35 2 2012 2 GEOMATICS & SPATIAL INFORMATION TECHNOLOGY Vol. 35 No. 2 Feb. 2012 1 2 3 4 1. 450008 2. 450005 3. 450008 4. 572000 20 J 101 20 ARMA TU196 B 1672-5867 2012 02-0213 - 04 Application of Time Series Model in Observing Building Subsidence ZHU Rui 1 ZHANG Jun - zhong 2 LONG Yang 3 WANG Zhong - wei 4 1. Henan Surveying and Mapping Academy of Engineering Zhengzhou 450008 China 2. Henan Provincial Academy of Architecture Research Zhengzhou 450053 China 3. Henan Institute of Remote Sensing Surveying and Mapping Zhengzhou 450008 China 4. Hainan Environmental and Geological Prospecting Institute Sanya 572000 China Abstract This paper briefly introduces the basic principles methods data recognition modeling and forecast of time series analysis as well as its application in data processing in deformation monitoring. Practical engineering application which calculates and analyses 20 consecutive observation data of a monitor point of Building 20 of stage 6 of area 2 of Huading New City shows that this model is able to accurately monitor and forecast building deformation and is therefore proved to be of high practical application value. Key words time series model deformation monitoring ARMA forecasting 0 EVIEWS 3. 1 1 2 1. 1 1 x t n x t - 1-2 - 3 - n m Time series analysis a t - 1 a t - 2 a t - 3 a t - m AR- MA -1-2 + + φ n -n - θ 1 - θ m a t-m 1 2011-02 - 11 1983-3 20 J101
214 2012 θ 1 = 0 1-1 -2 + + φ n -n 2 2 n AR n φ i = 0 1 = a t - θ 1 - - θ m a t-m 3 3 m MA m 1. 2 ρ k = R k /R 0 5 Akaike 1973 0 ρ k 1 AIC = n ln δ 2 ε + 2 p + q + 1 = min 11 n δ ε 2 p q MA AR p = ^p q = ^q 11 ARMA ^p ^q k 1. 4 φ k1 φ k2 φ kk - i x k k = k -i 6 x k + 1 ^x k 1 i = 1 ARMA p q x k + 1 x k + l - 1 + + φ p x k + l - p + J = E - k -i 2 i = 1 i k 7 φ kk k k D ε k 1 = E x k + 1 - ^x k 1 2 = min ARMA p i q 7 ρ i = k ρ j - 1 i = 1 2 3 k ^x k l = ρ 0 ρ 1 ρ k-1 ρ 1 ρ 0 ρ k-2 ρ k-1 ρ k-2 ρ 0 φ k1 φ k1 φ k 1 = ρ 1 ρ ρ 2 k 8 φ k1 φ k2 φ kk AR MA 57 14 1 1 Tab. 1 Model type AR n MA m ARMA n m φ B = a t = θ B a t φ B = θ B a t 1. 3 1 p p AR P -1-2 + + φ p -p 9 2 q q MA q = a t - θ 1 - - θ m a t-q 10 3 ARMA p q ARMA p q R k = E -k k = 1 2 4 p q AIC Akaike Information Criterion 5 AIC a k + 1 - - θ q a k + l - q ε k 1 = x k + 1 - ^x k 1 l -1 φ j ^x k l - j + p φ j ^x k+l-j - q -1 θ l+j a k-1 1 k { φ j ^x k l - j + p φ j ^x k+l-j l > p J101 J101 l -1 2 12 20 57 58 59 58 22 59 20 10 ~ 20 m 8 57 J101 MI243 EVIEWS 3. 1
2 215 J101 + 2 57 J101 1 20 6 1 2 ARMA ARMA 3. 2 ARMA 3. 3 ARMA 2 2 J101 Fig. 2 Chart of first - order differential autocorrelation Tab. 2 Part of the information of the J101 subsidence observation points function and partial autocorrelation function / /m / /m 2010-1 - 5 17. 714 2010-3 - 12 17. 720 7 2010-1 - 10 17. 713 7 2010-3 - 13 17. 723 1 2010-1 - 20 17. 713 8 2010-3 - 14 17. 728 7 2010-2 - 5 17. 714 3 2010-3 - 15 17. 730 4 2010-2 - 16 17. 715 7 2010-4 - 2 17. 731 3 2010-3 - 4 17. 715 6 2010-4 - 5 17. 731 1 2010-3 - 5 17. 716 6 2010-4 - 10 17. 732 4 2010-3 - 7 17. 716 2 2010-4 - 15 17. 732 4 2010-3 - 9 17. 717 4 2010-4 - 20 17. 732 8 2010-3 - 10 17. 718 8 2010-4 - 25 17. 732 6 Fig. 3 3 ARMA 3 2 ARMA 3 2 model parameter estimation and related test results Forecast 19 20 4 5 Fig. 1 1 Chart of autocorrelation function and partial autocorrelation function Quick \ Estimate \ Equation AR- MA 3. 2 3 4 ARMA 3. 2 19 20 J101 Fig. 4 ARMA 3. 2 Test results of ARMA 3. 2 models prediction
216 2012 Fig. 5 5 Residual error graph MAPE 10 ARMA 3. 2 3 4 Adjusted R 2 AIC SC MAPE ARMA 3 3 Tab. 3 3 Results of parameter estimations of each model p q φ1 φ2 φ3 θ1 θ2 θ3 3. 2 0. 859 6 0. 724 0-0. 559 3-1. 109 5-1. 113 1 0 3. 3 0. 788 2 0. 825 1-0. 517 3-0. 894 1-1. 319 8-0. 304 2 Tab. 4 4 Test results of each model p q Adjusted R2 AIC SC MAPE 3. 2 0. 511 1-10. 686 6-10. 455 2 0. 002 225 3. 3 0. 630 0-10. 706 3-10. 616 6 0. 001 982 J101F 21 25 5 5 d 5 2010-4 - 30 2010-5 - 20 5 5-6. 2 mm X t = 0. 788 2X t-1 + 0. 825 1X t-2-0. 517 3X t-3 + μ t - 0. 894 1μ t-1-1. 139 8μ t-2-0. 304 2μ t-3 X t J101 ARMA 3 3 J101 EXPAND 21 25 Forecast 21 25 OK Tab. 5 5 J101 Comparison between the last five predicted elevation value and actual elevation value of J101 / /m /m / /% 2010-4 - 30 17. 732 6 17. 734 3-1. 734 3 0 2010-5 - 5 17. 732 7 17. 735 3-2. 586 4-0. 000 1 2010-5 - 10 17. 732 7 17. 736 8-4. 141 3-0. 000 2 2010-5 - 15 17. 732 9 17. 737 8-4. 908 6-0. 000 3 2010-5 - 20 17. 733 17. 739 2-6. 218 3-0. 000 4 3 220
220 2012 3. J. 2002 57 2 127-134. 3 4. J. 2007 21 4 1-5. 5. J. 2010 1 IGBP&HDP. Science /Reseal Plan. IGBP Report No. 35&- HDP Report No. 7 R. Stockholm Sweden 1995. 2 D. Barkin R. I. Bart B. R. De Walt. Food Crops vs. Feed Crops The Global Substitution of Grains in Production M. Lynne Renner Publications Inc. USA. 1990. 7 19 765-767. 6. 50 J. 2001 16 2 121-127. 7. J. 2003 23 4 513-515. 216 3. D. ARMA p q 4. J. 2006 4 426-429. 5. J. 2004 2 13-14. 6. M. 7. D. 1. M. 2007. 2003. 2. J. 2004 2 34-40. 2004. 2003. 檸檸檸檸檸檸檸檸檸 檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸檸 檺檺檺檺檺檺 檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺