THE STUDY OF DETECTING OUTLIER BY OPTIMAL WEIGHT MATRIX

利用最佳化權矩陣進行偵錯之研究

10.6652/JoCICHE.201910_31(6).0004

甯方璽(Fang-Shii Ning)；張宏嘉(Hung-Chia Chang)

outlier detection ； Optimal Weight Matrix ； particle swarm optimization algorithm ； 偵錯 ； 最佳化權矩陣 ； 粒子群最佳化演算法

中國土木水利工程學刊

31卷6期（2019 / 10 / 01）

553 - 568

英文

The traditional way of surveying adjustment is using the least square adjustment, random error, the result of surveying and it will be reasonably allocated. However, because of the ability of error, the allocating is perfect. Therefore, the parameter estimated by the least square adjustment is highly affected by an unknown outlier. Thus the process to locate and exclude the outlier is a great deal to do. Generally speaking, the observations with bigger residuals are not always the outlier, we have to judge them by the more effective test statistic. This is through Baarda's data snooping method when the observations only have one outlier, they can be easily identified. Nevertheless, when the observations have multiple outliers, there is a high probability that the data snooping method will misjudge. In recent years, the technique of the optimal algorithm is getting more developed and it is more convenient to calculate the math problems which were difficult to solve in the past. The particle swarm optimization algorithm's advantage is to calculate correctly in a high speed and is one of the optimal algorithms. In this study, we tried to use the particle swarm optimization algorithm; this was under the presumption of the minimized sum of absolute value of the target function's standardized residual. This was also to find the most appropriate weight of every observation. Thereby creating an optimal weight matrix: to calculate every observation's standardized residual by the weight of the matrix, and use it to identify multiple outliers. The result of the experiment showed, that the optimal weight matrix calculated by the algorithm was surely successful in lowering the weight of the outlier and located it.

傳統的測量調整方法是採用最小平方法進行觀測量平差，經處理後由成果中可見合理的配置及定位出隨機誤差。然而，由於偵錯能力及完美的誤差分配，在最小平方法平差之估計參數受到未知異常值的影響度高。因此，定位出及排除異常值的過程是在平差過程中是很重要的課題。一般來說，殘差較大的觀測結果並不總是異常值，我們必須用更有效的測試統計來判斷它們。當觀測量中只有一個異常值時通過Baarda's data snooping的方法可以很容易地辨識它們。然而，當觀測量中具有多個異常值時，很有可能會誤判。近年來，優化演算法技術越來越發展，能更加容易的計算出過去難以解決的數學問題。粒子群演算法為快速正確之演算法之一，本研究使用粒子群演算法,以目標函數標準化殘差絕對值絕對值為最小的假設下進行每個觀測量之權重計算，從而創建一個最佳化的權矩陣，然後利用這矩陣的權重計算每個觀測的標準化殘差,並使用它進行異常值定位。由本研究成果顯示，以最佳化權矩陣可降低誤差對平差結果的影響並定位出異常值。

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