JOURNAL OF SOUTHWEST JIAOTONG UNIVERSITY Vol. 52 No. 1 Feb. 2017!: (2017) DOI: / j. issn

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1 JOURNAL OF SOUTHWEST JIAOTONG UNIVERSITY Vol. 52 No. 1 Feb. 2017!: (2017) DOI: / j. issn CPⅢ"#$%&' () 1,2, 3, 1,2, 1,2 (1.?@A 2BC D,E ;2. FGHIJKL MNO?/,E ;3. P QRST%DU!VWXY,E ) * +: PZ[ CPⅢ <=/>\]^ _`_ 2 mm a b c, ^ `_W_ 3 mm a b ;, ^ _`_^ `_a cw_, CPⅢ a <= />. /> CPⅢ ^ a _ % CPⅢ P V a^ 2 _`_, W_ CPⅢ P Vb a ; [ b Pa CPⅢ < % a `_W_, b Pa b, CPⅢ a <=. c <=,CPⅢ P J a^ _`_W_ mm,? Pb a CPⅢ.,-.:CPⅢ ; ; <=; ; _;`_ /0 1!:P258;TU12 :A New Methodology for Stability Analysis on Repeated Measurement of CPⅢ Vertical Control Network LIU Chenglong 1,2, LIU Zhujun 3, YANG Xuefeng 1,2, LIU Zhi 1,2 (1. Faculty of Geosciences and Environment Engineering,Southwest Jiaotong University,Chengdu ,China; 2. State province Joint Engineering Laboratory of Spatial Information Technology of High Speed Rail Safety,Chengdu ,China;3. China Railway Eryuan Engineering Group Co. Ltd.,Chengdu ,China) Abstract:In the current code on the stability analysis of repeated measurements for the CPⅢ vertical control network of high speed railways,the divergence tolerance of elevation between original and repeated measurements should be no more than 2 mm,which is not reasonable due to misjudging stable points. Besides,there is also poor evidence to set the altitude difference between original and repeated measurements to be no more than 3 mm. Thus,more reasonable divergence tolerance of elevation and altitude difference between the original and repeated measurements were deduced,and a new method on the stability analysis of CPⅢ vertical control network was proposed. This new method calculates the altitude difference for every segment of the CPⅢ vertical control network and detects unstable segments in the whole network according to the original and repeated measurement limits. Then,for the two CP Ⅲ points on each unstable segment,the divergence tolerances of elevation were computed respectively to detect the unstable CPⅢ points of the unstable segments and analyze the stability of CPⅢ vertical control network. Both the theoretical and test data show that when the divergence tolerance of elevation : :!"#$%&' (PCSIRT) : (1962 ),(,)*,+,,-./ ,E mail:lclzwy@ vip. sina. com :, 67,89:,;. CPⅢ <=/>-.[J].,2017,52(1): LIU Chenglong,LIU Zhujun,YANG Xuefeng,et al. New methodology for stability analysis on repeated measurement of CPⅢ verti cal control network[j]. Journal of Southwest Jiaotong University,2017,52(1):91 97.

2 92 52 between original and repeated measurements for the neighboring points is less than 1. 4 mm,the proposed method can reliably detect the unstable points from the CPⅢ vertical control network. Key Words:CPⅢ vertical control network;repeated measurement;stability analysis;measured segment; divergence tolerance of elevation;altitude difference Key words: CP Ⅲ vertical control network;repetition measurement;stability analysis;measure segment;divergence tolerance of elevation; altitude difference between original and repeated measurements ( CPⅢ)] O T O, J CPⅢ 1 G a 2, FJ 1, [1] P F a a [2]. CPⅢ, CPⅢ IJ, CPⅢ CPⅢ [3]. CPⅢ H a [4], 1 a (CPⅡ);CPⅢ a [5], [ a [6 7], 1 a., [!" # $ %& ab, ' a CPⅢ b, 1 a, CPⅢ <=, b a CPⅢ a. ] FJ, CPⅢ a a 5,1 (a FGH)*, + CPⅢ <=.,- a,. a /c0 1 a <=,+ <=a/ > <= <= Z [8 13]. 2 CPⅢ <=/> \]a $3-., a/>2. 1, CPⅢ"#$ 2& : CPⅢ 2 CPⅢ 4,56 P/ m 8T CPⅢ, a90j: ;1 10 ~ 20 m. [ CPⅢ 4> [14] V _ [ < _ _ Pa=_ >? a@a, Oa CPⅢ BCDE 4>., [ ab, CPⅢ ] F J. CPⅢ, P _3 a,f P CPⅢ a <=, G b a CPⅢ.,CPⅢ Ga <= H,7 I [1] (G )a Z,DE office excel J _a <=b CPⅢ a,\] <= b c b H K /> blm >?b N Oa,1 CPⅢ Ga <=/> -., G a />,- Pa /cqr, D ES aqr CPⅢ Ga T a<= a a. CPⅢ a 1, ; a/> DE a ;,2O Q; a/>lh ',2Q; b 'au1vw _`_aw_, aw_1 8 槡 L(L 1,km),+Q ; aw_1 4 槡 L [15]. [ CPⅢ F a, X /> ;Y2Q; LH ', 1 CPⅢ a P 1Q;+b, CPⅢ 1 b c a,1,] P 2 Q; a ZMN CPⅢ a <= /> -..

3 1, :CPⅢ!"#$%&' 2 ; CPⅢ"#$' 26789: 2. 1 ; CPⅢ"#$' V/> a Z CPⅢ <=. :CPⅢ DEa 4 P2 ^ ;CPⅢ 2^ a `_ 3 mm, a _2^ _`_ 2 mm, DE^ ;`_ZW P<= ZW^, KG,P ZWa CPⅢ DE [$/\. Va CPⅢ Ga <= />, ]^ : (1) a CPⅢ _ G, DE a a, a CPⅢ `a _. (2) G,% CPⅢ P V CPⅢ a 2^ a`_, bc`_ 3 mm aw_ ;,F % 2b c CPⅢ a _2^ _a` _, bc`_ 2 mm aw_. R7, bc CPⅢ 1 ; b R, b a CPⅢ 1b ; 6789: -.#, V CPⅢ <=/>\] : (1)^ _`_ 2 mm a b c,b Oa CPⅢ F Oa CPⅢ, CPⅢ Ja _a PK_ m hij P [ 0. 5 mm, b CP Ⅲ a. m hij 0. 5 mm 1, CPⅢ P Ja, ^ _2 _a `_. P 1. T h ij_old h ij_re < 1 CPⅢ ij a ^ _2 _,m hij_old m hij_re < 1 ^ _ _apk_, ]^ J, _`_1 Δh ij = h ij_re - h ij_old. (1) K_1 K_ [16], _`_ap 槡 _old m Δhij = m 2 hij_re + m 2 hij [ Ja CPⅢ,b m hij_old, F m hij_re, 7P 0. 5 mm. 7. (2) mm, \(2) m Δhij =槡 m 2 hij_re + m 2 hij_old = 0. 5 槡 2 = 0. 7 mm. (3) a 7 apk_ 1 K_, #,c CPⅢ ^ _2 _a `_P mm., CPⅢ a 1Q ; 0 ;1 60 m 90 ;1 10 ~ 20 m, Q; _ a K_1 6 槡 L [15] a, L = 60 m,6 槡 L = mm, Q; _ # 3 a mm,2 CPⅢ _apk_ a^ 2 _ `_ K_ mm. + CPⅢ J a _2^ _`_aw_1 2 mm, ] CPⅢ G ^ _ a 2 mm a b ca,+ P mm. (2) 1b a K T CPⅢ P i a^ 2 `_ 3 mm,+2 CPⅢ a CPⅢ j a ij, ^ _2 _ b 2 mm aw_, P i j 71b.,b a V Ka, K, 1 ij 1b,V i 1 + j 1b a, ^ _2 _b 2 mm aw_. (3)^ `_W_ 1 3mm b T CPⅢ P i a^ < 1 H i_old H i_re,^ a CPⅢ `a _G, a ^ a P K _ < 1 H i_old H i_re, ^ 2 a `_1 ΔH = H i_re - H i_old. (4) K_ [16],ΔH apk_1 槡 _old 93 m ΔH = m 2 Hi_re + m 2 Hi apk_1 K_,,ΔH. (5) a K_P 1 2m ΔH, ^ 2 a `_P 2 CPⅢ a^

$94 52 PK_VZ,? ^ `_W_ 1 3 mm b., [^V <=/> \]b ca,bu2 ' c a K,F2 b K 1 a K,+ K2 1 a W. 3 8 CPⅢ"#$' [ V CPⅢ G <=/> \], P DE / >]^ CPⅢ a <=: (1) CPⅢ Pb a CPⅢ ^ a _,% CPⅢ P V a^ 2 _` _, a ^ 2 _`_P 1.$

4 94 52 PK_VZ,? ^ `_W_ 1 3 mm b., [^V <=/> \]b ca,bu2 ' c a K,F2 b K 1 a K,+ K2 1 a W. 3 8 CPⅢ"#$' [ V CPⅢ G <=/> \], P DE / >]^ CPⅢ a <=: (1) CPⅢ Pb a CPⅢ ^ a _,% CPⅢ P V a^ 2 _` _, a ^ 2 _`_P 1. 4 mm aw_, CPⅢ P Vb a,b b a ]^ 2 J _# 3 a. (2) ] b Pab [ b Pa CPⅢ, \(4)(5)< % a `_ ΔH K_ 2m ΔH, ΔH 2m ΔH, 1 a CPⅢ, 1b a CPⅢ. 1, />]^ CPⅢ a />,bu? CPⅢ Pb a CPⅢ,+ ] c ca. 4 ( 2 < 4. 1 CPⅢ"#$' a CPⅢ <= />, DE O QXY] 2000 # 8a C #(C Sharp), CPⅢ <=QR. QR c CPⅢ ^ KL _`_2 `_ > <=; #, 1. Fig. 1 1 CPⅢ <=QR Function block diagram of high speed railway CPⅢ elevation network for stability analysis software of repeated measurements 4. 2 < -.a CPⅢ <= />, P^c- a CPⅢ < =QR, [ a` 1. 5 km CPⅢ <=%. CPⅢ DE 4>, % <= E ^, _% <=, J _ G CP Ⅲ ` _ 7 b [ 3 mm CPⅢ J _`_7 [ 2 mm, a, CPⅢ P V V a43#, [. I1?] P a, a CPⅢ <=] b a. ]b 1. 5 km CPⅢ a ^ P 6, KL 1. ^ ^ I,< E V CPⅢ <= /> a CPⅢ <=/> b, L a < = : (1) V CPⅢ <=/>, V CPⅢ <= % CPⅢ P V CPⅢ a 2 ^ a ` _, b c ` _ 3 mm aw_, 2 % K_ _ G 2^ a`_, ZW.

5 1, :CPⅢ!"#$%&' 95 = 1 >?@>?3ABCD= Tab. 1 Statistics of settlement measurement / mm = 2 >?@E "# CD= Tab. 2 Statistics of altitude difference between original and repeated measurements after adjustment % `_ / mm ZW 2, `_Z W CPⅢ `_7 ZW, b. 6, % CPⅢ a _2^ _a`_, b c`_ 2 mm aw_, 3 P V`_ [ 2 mm a L a %. Tab. 3 = 3 & " CD= Statistics of measured segment divergence of altitude difference ( ~ ) ( ~ ) ( ~ ) ( ~ ) ( ~ ) ( ~ ) ( ~ ) ( ~ ) ( ~ ) ( ~ ) `_ / mm a Vb />, 3 a b ,4% 12 b, P 2^ a`_zw ,b 12 U 6 I Pa b 3, 3 I [ `, 7 1, b K ; ] 1b a 12 P, a 3 b, 9 7 K 1 b,, V CPⅢ <=/>] \ / a,] b LH b a,f2 K 1 b,b [ a CPⅢ b ca. (2) -.a CPⅢ <=/> a <=, 1^ 2 _`_P 1. 4 mm, P ^ 2 _`_, _`_ [ 1. 4 mm, 1 a 1 b ; 6 2^ a`_ Pa `_PK_, ΔH 2m ΔH, 1b. E CPⅢ <=a, ^ 2 _`_ %, P _`_ [ 1. 4 mm 4. Tab. 4 = 4 & %&" CD= Statistics of measured segment divergence of altitude difference between original and repeated measurements ( ~ ) ( ~ ) ( ~ ) ( ~ ) ( ~ ) ( ~ ) ( ~ ) ( ~ ) ( ~ ) ( ~ ) `_ / mm ( ~ ) ( ~ ) ( ~ ) ( ~ ) ( ~ ) ( ~ ) ( ~ ) ( ~ ) ( ~ ) ( ~ ) `_ / mm % b, ,4% 24 b,b 24 P

6 96 52 H 6 I a, -] 24 P? 6 F ]a% <=. ] G, a `_ Pa `_PK_, 5 P % V `_ [ `_PK_a. Tab. 5 % = 5 "# 2FG/H IJKLCD= Statistics of violations of altitude difference and twice mean squared error `_ / mm PK_ , `_azw %, `_ZWa 6, a/>? V b, b2 K 1b,b. 5 M N CPⅢ </>a -., DE aqr CPⅢ ^ 2 a <=, : (1) PZ[ CPⅢ <=/>,\]^ _`_ 2 mm a b c 1b a K, ^ `_W_ 1 3 mm b a ; (2) ^ _`_^ `_a cw_, G b W_, CPⅢ Pab, b Pab a/>, CPⅢ a <=,bu CPⅢ Pb a CPⅢ,+ < ; (3) a <=/> a CPⅢ <=QR,? Pb a b a CPⅢ, ] CPⅢ a <= P E; (4) a-. LM a V a. O : [1] PI4O. TB [S]. :PO,2009. [2],8,. CPⅢ a % [J].,2008, 43(6): LIU Chenglong,YANG Youtao,XU Xiaozuo. Simulated determination of accuracy requirement for control points Ⅲ intersection networks in high speed railway[j]. Journal of Southwest Jiaotong Uniwersity, 2008, 43(6): [3] -,,!",;. />[J]. A 2,2014, 11(6): HE Linxuan,LIU Chenglong,DA Qianlong,et al. New method for elevation network measurement of high speed railway track control network[j]. Journal of Railway Science and Engneering,2014,11(6): [4],#O$,89:,;. ] $ 0 PaPE-.[J].,2014,49(1):1 7. LIU Chenglong,JIN Guoqing,YANG Xuefeng,et al. Using free station linear angular intersection network in tunnel horizontal survey of high speed railway[j]. Journal of Southwest Jiaotong Uniwersity,2014,49(1): 1 7. [5],89:,% &,;. CPⅢ # 2 _% />[J]., 2011,46(3): LIU Chenglong,YANG Xuefeng,LU Jiankang,et al. Construction and adjustment method for CPⅢ trigonometric leveling network of high speed railway[j]. Journal of Southwest Jiaotong Uniwersity, 2011,46(3): [6] ',,% &,;. [ a CPⅢ />-.[J].,2010(11): FU Jianbin,LIU Chenglong,LU Jiankang,et al. Study on the CPⅢ vertical control network establishing method of high speed railway based on free station[j]. Journal of Railway Engineering Society,2010(11): [7],,,;. [ W_a CPI

7 1, :CPⅢ!"#$%&' 97 <= />-.[J]. RS, 2015(5): LIU Zhi,LIU Chenglong,CAO Chengdu,et al. New method of CPI control network repetition survey stability analysis based on multi tolerances[j]. Railway Investigation and Surveying,2015(5): [8],, (. ) CPⅢ / >-.2PE[J]. *MN,2013(8):72 75, 83. REN Xiaochun, ZHOU Dongwei. Research and application of CP Ⅲ plane network repetition surveying technique for high speed railway at operating and maintenance stage[j]. Railway Construction Technology,2013(8):72 75,83. [9]. CPⅢ _`_W_ a [J].,2010(10): XU Xiaozuo. Determination of divergence tolerance of elevation and altitude difference between adjoining points of high speed railway with CP Ⅲ network[j]. Journal of Railway Engineering Society,2010(10): [10],, (. F) CPⅢ /> -.2PE[J].,2013(2): RENG Xiaochun, ZHOU Dongwei. Research and application of method for retesting CPⅢ control network during operation and maintenance stages of high speed railway[j]. Journal of Railway Engineering Society,2013(2): [11] +,,,-.. c /[J]. 0,2015(6): LIU Sheng,LIU Chenglong,WANG Lipeng. Research on the reasonable accuracy specifications of re measuring the CPⅢ plane control network[j]. Engineering of Surveying and Mapping,2015(6): [12] 1,,,;. c -.[J]. *, 2013(4): PU Xinggang,LIU Chenglong,LIN Yuanhu,et al. Research on the rationality of the accuracy index of elevation control network based on track reference network[j]. Railway Engineering,2013 (4): [13],,1,;. c -.[J]. *, 2013(5): LIN Yuanhu,LIU Chenglong,PU Xinggang,et al. Research on the rationality of the accuracy index of plane network based on track reference network[j]. Railway Engineering,2013(5): [14],,2 3. CPⅢ />-.[J]. 0A,2011,36(1): LI Shuliang,LIU Chenglong,NI Xiantao. Study on the surverying method of CPⅢ vertical control network in high speed railway[j]. Science of Surveying and Mapping,2011,36(1): [15] PI4OO _ PO O c89. GB / T O Q; [S]. :PO, [16] :; 0 D _ A. K_c 2 _ [M]. :;::;,2003: ( (:) * + (:, -)

( 1 ) Show that P ( a, b + c ), Q ( b, c + a ) and R ( c, a + b ) are collinear.

Problems 01 - POINT Page 1 ( 1 ) Show that P ( a, b + c ), Q ( b, c + a ) and R ( c, a + b ) are collinear. ( ) Prove that the two lines joining the mid-points of the pairs of opposite sides and the line