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題名 利用不同目標函數之演算法進行粗差偵測之研究
The study of using different objective functions with algorithm in gross error detection作者 張宏嘉
Chang, Hung-Chia貢獻者 甯方璽
Ning, Fang-Shii
張宏嘉
Chang, Hung-Chia關鍵詞 粗差定位
最小一乘法
權迭代法
最佳化權矩陣
Gross error
LAD
OWM
Reverse weight matrix of LAD日期 2018 上傳時間 27-Aug-2018 14:56:28 (UTC+8) 摘要 在測量領域中，最小二乘法為最常被使用的平差方法，然而最小二乘法建立於觀測量僅含有偶然誤差的前提之下，當觀測量含有粗差時，最小二乘法的成果容易受到影響。因此，本研究透利用不同演算法對不同目標函數進行計算，並以統計檢定量分析各方法偵測粗差的能力。本研究所使用的方法分別為等權最小二乘法、權迭代法、最小一乘法及最佳化權矩陣。此外，本研究提出最小一乘法的反求權矩陣的概念，藉此解決最小一乘法缺乏統計檢定量的問題。並以權重、標準化殘差及多餘觀測分量分析各方法之成果。在模擬實驗中，當多餘觀測量較少時，最佳化權矩陣及最小一乘法的反求權矩陣具有較佳的粗差定位能力，並降低含有粗差的觀測量之權重；當觀測量越來越多時，則是權迭代法具有較佳的成果。在實測資料的部分，各方法之成果容易受到多餘觀測分量及後驗中誤差的影響，導致各方法皆無法順利定位粗差，而最佳化權矩陣及最小一乘法的反求權矩陣能夠使含有粗差的觀測量具有較大的標準化殘差，以利使用者後續對該觀測量優先進行檢核。
In the field of surveying, Least Square (LS) methods are often used in adjustment. However, LS built on observations usually show with random errors. If observations have gross errors, the solution of LS will be effected easily. So this study uses different objective functions to calculate with different algorithms, and analyzes the ability of gross errors detection with test statistic.The methods in this study are equal weight LS、Iteratively Reweighted LS (IRLS)、Least Absolute Deviation (LAD) and Optimal Weight Matrix (OWM). This study proposes a concept “inverse weight matrix of LAD” to solve the problem that LAD lacks test statistics. And assess the different methods’ results with weight value、 standardized residual and redundant observation component.In simulated data, when observations have less redundant observations, OWM and “inverse weight matrix of LAD” have better ability of gross error detection, and them make the gross errors have lower weight value. With more observations, the IRLS has better result. In real data, the posteriori variance will be effected easily, and lead to every methods can’t locate the gross error. However, OWM and “inverse weight matrix of LAD” can enlarge the standardized residual of gross errors and help user to check the observations.參考文獻 牛國軍、陳芳，2005，「抗差估計(IGGI方案)在粗差探測中的應用」，『西部探礦工程』，17(8)：64-66。王文峰，2006，「基于LINGO的最小一乘线性回归的参数估计」，『貴州財經學院學報』，2006(6)：106-108.劉文生、唐守路，2015，「稳健估计的两种粗差探测方法」，『辽宁工程技术大学学报 (自然科学版) 』，35(1)：54-58.李仲來，1992，「最小一乘法介紹」，『數學通報』，2：40-45。李德仁，1984，「利用選擇權迭代法進行粗差定位」，『武漢測繪學院學報』，9(1)：46-68。李德仁、袁修孝，2005，『誤差處理與可靠性理論』，第二版，武昌：武漢大學出版社。林老生、林怡君，2014，「基於最小一乘法的穩健地籍坐標轉換」，『中正嶺學報』，43(2)：199-218。林怡君，2013，「利用最小一乘法在地籍坐標轉換資料偵錯之研究」，國立政治大學地政學系研究所碩士論文：台北。郭信川、官佳慶，2000，「隨機搜尋法於多極值最佳化問題之應用」，『中國造船暨輪機工程師學刊』，19(4)：33-40。章棟恩、馬玉蘭、徐美萍，2008，『MATLAB 高等數學實驗』，北京：電子工業出版社。趙言、黎慕韓、王鵬、周磊，2016，「一次範數最小和選權反覆運算聯合的抗差法」，『大地測量與地球動力學』，36(4)：331-333。蔡名曜，2014，「運用曲面擬合提升幾何法大地起伏值精度之研究」，國立政治大學地政學系碩士論文：台北。謝開貴、宋乾坤、周家啟，2002，「最小一乘線性回歸模型研究」，『系統彷真學報』，14(2)：189-192。顏上堯、李旺蒼、施佑林，2007，「路徑基礎類粒子群最佳化演算法於求解含凹形節線成本最小成本轉運問題之研究」，『運輸計劃季刊』，36(3)：393-424。Argeseanu, V., 1986, “Three-Dimensional Adjustment of a Terrestrial Geodetic Network-A Collocation Solution”, Australian Journal of Geodesy, Photogrammetry and Surveying, 44： 1-37.Baarda, W., 1968, “A testing procedure for use in geodetic networks”, Netherlands Geodetic Commission, New Series, Delft, Netherlands, 2(5).Bektas, S. & Sisman, Y., 2010, “The comparison of L1 and L2-norm minimization methods”, International Journal of the Physical Sciences 5(11) 1721-1727.Boscovich, R. J., 1757, De litteraria expeditione per pontificiam ditionem, et synopsis amplioris operis, ac habentur plura ejus ex exemplaria etiam sensorum impressa. Bononiesi Scientiarum et Artum Instituto atque Academia Commentarii, 4： 353–396.Caspary & Borutta, 1987, Robust Estimation in Deformation Models. Survey Review 29(233), 29-46.Charnes, A., Cooper, W. W., & Ferguson, R. O., 1955, Optimal estimation of executive compensation by linear programming. Management science 1(2), 138-151.Hawkins, D. M., 1980, Identification of outliers., London： Chapman and Hall.Eberhart, R. C., & Shi, Y., 1998, “Comparison between genetic algorithms and particle swarm optimization”, Evolutionary Programming 7： 611- 616.FANG Yang, HE Wei, WANG Guang-xing, DU Yu-jun, LI Hui-mei., 2011, “Comparison and Analysis of Three Methods of Gross Error Detection”, Journal of Huaihai INstitute of Technology(Matural Sciences Edition), 1： 129- 131.Guo, J., 2014, "Analytical quality assessment of iteratively reweighted least-squares (IRLS) method.", Boletim de Ciências Geodésicas, 20(1)： 132-141.Hampel F.R., Ronchetti, E., Rousseeuw, P.J., and Stahel, W.A., 2011, Robust Statistics： The Approach Based on Influence Functions, New York： John Wiley and Sons.Huber P. J., 1981, Robust Statistics. New York： John Wiley and Sons.Kennedy, J., & Eberhart, R., 1997, “A discrete binary version of the particle swarm algorithm.”, IEEE International Conference 5, 4104-4108.K. Kubik, K. Lyons & D. Merchant, 1988, “Photogrammetric work without blunders.”, Photogramm. Eng. Remote Sensing, 54(1)： 51-54.Lehmann R., 2013, "3σ-Rule for Outlier Detection from the Viewpoint of Geodetic Adjustment.", Journal of Surveying Engineering, 139(4)： 157- 165.Lehmann R., 2013, “On theformulation of the alternative for geodetic outlier detection”, Journal of Geodesy, 87(4)： 373- 386Li Deren, 1984, " Gross Error Location by means of the Iteration Method with variable Weights.", Geomatics and inform ation science of wuhan univers, 9(1)： 46-68.Nobakhti, A., Wang, H., & Chai, T. (2009, June). Algorithm for very fast computation of Least Absolute Value regression. In American Control Conference, 2009. ACC`09, 14-19. IEEE.Robert G. Staudte, 1990, Robust Estimation and Testing, New York： John Wiley and Sons.Schaffrin, 1985, “On Robust Collocation.”, In Proc 1st Marussi Symp Math Geod, Milano, 343- 361.Schwarz C. R., Kok J. J., 1993, “Blunder detection and data snooping in LS and robust adjustment.”, Journal of Surveying Engineering, 119(4), 128- 136.Shi, Y., & Eberhart, R. (1998, May). A modified particle swarm optimizer. In Evolutionary Computation Proceedings, 1998. IEEE World Congress on Computational Intelligence., The 1998 IEEE International Conference on (pp. 69-73). IEEE.Sun, J., Feng, B., & Xu, W. (2004, June). Particle swarm optimization with particles having quantum behavior. In Evolutionary Computation, 2004. CEC2004. Congress on 1： 325-331. IEEE.Yang, Y., 1992, “Robustifying collocation.”, Manuscr Geod, 17(1), 21-28.Gao, Y., Krakiwsky, E. J., & Czompo, J., 1992, “Robust testing procedure for detection of multiple blunders.”, Journal of Surveying Engineering, 118(1)： 11-23. 描述 碩士
國立政治大學
地政學系
105257032資料來源 http://thesis.lib.nccu.edu.tw/record/#G0105257032 資料類型 thesis dc.contributor.advisor 甯方璽 zh_TW dc.contributor.advisor Ning, Fang-Shii en_US dc.contributor.author (Authors) 張宏嘉 zh_TW dc.contributor.author (Authors) Chang, Hung-Chia en_US dc.creator (作者) 張宏嘉 zh_TW dc.creator (作者) Chang, Hung-Chia en_US dc.date (日期) 2018 en_US dc.date.accessioned 27-Aug-2018 14:56:28 (UTC+8) - dc.date.available 27-Aug-2018 14:56:28 (UTC+8) - dc.date.issued (上傳時間) 27-Aug-2018 14:56:28 (UTC+8) - dc.identifier (Other Identifiers) G0105257032 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/119593 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 地政學系 zh_TW dc.description (描述) 105257032 zh_TW dc.description.abstract (摘要) 在測量領域中，最小二乘法為最常被使用的平差方法，然而最小二乘法建立於觀測量僅含有偶然誤差的前提之下，當觀測量含有粗差時，最小二乘法的成果容易受到影響。因此，本研究透利用不同演算法對不同目標函數進行計算，並以統計檢定量分析各方法偵測粗差的能力。本研究所使用的方法分別為等權最小二乘法、權迭代法、最小一乘法及最佳化權矩陣。此外，本研究提出最小一乘法的反求權矩陣的概念，藉此解決最小一乘法缺乏統計檢定量的問題。並以權重、標準化殘差及多餘觀測分量分析各方法之成果。在模擬實驗中，當多餘觀測量較少時，最佳化權矩陣及最小一乘法的反求權矩陣具有較佳的粗差定位能力，並降低含有粗差的觀測量之權重；當觀測量越來越多時，則是權迭代法具有較佳的成果。在實測資料的部分，各方法之成果容易受到多餘觀測分量及後驗中誤差的影響，導致各方法皆無法順利定位粗差，而最佳化權矩陣及最小一乘法的反求權矩陣能夠使含有粗差的觀測量具有較大的標準化殘差，以利使用者後續對該觀測量優先進行檢核。 zh_TW dc.description.abstract (摘要) In the field of surveying, Least Square (LS) methods are often used in adjustment. However, LS built on observations usually show with random errors. If observations have gross errors, the solution of LS will be effected easily. So this study uses different objective functions to calculate with different algorithms, and analyzes the ability of gross errors detection with test statistic.The methods in this study are equal weight LS、Iteratively Reweighted LS (IRLS)、Least Absolute Deviation (LAD) and Optimal Weight Matrix (OWM). This study proposes a concept “inverse weight matrix of LAD” to solve the problem that LAD lacks test statistics. And assess the different methods’ results with weight value、 standardized residual and redundant observation component.In simulated data, when observations have less redundant observations, OWM and “inverse weight matrix of LAD” have better ability of gross error detection, and them make the gross errors have lower weight value. With more observations, the IRLS has better result. In real data, the posteriori variance will be effected easily, and lead to every methods can’t locate the gross error. However, OWM and “inverse weight matrix of LAD” can enlarge the standardized residual of gross errors and help user to check the observations. en_US dc.description.tableofcontents 第一章 緒論 1第一節 研究背景與動機 1第二節 研究目的 3第三節 論文架構 4第二章 文獻回顧 5第一節 粗差對最小二乘法的影響 5第二節 單一粗差的偵錯方法 6第三節 多個粗差時的偵測方法 9第四節 最佳化演算法與最佳化權矩陣 12第五節 最小一乘法 14第三章 研究方法與理論基礎 16第一節 最小二乘法 16第二節 李德仁權迭代法 18第三節 最佳化權矩陣 19第四節 最小一乘法 26第五節 評估模式 31第六節 模擬資料設計 36第七節 實測測資料 38第四章 實驗成果與分析 43第一節 模擬資料 43第二節 實測資料 73第五章 結論與建議 95第一節 結論 95第二節 建議 96參考文獻 97 zh_TW dc.format.extent 3620059 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0105257032 en_US dc.subject (關鍵詞) 粗差定位 zh_TW dc.subject (關鍵詞) 最小一乘法 zh_TW dc.subject (關鍵詞) 權迭代法 zh_TW dc.subject (關鍵詞) 最佳化權矩陣 zh_TW dc.subject (關鍵詞) Gross error en_US dc.subject (關鍵詞) LAD en_US dc.subject (關鍵詞) OWM en_US dc.subject (關鍵詞) Reverse weight matrix of LAD en_US dc.title (題名) 利用不同目標函數之演算法進行粗差偵測之研究 zh_TW dc.title (題名) The study of using different objective functions with algorithm in gross error detection en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) 牛國軍、陳芳，2005，「抗差估計(IGGI方案)在粗差探測中的應用」，『西部探礦工程』，17(8)：64-66。王文峰，2006，「基于LINGO的最小一乘线性回归的参数估计」，『貴州財經學院學報』，2006(6)：106-108.劉文生、唐守路，2015，「稳健估计的两种粗差探测方法」，『辽宁工程技术大学学报 (自然科学版) 』，35(1)：54-58.李仲來，1992，「最小一乘法介紹」，『數學通報』，2：40-45。李德仁，1984，「利用選擇權迭代法進行粗差定位」，『武漢測繪學院學報』，9(1)：46-68。李德仁、袁修孝，2005，『誤差處理與可靠性理論』，第二版，武昌：武漢大學出版社。林老生、林怡君，2014，「基於最小一乘法的穩健地籍坐標轉換」，『中正嶺學報』，43(2)：199-218。林怡君，2013，「利用最小一乘法在地籍坐標轉換資料偵錯之研究」，國立政治大學地政學系研究所碩士論文：台北。郭信川、官佳慶，2000，「隨機搜尋法於多極值最佳化問題之應用」，『中國造船暨輪機工程師學刊』，19(4)：33-40。章棟恩、馬玉蘭、徐美萍，2008，『MATLAB 高等數學實驗』，北京：電子工業出版社。趙言、黎慕韓、王鵬、周磊，2016，「一次範數最小和選權反覆運算聯合的抗差法」，『大地測量與地球動力學』，36(4)：331-333。蔡名曜，2014，「運用曲面擬合提升幾何法大地起伏值精度之研究」，國立政治大學地政學系碩士論文：台北。謝開貴、宋乾坤、周家啟，2002，「最小一乘線性回歸模型研究」，『系統彷真學報』，14(2)：189-192。顏上堯、李旺蒼、施佑林，2007，「路徑基礎類粒子群最佳化演算法於求解含凹形節線成本最小成本轉運問題之研究」，『運輸計劃季刊』，36(3)：393-424。Argeseanu, V., 1986, “Three-Dimensional Adjustment of a Terrestrial Geodetic Network-A Collocation Solution”, Australian Journal of Geodesy, Photogrammetry and Surveying, 44： 1-37.Baarda, W., 1968, “A testing procedure for use in geodetic networks”, Netherlands Geodetic Commission, New Series, Delft, Netherlands, 2(5).Bektas, S. & Sisman, Y., 2010, “The comparison of L1 and L2-norm minimization methods”, International Journal of the Physical Sciences 5(11) 1721-1727.Boscovich, R. J., 1757, De litteraria expeditione per pontificiam ditionem, et synopsis amplioris operis, ac habentur plura ejus ex exemplaria etiam sensorum impressa. Bononiesi Scientiarum et Artum Instituto atque Academia Commentarii, 4： 353–396.Caspary & Borutta, 1987, Robust Estimation in Deformation Models. Survey Review 29(233), 29-46.Charnes, A., Cooper, W. W., & Ferguson, R. O., 1955, Optimal estimation of executive compensation by linear programming. Management science 1(2), 138-151.Hawkins, D. M., 1980, Identification of outliers., London： Chapman and Hall.Eberhart, R. C., & Shi, Y., 1998, “Comparison between genetic algorithms and particle swarm optimization”, Evolutionary Programming 7： 611- 616.FANG Yang, HE Wei, WANG Guang-xing, DU Yu-jun, LI Hui-mei., 2011, “Comparison and Analysis of Three Methods of Gross Error Detection”, Journal of Huaihai INstitute of Technology(Matural Sciences Edition), 1： 129- 131.Guo, J., 2014, "Analytical quality assessment of iteratively reweighted least-squares (IRLS) method.", Boletim de Ciências Geodésicas, 20(1)： 132-141.Hampel F.R., Ronchetti, E., Rousseeuw, P.J., and Stahel, W.A., 2011, Robust Statistics： The Approach Based on Influence Functions, New York： John Wiley and Sons.Huber P. J., 1981, Robust Statistics. New York： John Wiley and Sons.Kennedy, J., & Eberhart, R., 1997, “A discrete binary version of the particle swarm algorithm.”, IEEE International Conference 5, 4104-4108.K. Kubik, K. Lyons & D. Merchant, 1988, “Photogrammetric work without blunders.”, Photogramm. Eng. Remote Sensing, 54(1)： 51-54.Lehmann R., 2013, "3σ-Rule for Outlier Detection from the Viewpoint of Geodetic Adjustment.", Journal of Surveying Engineering, 139(4)： 157- 165.Lehmann R., 2013, “On theformulation of the alternative for geodetic outlier detection”, Journal of Geodesy, 87(4)： 373- 386Li Deren, 1984, " Gross Error Location by means of the Iteration Method with variable Weights.", Geomatics and inform ation science of wuhan univers, 9(1)： 46-68.Nobakhti, A., Wang, H., & Chai, T. (2009, June). Algorithm for very fast computation of Least Absolute Value regression. In American Control Conference, 2009. ACC`09, 14-19. IEEE.Robert G. Staudte, 1990, Robust Estimation and Testing, New York： John Wiley and Sons.Schaffrin, 1985, “On Robust Collocation.”, In Proc 1st Marussi Symp Math Geod, Milano, 343- 361.Schwarz C. R., Kok J. J., 1993, “Blunder detection and data snooping in LS and robust adjustment.”, Journal of Surveying Engineering, 119(4), 128- 136.Shi, Y., & Eberhart, R. (1998, May). A modified particle swarm optimizer. In Evolutionary Computation Proceedings, 1998. IEEE World Congress on Computational Intelligence., The 1998 IEEE International Conference on (pp. 69-73). IEEE.Sun, J., Feng, B., & Xu, W. (2004, June). Particle swarm optimization with particles having quantum behavior. In Evolutionary Computation, 2004. CEC2004. Congress on 1： 325-331. IEEE.Yang, Y., 1992, “Robustifying collocation.”, Manuscr Geod, 17(1), 21-28.Gao, Y., Krakiwsky, E. J., & Czompo, J., 1992, “Robust testing procedure for detection of multiple blunders.”, Journal of Surveying Engineering, 118(1)： 11-23. zh_TW dc.identifier.doi (DOI) 10.6814/THE.NCCU.LE.016.2018.A05 -
