Grey interpolation approach for small time-lag samples based on grey dynamic relation analysis

doi:10.21629/JSEE.2018.01.11

Journal of Systems Engineering and Electronics ›› 2018, Vol. 29 ›› Issue (1): 105-115.doi: 10.21629/JSEE.2018.01.11

• Systems Engineering • Previous Articles Next Articles

Grey interpolation approach for small time-lag samples based on grey dynamic relation analysis

Junjie WANG^1,*(), Yaoguo DANG¹(), Ning XU²(), Song DING¹()

¹ College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, China
² College of Management Science and Engineering, Nanjing Audit University, Nanjing 211815, China

Received:2016-12-07 Online:2018-02-26 Published:2018-02-23
Contact: Junjie WANG E-mail:junjie881129@163.com;iamdangyg@163.com;nuaa_xuning@163.com;dingsong1129@163.com
About author:WANG Junjie was born in 1988. He received his B.S. degree from College of Economics and Management in Nanjing University of Aeronautics and Astronautics in 2011. Then, he got his M.S. degree in management science and engineering from Nanjing University of Aeronautics and Astronautics in 2014. He is currently a Ph.D. candidate majored in grey systems containing grey relational analysis and grey predictions in College of Economics and Management of Nanjing University of Aeronautics and Astronautics. He was a visiting scholar in University of Waterloo for one year from 2015 to 2016. He is also interested in conflict analysis using the graph model. E-mail: junjie881129@163.com|DANG Yaoguo was born in 1964. He is currently a professor and Ph.D. supervisor of College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, China. He is the academic leader of management science and engineering of College of Economics and Management in Nanjing University of Aeronautics and Astronautics. His major research interests are grey system theory, quantitative economics, and post project evaluation. He is now undertaking a project of national natural science foundation of China, and a major project of key research base of philosophy and social science in Jiangsu colleges. E-mail: iamdangyg@163.com|XU Ning was born in 1983. He is currently a lecturer in Nanjing Audit University. He got his Ph.D. degree from College of Economics and Management of Nanjing University of Aeronautics and Astronautics in 2015. He majors in management science and engineering. He received his B.E. degree and M.S. degree from Nanjing University of Aeronautics and Astronautics in 2006 and 2011, respectively. His research focuses on grey system theory and the prediction modeling algorithm, which is applied on energy system prediction. He is also interested in quantitative economics, especially in the modeling and prediction of macro economy. E-mail: nuaa_xuning@163.com|DING Song was born in 1992. He is a Ph.D. candidate of College of Economics and Management of Nanjing University of Aeronautics and Astronautics and majors in management science and engineering. He received his M.S. degrees from Nanjing University of Aeronautics and Astronautics in 2015, and receives B.E. degree from Jiangsu University of Science and Technology in 2012. His research focuses on grey system theory and the prediction modeling algorithm, which is applied on energy system prediction, environment pollution, agricultural development, and so on. He is also interested in industrial economy. E-mail: dingsong1129@163.com
Supported by:
the National Natural Science Foundation of China(71371098);the National Natural Science Foundation of China(71071077);Funding of Jiangsu Innovation Program for Graduate Education(KYZZ15_0093);Fundamental Research Funds for the Central Universities(2017301);Natural Science Fund Project of Colleges in Jiangsu Province(16KJD120001);Funding for Major Project of Jiangsu Social Science(16GLA001);Funding for Outstanding Doctoral Dissertation in Nanjing University of Aeronautics and Astronautics(BCXJ15-10);This work was supported by the National Natural Science Foundation of China (71371098; 71071077), Funding of Jiangsu Innovation Program for Graduate Education (KYZZ15_0093), Fundamental Research Funds for the Central Universities (2017301), Natural Science Fund Project of Colleges in Jiangsu Province (16KJD120001), Funding for Major Project of Jiangsu Social Science (16GLA001), and Funding for Outstanding Doctoral Dissertation in Nanjing University of Aeronautics and Astronautics (BCXJ15-10)

Abstract

Abstract:

Given a non-equidistant sequence or an equidistant series with one or more outliers, a grey interpolation approach considering the time lags is established for producing the missing data or correcting the abnormal values. To accomplish this, a new grey incidence model, called the grey dynamic incidence model GDIM(t), is constructed for determining whether the factors are effective to the known factor and what the time lag is between a useful factor and the specified sequence. Based on the results of the GDIM(t) model, two programming problems are designed to obtain the upper and lower bounds of the unknown or abnormal values which are regarded as grey numbers. The solutions based on the particle swarm optimization (PSO) for the nonlinear programming problems are given. To explain how it can be used in practice, this new grey interpolation approach is applied to correct an abnormal value in the sequence of an agriculture environment problem.

Key words: grey interpolation, grey relational analysis, time lags, programming problems

Junjie WANG, Yaoguo DANG, Ning XU, Song DING. Grey interpolation approach for small time-lag samples based on grey dynamic relation analysis[J]. Journal of Systems Engineering and Electronics, 2018, 29(1): 105-115.

Figures/Tables 11

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References 26

1	HACKBUSCH W. Fast and exact projected convolution for non-equidistant grids. Computing, 2007, 80 (2): 137- 168. doi: 10.1007/s00607-007-0229-z
2	BOCHE H, NICH U J. Convergence behavior of nonequidistant sampling series. Signal Processing, 2010, 90 (1): 145- 156.
3	LI C P, YI Q, CHEN A. Finite difference methods with nonuniform meshes for nonlinear fractional differential equations. Journal of Computational Physics, 2016, 316, 614- 631. doi: 10.1016/j.jcp.2016.04.039
4	JANSEN M. Multiscale local polynomial smoothing in a lifted pyramid for non-equispaced data. IEEE Trans. on Signal Processing, 2013, 61 (3): 545- 555. doi: 10.1109/TSP.2012.2225059
5	XIE N M, LIU S F, YANG Y J, et al. On novel grey forecasting model based on non-homogeneous index sequence. Applied Mathematical Modelling, 2013, 37 (7): 5059- 5068. doi: 10.1016/j.apm.2012.10.037
6	HE Z, SHEN Y, WANG Q, et al. Mitigating end effects of EMD using non-equidistance grey model. Journal of Systems Engineering and Electronics, 2012, 23 (4): 603- 611. doi: 10.1109/JSEE.2012.00075
7	SHEN Y, HE B, QING P. Fractional-order grey prediction method for non-equidistant sequences. Entropy, 2016, 18 (6): 1- 16.
8	ZOU R B. The non-equidistant new information optimizing MGM(1, n) based on a step by step optimum constructing background value. Applied Mathematics & Information Sciences, 2012, 6 (3): 745- 750.
9	FERRANTI F, ROLAIN Y. A local identification method for linear parameter-varying systems based on interpolation of state-space matrices and least-squares approximation. Mechanical Systems and Signal Processing, 2017, 82, 478- 489. doi: 10.1016/j.ymssp.2016.05.037
10	JIANG X, ZHANG S G, SHANG B X. The discretization for bivariate ideal interpolation. Journal of Computational and Applied Mathematics, 2016, 308, 177- 186. doi: 10.1016/j.cam.2016.05.012
11	WANG X J, YANG S L. The improvements and applications for forecasting method in GM(1, 1) model based on combinative interpolation. Chinese Journal of Management Science, 2012, 20 (2): 129- 134.
12	KE H F, CHEN Y G, LIU Y. Data processing of small samples based on grey distance information approach. Journal of Systems Engineering and Electronics, 2007, 18 (2): 281- 289. doi: 10.1016/S1004-4132(07)60088-7
13	WANG J M, WANG J B, ZHANG T, et al. Probability estimation based on grey system theory for simulation evaluation. Journal of Systems Engineering and Electronics, 2016, 27 (4): 871- 877. doi: 10.21629/JSEE.2016.04.15
14	DENG J L. Grey incidence space in grey systems theory. Fuzzy Mathematics, 1985, 4 (2): 1- 10.
15	SHIH C S, HSU Y T, YEH J, et al. Grey number prediction using the grey modification model with progression technique. Applied Mathematical Modelling, 2011, 35 (3): 1314- 1321. doi: 10.1016/j.apm.2010.09.008
16	WANG J J, DANG Y G, LI X M. Study on construction of whitenization weight function with interval grey number and its solving algorithm. The Journal of Grey System, 2014, 26 (3): 40- 54.
17	ZHANG K, YE W, ZHAO L P. The absolute degree of grey incidence for grey sequence based on standard grey interval number operation. Kybernetes, 2012, 41 (7/8): 934- 944. doi: 10.1108/03684921211257784
18	WANG Z X. Correlation analysis of sequences with interval grey numbers based on the kernel and greyness degree. Kybernetes, 2013, 42 (2): 309- 317. doi: 10.1108/03684921311310620
19	LIU S F, XIE N M, JORREST F. On new models of grey incidence analysis based on visual angle of similarity and nearness. Systems Engineering-Theory & Practice, 2010, 30 (5): 882- 887.
20	ZHANG K, QU P P. Grey mode incidence analysis model based on series symbolization method. Journal of Grey System, 2013, 25 (2): 91- 99.
21	DANG Y G, LIU S F, LIU B, et al. Improvement on degree of grey slope incidence. Engineering Science, 2004, 6 (3): 41- 44.
22	SHI H X, LIU S F, FANG Z G. Grey amplitude incidence model. Systems Engineering-Theory & Practice, 2010, 30 (10): 1828- 1833.
23	LIANG L T, FENG S Y, QU F T. Forming mechanism of agricultural non-point source pollution: a theoretical and empirical study. China Population, Resources and Environment, 2010, 20 (4): 74- 80.
24	ZHANG K, QU P P, ZHANG Y T. Delay multi-variables discrete grey model and its application. Systems EngineeringTheory & Practice, 2015, 35 (8): 2092- 2013.
25	JIWARI R. Lagrange interpolation and modified cubic Bspline differential quadrature methods for solving hyperbolic partial differential equations with Dirichlet and Neumann boundary conditions. Computer Physics Communications, 2015, 193, 55- 65. doi: 10.1016/j.cpc.2015.03.021
26	WANG J, HIPEL K W, DANG Y. An improved grey dynamic trend incidence model with application to factors causing smog weather. Expert Systems with Applications, 2017, (87): 240- 251.

Year	1994	1995	1996	1997	1998	1999	2000	2011
X₁(COD)	5.345 5	5.52	5.661 6	5.592 9	5.766 2	5.808 2	5.874 8	5.913 8

Year	Possibly related factors
Year	X₂(GAP)	X₃(PAH)	X₄(SA)	X₅(IA)
1990	506.2	25.7	47 403	148 362
1991	534.2	26.5	47 822	149 586
1992	586.7	27.1	48 590	149 007
1993	696.4	27.4	48 728	147 741
1994	957.3	29.7	48 759	148 241
1995	1 213.6	29.7	49 281	149 879
1996	1 401.5	26.9	50 381	152 381
1997	1 444.2	28.7	51 239	153 969
1998	1 481.8	28.6	52 296	155 706
1999	1 486.0	28.5	53 158	156 373
2000	1 494.5	29.7	51 239	156 300
2001	1 578.1	30.4	52 396	155 708
2002	1 653.7	30.9	53 158	154 636
2003	1 738.2	32.1	53 820	152 415
2004	2 141.3	33.6	54 249	153 553
2005	2 242.0	33.7	55 029	155 488

	t_ij	1994	1995	1996	1997	1998	1999	2000	2001
$\gamma _{12}^{t_{12} } (k)$	1	0.991	0.897	$\gamma_{12}^1 (3)$	$\gamma _{12}^1 (4)$	0.914	0.687	0.827	0.991
$\gamma _{14}^{t_{14} } (k)$	-1	0.814	0.812	$\gamma _{14}^{-1}(3)$	$\gamma _{14}^{-1} (4)$	0.863	0.905	0.856	0.863

	Fitness value	Restored value
$Z^-(\otimes x_1 (4)^-)$	0.129 7	5.723 0
$Z^+(\otimes x_1 (4)^+)$	0.181 2	5.733 0

	Fitness value	Restored value
$Z^-(\otimes x_2 (7)^-)$	0.213 8	13 234
$Z^+(\otimes x_2 (7)^+)$	0.490 1	13 887

Grey interpolation approach for small time-lag samples based on grey dynamic relation analysis

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Figures/Tables 11

References 26

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	GIA	LaI	LiI	CSI	GM(1, 1)
Results	13 887	14 785	14 681	14 794	14 827
Absolute errors	128	770	666	779	812
Relative errors/%	0.91	5.49	4.755	5.56	5.57

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