虛擬測量儀器之誤差模擬

Error Modeling for Virtual Survey Instruments

許睿(Ruei-Shiue Shiu)

指導教授 ： 康仕仲

國立臺灣大學/工學院/土木工程學研究所/碩士(2008年)

https://doi.org/10.6342/NTU.2008.02789

摘要

隨著科技的進步與教學的多元化，利用資訊科技來來提供先進的教學訓練( Noéh，1999；Ghilani，2000；Muench，2006 )已十分普遍。在測量教學訓練上，Bai (2007), Lu (2007) and Yeh (2005)也使用了資訊科技來提高學習測量原理及實作的成效。Yeh(2006)及Kuo等人(2007)也實證使用產生的虛擬測量輔助訓練程式不只減少實體儀器的管理修繕成本，同時也提高在課堂上教師教授與同學學習的效率。
經過評估後發現，虛擬測量儀器之儀器誤差是輔助測量訓練上的一個重點。在測量教學訓練中，使用正確的方法消除這些誤差的原理及步驟對學生來說經常是一個抽象且困難的議題，對老師來說，更是一個難以簡化描述部份。
本研究使用齊次座標轉換矩陣(Homogeneous Transformation Matrices)來模擬儀器誤差，並提供一個建置儀器誤差進入虛擬環境中的構架。這些儀器誤差都是參考真實世界的儀器之物理行為，誤差來源主要一些儀器的缺陷，本研究主要建立七個儀器誤差：(1)水準軸不平行於水平方向(地球表面)；(2)直立軸不垂直於水平軸；(3)橫軸不垂直直立軸；(4)視準軸不垂直橫軸； (5)垂直度盤零度方向不在正上方；(6)橫軸不通過垂直度盤中心；以及(7)直立軸不通過水平度盤中心。本研究亦考慮腳架引起的定心、定平之儀器誤差及測距引起之距離測量誤差來模擬整個儀器從已知參考點位到欲觀測之未知點位之間的儀器誤差。
本研究轉換其中非讀數顯示問題之些物理行為成為齊次座標轉換矩陣並將其建置成為虛擬測量儀器SimuSurvey(Lu，2007)的一部份。並用該測量輔助軟體設計任務來驗證評估其正確性，評估結果顯示未使用SimuSurvey的前測與使用SimuSurvey後的後測結果有顯著的提升(t(9)=-11,p<0.01)，證明學生可透過具有誤差模組的SimuSurvey來了解儀器誤差之行為，並透過讀數來練習使用特定方法消除誤儀誤差。

關鍵字

測量 ； 儀器誤差 ； 工程教育 ； 模擬 ； 虛擬實境

並列摘要

The minimization and elimination of errors caused by instrumental imperfections is an important topic in survey education. Students need to learn the theories and correct procedures to compensate the errors by manipulating the instrument properly. However, to understand the theories behind the error causes requires understanding complicated spatial relationship between the parts of the instruments and the survey targets. In addition, the instrumental errors often result from the combination of imperfections in different part of the instrument. Traditional teaching methods, lack of interactive and three-dimensional illustrations, may not support the teaching activities. Students often encounter difficulties to clearly understand the reasons behind the tedious survey procedures used to eliminate errors.
In this research, I would like to simulate and visualize the causes of the errors on computers by which the students can learn and practice the survey instrument more effectively. I particularly modeled the errors by using homogeneous transformation matrices, a format which can facilitate the implementation on computers. Ten kinds of instrumental errors were included in the virtual instruments. They are caused by the imperfections in (1) the plate level axis; (2) the vertical axis; (3) the tilting axis; (4) the sighting axis; (5) the vertical circle index; (6) tripod centering; (7) tripod leveling; (8) distance measurement; (9) eccentricity of the vertical circle; and (10) eccentricity of the horizontal circle.
The error models were implemented as a module and integrated with SimuSurvey, a computer-aided instruction tool for surveying training developed previously. A user test was conducted to verify the effectiveness of using teaching-aid in surveying training. Ten students, who were taking surveying course, were involved in the test. A pretest was conducted as a base line to identify their understanding about the instrumental errors. After a sixty-minute learning section by using SimuSurvey (with error module), we conducted a posttest. The correctness rate in the pretest is 34% and the one in the pretest is 77%. By using t test analysis, we also find that posttest is significantly better than the pretest (t(9) = -11, p < 0.01). This result indicates that error module is an effective method for assisting the surveying training.

並列關鍵字

survey ； instrumental errors ； engineering education ； simulation ； virtual reality

參考文獻

Daniel, V. A. (1994). Homogeneous Transformation Matrices for Computer Graphics, Computers & Graphics, vol. 18, no. 2, pp. 177-191.

Kuo, H. L., Kang, S. C., Lu, C. C., Hsieh, S. H. and Lin, Y. H. (2007). "Using Virtual Instruments to Teach Surveying Courses: Application and Assessment," Computer Applications in Engineering Education.

Kuo, H.L., Kang, S.C. and Lu, C. C. (2007). "The Feasibility Study of Using A Virtual Survey instrument in Surveyor Training," International Conference on Engineering Education ICEE 2007, Coimbra, Portugal, September 3-7.

Lu, C. C., Kang, S. C. and Hsieh, S. H. (2007). "SimuSurvey: A Computer-based Simulator for Survey Training," The 2007 W78 Conference, Maribor, Slovenia.

Lu, C. C., Kang, S. C., Hsieh, S. H. and Shiu, R. S. (2008). "Improvement of a Computer-Based Surveyor-training Tool Using a User-centered Approach," Advanced Engineering Informatics.