Analysis on deformation of partial control network of particle accelerator
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摘要: 基于泰勒展开的方法实现局部控制网的拟合，使用卡方检验判断局部控制网中是否存在形变点。若存在形变点，则在选权迭代的过程中找到局部控制网中所有的形变点，并将卡方检验通过作为迭代终止条件。对哈尔滨工业大学空间地面模拟装置2号终端控制网的两期观测成果进行了分析，实验表明，将卡方检验和选权迭代法加入控制网拟合之后，可以很好地探测出局部控制网中的形变点。在找出所有形变点之后，可以求得更为准确的局部控制网拟合参数。Abstract: The fitting of the local control network is realized based on the method of Taylor expansion, and the chi-square test is used to judge whether there is a deformation point in the local control network. If there are deformation points, find all the deformation points in the local control network in the process of weight selection iteration, repeat the above process until the chi-square test passes. The two-phase observation results of the Harbin Institute of Technology Space Environment Simulation and Research Infrastructure (SESRI) No.2 terminal control network are analyzed. The experiments show that after adding the chi-square test and the weight selection iteration method to the control network fitting, the deformation points in the local control network can be well detected. After finding all the deformation points, more accurate local control network fitting parameters can be obtained.
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图 1 三维坐标系变换示意图
Figure 1. Schematic diagram of three-dimensional coordinate system transformation
图 3 初次平差后各点残差和权
Figure 3. Residuals and weights of each point after the initial adjustment
图 4 二次平差后各点残差与权
Figure 4. Residuals and weights of each point after the second adjustment
表 1 模拟计算
Table 1. Simulation calculation
calculations translation factor/mm rotation factor/(°) factor number of iterations ΔX ΔY ΔZ α β γ k 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 2 5 5 5 5 5 5 1.002 947 5 5 5 5 4.999 999 5 1.002 3 10 10 10 10 10 10 1.001 1005 10 10 10 10 9.999 999 10 1.001 4 20 20 20 20 20 20 0.999 1085 20 20 20 20 20 20 0.999 5 40 40 40 40 40 40 0.998 1521 40 40 39.999 999 40 40 40 0.998 6 60 60 60 60 60 60 0.997 1068 60 60 60 59.999 999 60 60 0.997 
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表 2 SESRI实验终端2的两期观测值
Table 2. Two-phase observations of SESRI Experimental Terminal 2
point the first phase (2021.4) the second phase (2021.6) X/mm Y/mm Z/mm X/mm Y/mm Z/mm L55 −5092.17 879.62 14895.65 6286.72 −15526.63 821.79 L57 −2 261.04 879.28 17717.09 2815.70 −17509.32 822.15 L59 −3120.62 879.22 21412.56 −520.04 −15701.26 822.40 L60 −4107.95 −821.72 24779.41 −3505.58 −13857.21 −878.36 L61 −4107.01 877.20 24777.54 −3503.76 −13858.44 820.70 L62 −4074.18 −817.67 27037.53 −5692.02 −13291.53 −874.05 L63 −4077.77 876.91 27033.99 −5687.46 −13288.83 820.64 L64 −6897.19 −773.87 29870.60 −7676.14 −9818.57 −830.23 L65 −6897.30 880.72 29867.91 −7673.23 −9819.01 824.42 L67 −9746.56 894.02 32716.15 −9665.07 −6316.66 837.73 L68 −13217.29 −822.38 31985.43 −8041.08 −3163.51 −879.28 L69 −13215.11 879.59 31991.11 −8046.88 −3164.01 822.76 L70 −16050.40 −820.92 29166.76 −4572.37 −1178.27 −878.59 L71 −16047.74 874.53 29165.73 −4571.81 −1180.86 816.96 L72 −18878.70 −809.52 26339.60 −1096.73 800.14 −867.90 L73 −18879.30 879.65 26340.53 −1097.19 801.22 821.38 L74 −21711.32 −841.15 23519.47 2373.33 2784.62 −900.23 L75 −21710.28 846.76 23519.11 2373.62 2783.72 787.79 L76 −23062.45 −815.86 20935.80 5222.75 3403.02 −875.45 L77 −23061.11 882.09 20947.33 5211.70 3405.02 822.63 L78 −22368.90 −818.96 19093.13 6816.01 2245.99 −878.70 L79 −22309.74 883.25 19037.43 6854.43 2174.44 823.70 L80 −19511.28 −781.72 16233.69 8816.34 −1267.34 −841.25 L81 −19509.35 875.00 16238.17 8811.89 −1267.75 815.53 L82 −16684.40 −808.82 13405.92 10794.26 −4742.76 −868.25 L83 −16690.55 881.77 13407.80 10794.50 −4735.99 822.43
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表 3 两种方法求得的拟合参数
Table 3. Fitting parameters obtained by two methods
calculation translation factor/mm rotation factor/(°) factor ΔX ΔY ΔZ α β γ k SA −18 397.56 58.4 25 070.31 89.974 03 74.637 72 179.9675 0.999 926 this article −18 397.55 58.40 25 070.31 89.9743 74.637 71 179.967 8 0.999 926 difference 0.009 4 −0.001 5 0.000 3 0.00027 −0.000 01 0.000 234 −0.000 000 4
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