Grey Model for Residual Modification and its Application in Honing Size Prediction
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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。
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关键词:
- GM(1, 1)模型 /
- 预测 /
- 参数估计 /
- 残差修正 /
- 马尔科夫链
Abstract: To improve the prediction accuracy and robustness of the grey model with first order and one variable (GM(1, 1)), an improved GM (1, 1) model is proposed. The prediction formula of the GM(1, 1) model is rededuced with the background value optimization and parameter estimation, and the prediction values are modified two times by introducing the residual modification coefficients and the weighted Markov processes to improve the prediction accuracy. The prediction results of the plunger bushing internal honing size show that the model has the highest prediction accuracy under the original data fluctuation, it can cover the shortages of the other GM (1, 1) models and predict the honing size.-
Key words:
- GM (1, 1) model /
- prediction /
- parameter estimation /
- residual modification /
- Markov processes
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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 
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表 3 rk和ωk
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
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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
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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
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[1] 李鹏飞, 张琳娜, 郑鹏, 等.机械加工尺寸预报建模研究[J].机床与液压, 2016, 44(11):101-103, 108 doi: 10.3969/j.issn.1001-3881.2016.11.024Li P F, Zhang L N, Zheng P, et al. Research on dimension forecast modeling of mechanical machining[J]. Machine Tool & Hydraulics, 2016, 44(11):101-103, 108(in Chinese) doi: 10.3969/j.issn.1001-3881.2016.11.024 [2] 魏丽娜, 宁会峰, 龚俊, 等.PSO优化灰色神经网络的珩磨油石磨损预测[J].工具技术, 2017, 51(9):63-66 doi: 10.3969/j.issn.1000-7008.2017.09.014Wei L N, Ning H F, Gong J, et al. Wear prediction of honing oil stone based on PSO optimize grey neural network[J]. Tool Engineering, 2017, 51(9):63-66(in Chinese) doi: 10.3969/j.issn.1000-7008.2017.09.014 [3] 龙会典, 严广乐.基于SARIMA、GM(1, 1)和BP神经网络集成模型的GDP时间序列预测研究[J].数理统计与管理, 2013, 32(5):814-822 http://d.old.wanfangdata.com.cn/Periodical/sltjygl201305006Long H D, Yan G L. Researeh on GDP time series forecasting based on integrating SARIMA, GM(1, 1) and BP neural networks[J]. Journal of Applied Statistics and Management, 2013, 32(5):814-822(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/sltjygl201305006 [4] Contreras J, Espinola R, Nogales F J, et al. ARIMA models to predict next-day electricity prices[J]. IEEE Transactions on Power Systems, 2003, 18(3):1014-1020 doi: 10.1109/TPWRS.2002.804943 [5] Sousa J C, Neves L P, Jorge H M. Assessing the relevance of load profiling information in electrical load forecasting based on neural network models[J]. International Journal of Electrical Power & Energy Systems, 2012, 40(1):85-93 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=068ea806196ed80f0804b322873ed27f [6] Cui J, Liu S F, Zeng B, et al. A novel grey forecasting model and its optimization[J]. Applied Mathematical Modelling, 2013, 37(6):4399-4406 doi: 10.1016/j.apm.2012.09.052 [7] Xiao X P, Hu Y C, Guo H. Modeling mechanism and extension of GM (1, 1)[J]. Journal of Systems Engineering and Electronics, 2013, 24(3):445-453 doi: 10.1109/JSEE.2013.00053 [8] Shih C S, Hsu Y T, Yeh J, et al. Grey number prediction using the grey modification model with progression technique[J]. Applied Mathematical Modelling, 2011, 35(3):1314-1321 doi: 10.1016/j.apm.2010.09.008 [9] Zeng X Y, Shu L, Huang G M, et al. Triangular fuzzy series forecasting based on grey model and neural network[J]. Applied Mathematical Modelling, 2016, 40(3):1717-1727 doi: 10.1016/j.apm.2015.08.009 [10] Lin Y H, Chiu C C, Lee P C, et al. Applying fuzzy grey modification model on inflow forecasting[J]. Engineering Applications of Artificial Intelligence, 2012, 25(4):734-743 doi: 10.1016/j.engappai.2012.01.001 [11] 高貂林, 王新宏, 彭华.一种基于累积法的K分布的参数估计方法[J].系统仿真学报, 2014, 26(6):1297-1300 http://d.old.wanfangdata.com.cn/Periodical/xtfzxb201406019Gao D L, Wang X H, Peng H. Method for estimating K-distribution parameters based on accumulation method[J]. Journal of System Simulation, 2014, 26(6):1297-1300(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/xtfzxb201406019 [12] 袁江, 周成一, 邱自学, 等.机床主轴热误差的累积法建模研究[J].组合机床与自动化加工技术, 2016, (8):105-107, 123 http://d.old.wanfangdata.com.cn/Periodical/zhjc201608029Yuan J, Zhou C Y, Qiu Z X, et al. Modeling research on machine tool spindle thermal error based on cumulative method[J]. Modular Machine Tool & Automatic Manufacturing Technique, 2016, (8):105-107, 123(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/zhjc201608029 [13] Wu L F, Liu S F, Yao L G, et al. The effect of sample size on the grey system model[J]. Applied Mathematical Modelling, 2013, 37(9):6577-6583 doi: 10.1016/j.apm.2013.01.018 [14] Zhou D J, Yu Z Q, Zhang H S, et al. A novel grey prognostic model based on Markov process and grey incidence analysis for energy conversion equipment degradation[J]. Energy, 2016, 109:420-429 doi: 10.1016/j.energy.2016.05.008 [15] Ye J, Dang Y G, Li B J. Grey-Markov prediction model based on background value optimization and central-point triangular whitenization weight function[J]. Communications in Nonlinear Science and Numerical Simulation, 2018, 54:320-330 doi: 10.1016/j.cnsns.2017.06.004 [16] 亓四华, 费业泰.基于灰色系统理论的柱塞套内圆珩磨过程模型研究[J].机床与液压, 2002, (3):3-4, 25 doi: 10.3969/j.issn.1001-3881.2002.03.001Qi S H, Fei Y T. A model study of internal honing process for plunger bushing based on grey system theory[J]. Machine Tool & Hydraulics, 2002, (3):3-4, 25(in Chinese) doi: 10.3969/j.issn.1001-3881.2002.03.001 -
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