
    rk -0.426 5 0.308 5 -0.337 4 0.164 6
    ωk 0.344 8 0.249 4 0.272 8 0.133 1
    下载: 导出CSV

    表  4  状态预测表

    数据序号 初始状态 转移步数 权重 状态
    1 2 3 4
    15 1 1 0.344 8 0 0 0 1
    14 4 2 0.249 4 1/5 1/5 0 3/5
    13 1 3 0.272 8 0 0 0 1
    12 4 4 0.133 1 1/4 0 0 1/4
    合计 0.063 7 0.041 6 0.382 7 0.512 0
    下载: 导出CSV

    表  5  预测结果统计分析表

    模型 GM(1, 1) AGM(1, 1) GAGM(1, 1) MGAGM(1, 1)
    MSE 0.339 9 0.303 9 0.247 4 0.257 9
    MAPE 0.143 7 0.128 2 0.103 7 0.099 5
    下载: 导出CSV
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  • 收稿日期:  2018-06-01
  • 刊出日期:  2019-05-05

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