A RESEARCH ON DATA PROCESSING MODEL OF GPS DAMDEFORMATION MONITORING NETWORKAbstract: Considering the particularity of the GPS dam deformation monitoring network, a data processing model based on the station orthogonal coordinate system for three-dimension GPS dam deformation monitoring network, was put forward. Also, a mathematical model of using the clustering analysis method in fuzzy mathematics to test the relative stability of quasi-stable points(or datum marks) was successfully brought forward. The adjustment method during the course of data processing was quasi-stable adjustment. At last, a software system of three-dimension GPS dam deformation monitoring network was designed and opened up with the help of Visual Basic Language. With three periods o'bservation data from the GPS deformation monitoring network of a dam, an adjustment calculation was done by the software.The calculation result shows that the mathematical models can be more suitable for the data processing in GPS dam deformation monitoring network.Key words: GPS, Dam deformation monitoring, Quasi-stable adjustment, Clustering analysis 1.IntroductionWGS-84 coordinate system is generally used in GPS. But local or independent coordinate systems are usually chosen in dam deformation monitoring networks for their small areas. During the course of past data processing, the adjustment under WGS-84 coordinate system forindependent networks or networks with several fixed points is often firstly made. Then, the transformation from WGS-84 coordinate system tolocal(or independent) coordinate systems is done. For GPS deformation monitoring networks with repetitive observation data, the obvious change of datum marks coordinates under the two different coordinate systems can be brought by the tiny deformation of datum marks among different periods of observation. And the greater error can be made during the coordinate transformation. If a local Gauss coordinate system is chosen, the projection distortions can also be produced by the transformation itself. For the reasons above, the station orthogonal coordinate system is chosen as the reference coordinate system for data processing of GPS dam deformation networks. And the mathematical model is put forward and deduced.2.Data processing model based on the station orthogonal coordinate system for three-dimension GPS deformation monitoring networks2.1 Coordinate systemThe station orthogonal coordinate system is a left-hand coordinate system. Its origin is set at one of the GPS monitoring points. The E(X) axis points at the meridian passing the origin. It is on the tangent plane of the origin. And the right north is taken as forward direction. The H(Z) axis is on thenormal line of WGS-84 ellipsoid at the point and takes outward as forward directi on . The E(Y) axis is also on the tangent pla ne of the origi n and uses east for forward directi on.If the positi on vector of the stati on orthogo nal coord in ate system origi nr TP o in WGS-84 is expressed as o 二X0 Y 0 Z o , according to the geodetic latitude and Iongitude ( B° , L。

) ' the position vector 门in the statio n orthogo nal coord in ate system origi n of a ran dom poi nt p i can be got through the translation and rotation of its WGS-84 positionTvector r i「i =H (「i-ro) ( 1)In the above equation, H can be written as-sin B o C os L o -sin B o sin L。

cos B oH= si n B o cos L o o (2)cos B o cos L o cos B o sin L。

sin B。

一If the baseli ne vectors of the two ran dom poi ntsp i an d p j in WGS-84 coord in ate system and the the stati on orthogo nal coord in ate system are writte n as" 1 1川' '1 1 1respectively, the expressi on can be easily gained as followsAr tf= r/-r i= H(r - r0)-H(r -r0) = H(r' -rjThe n, the relatio n equatio n betwee n the two baseli ne vectors is expressed Ar = HArasThere are two steps in the GPS observati on data process ing course. They are baseli ne calculati on and n etwork adjustme nt. The baseli ne vectors in WGS-84 can be firstly got using baseline calculation. Secondly, the baseline vector transformation from WGS-84 to the station orthogonal coordinate system can be done with (3). At last, the adjustment of GPS deformation monitoring networks in the station orthogonal coordinate system can be successfully finished.2.2 Adjustment method and mathematical modelDeformation monitoring networks usually require higher precision. And if several fixed points are adopted for datum, the observation precision can be greatly reduced, because the known dataprecision is o'fte s n lower than the required precision and the beginning points ' displacement ca make annexe effect to observation data especially during the course of repetitive observation. So the classical adjustment method, which has some given points, is generally not used. But it is important to choose the reference points with stable physical status as datum of deformation monitoring networks. Considering the above two cases, the quasi-stable adjustment can be employed to make the more stable unknown data( the coordinates of relatively stable points away from the dam) match their stable values. Then, there are no distortion of surveying result and relatively stable datum. And the goal to monitor the deformation can be reached well. The adjustment model of GPS rank-deficient networks can be written asV=AX-LT. , (4)S(L)二阮piWith the least square method, the normal equation is expressed asNX二W (5)T Twhere N equals A PA and W equals A PLAnd the equati on can be got as followsR(N)=R(A)=r where A denotes the rank-deficient matrix whose rank-deficient number d is (n-r)」f S is a set of radical of zero space N(A) and R(S) deno tes d, the equation is written asAS=0 (6)When the inner product space is defined as (X,Y)=X T RY and R(R) >d, under the constraint condition X RX=min, the following equation can be gotS T RX=0 (7)With (5) and (7), the solution equation of weighting rank-deficientn etworks can be expressed asQ 亠-Q H RSVRQ^I XXWhere Q R de notes"、R*% H.When R is a diagonal matrix and its value is 1 or 0, (8) canbecome the model of quasi-stable adjustme nt. The S matrix can be give naccording to the condition AS=0. And the S matrix of GPS 3-dimensional deformati on mon itori ng n etworks is writte n as10 0 loo 1 o o-s z = 0)0010 ……oio ⑼ooi ooi o o 12.3 Mathematical model of calculat ing quasistable poi nts ' relative stability with clusteri ng an alysis For GPS dam deformati on mon itori ng n etworks, the stability of datum marks must be firstly tested in the observati on data process ing. Though the relatively stable area is chose n for build ing datum marks whe n GPS dam deformati on mon itori ng n etworks are desig ned, the deformatio n of datum marks can come into being. Eve n if the quasi-stable adjustme nt method is used, the stability test n eeds to be made, too. The quasi-stable poin ts(quasi-stable points or datum marks in desig n scheme) with marked deformati on should be elim in ated. The mathematical model of calculati ng quasi-stable poin ts(or datum marks) relative stability with clustering analysis in fuzzy mathematics is put forward to en sure the stable quasi-stable points(or datum marks) in GPS observation data processing. One characteristic of quasi-stable adjustme nt is that the correcti on value V of observati on data after adjustme nt is in variable. So the adjusted value L of observati on data is also in variable. And it is show n that the n etwork shape after adjustme nt is un cha nged. The observati on data of GPS n etworks adjustme nt is baseli ne vectors(coord in ate differe nces in 3 coord in ate axis directi on s).Then, after the quasi-stable adjustme nt of two periods of observati on data,the differe nces of coord in ate differe nces of two ran dom quasi-stable poi nts in 3coord in ate axis directi ons betwee n the two periods areinvariable. So, these values can ' t be changed with differces .cAod work can be finished once for ado toavoid the trouble of some methods calculat ing step by step.匸 an df denote the coord in ate differe nces of two ran dom quasi-stable points (i and j)aftertwo periods ' seobati on1 data adjustme nt. is the differe nee of coord in ate differe nces betwee ntwo periods. And equati ons are as follows n叭+碍 Statistic is written as=— ⑴) %1 If the change of l ij between two periods is caused by the accidental error of GPS observati on, it is expressed as心 ~ MO,1)The fuzzy membership grade of the relative stability of the two ran domquasi-stable points (i and j) is defi ned as(12)That is to say, the fuzzy relation of the relative stability of quasi-stable points is theprobability densityvalue of standard normal distribution about^ .To 口，it can be defined asu =0 for supplement. It is also as follows(io )==口 =于(叫) (13)And the fuzzy relation of relative stability of quasi-stable points defined by (12) and (13) only satisfiesthe symmetry of equivale nee fuzzy relatio n. The reflexivity can besta ndardized. And 「「is re-defi ned as=/(0)The fuzzy relati on R has met the first two con diti ons of fuzzy equivale neerelation. Then R is a fuzzy similar matrix. To transitivity, the fuzzysimilar matrix can be cha nged to a fuzzy equivale nee matrix with the help of the tran sitive closed package t(R). And the fuzzy an alysis can be done.The sorted index parameter 入 of clustering analysis is computed with thestatistic hypothesis method .If the cha nge of betwee n two periods is caused by the accide ntal error of GPS observatio n, it is expressed asFor the given conspicuous level a , there is a c K ticaWfitHue 一,the corresponding valu. can be got from (14). And 「is the sortedstability. Tab.1 below shows the values ofa and 入Obviously should be changed in the practice. It is concluded that alarger a shouldhosen according to the operation rule in clustering analysis. And it canbe recommended that and 入 should use 5 %and 0 .1465respectively. 3.A computation example and result analysis The computation example was chosen from the GPS(14) in dex parameter 入 of clustering analysisepfasi-stable points relativedeformation monitoring network of some rock and soil gravity dam. There were 3 periods of observation data in total. The observation dates were Mar.4 to 7, Jun. 4 to 11, and Aug.31 to Sept.4 in 2001. There were 75 GPS monitoring points in this network. And 6 of the total were in the relatively stable area of the lower river of the dam. The other 69 points were at the dam body. All the monitoring points were built on observation piers and had compulsive centering equipment. And all the observation was finished by 6 Ashtech Z-Surveyor dual-frequency receivers. The periods of all the points were more than an hour. The baseline solution of GPS observation data was gained by the Ashtech associated software Solution 2.5. For every period, everyday observation data was processed singly. The periods of time with bad signals were first eliminated. If they were still not eligible, the observation data was deleted. Then, with everyday qualified baselines, the network adjustment was prepared. The baseline solution precision is listed in Tab.1.6 monitoring points in the relatively stable area of dam lower river banks were used as fixed in itial datum. And the adjustme nt with fixed poi nts was done. With the adjustme nt result being an alyzed, it was show n that the displacement among 6 initial points could reach about 2~3mm. And the monitoring points ' precision after the adjustment with 6 fixed points was 1~2 times larger tha n the precisi on using quasi-stable adjustme nt. The result also explained the displacement of initial points. Because fixed initial datum could react on observation data for compulsive fixing, the precisi on was bad. In order to test the stability of quasi-stable poin ts, the mathematical model of clusteri ng an alysis method was employed. It was found that the quasi-stable point KL3 in Y directi on was obviously differe nt from the other 5 points whe n the sec ond period of observatio n was compared with the first.And KL3 in Y and Z directions was distinctly differe nt from the others whe n the third was compared with the first.Then, KL3 was eliminated after integrating the clustering analysis result of the seco nd and the third periods. At last, KL1 KL2、KL7、KR1 and KR3 were take n as quasi-stable poin ts. Because there was no quasi-stable adjustme nt fun cti on in GPS associated software of GPS manu facturersdesig ned for GPS deformati on mon itori ng n etworks using VB programming Ianguage. It had the function of quasi-stable adjustment in the stati on orthog onal coord in ate system. With it, the three periods of observati on data were processed. Because there were too many points, on ly the adjusted 3-dime nsional coord in ate syn thetical precisi on in the stati on orthog onal coord in ate system was listed in Tab.2 below.It is show n in Tab.2 that the mea n square error(MSE) of pla ne coord in ates can reach 1 millimeter and the MSE of vertical coord in ates can reach 2 millimeters. And the precisi on can satisfy the comma nd of dam deformatio n mon itori ng en tirely.4. Con clusi onsThe stati on orthog onal coord in ate system is more suitable for the refere nee coord in ate system of GPS dam deformati on mon itori ng n etworks. The quasi-stable adjustme nt method is more suitable for the data process ing of GPS dam deformati on mon itori ng n etworks. The mathematical model of calculati ng quasistable poi nts ' relative stability with clustering analysis can be used for the stability analysis of fixed in itial datum marks in GPS deformati on mon itori ng n etworks and datum marks in n ormal deformatio n mon itori ng n etworks as settleme nt monitoringnetworks or survey triangulation andtrilateration networks. And the correctness and feasibility of the advanced model have been proved with a computation example.。