【摘要】：眾所周知,在開展測量工作時會受到地形條件、天氣、環(huán)境、人為等因素的影響,這些因素常常會導(dǎo)致觀測數(shù)據(jù)缺失或者含有粗差,使得觀測數(shù)據(jù)變得不完全�，F(xiàn)在,對于變形監(jiān)測的數(shù)據(jù)處理方法大多數(shù)都是基于完全數(shù)據(jù)的,若不對缺失數(shù)據(jù)處理,往往會影響到結(jié)果的準(zhǔn)確性。在出現(xiàn)數(shù)據(jù)缺失這種情況時,常常采用刪除法、普通填補法、擬合法或預(yù)測法對缺失數(shù)據(jù)進行處理,然后再利用常規(guī)方法對數(shù)據(jù)進行建模分析。但是這些方法都有一定的局限性,刪除法實施起來簡單、快捷,但是它導(dǎo)致了資源的浪費,當(dāng)缺失數(shù)據(jù)較多或處于較重要的位置時,該方法可能導(dǎo)致結(jié)果的錯誤。普通填補法、擬合法和預(yù)測法雖然能夠一定程度上提高變形監(jiān)測數(shù)據(jù)處理質(zhì)量,但是得到的并一定是最優(yōu)的結(jié)果,因為這些方法都是先對缺失的數(shù)據(jù)進行填補,然后再進行建模分析預(yù)測,由于這些方法自身的局限性,其填補的數(shù)據(jù)也存在一定的不確定性,再利用它來進行建模分析可能就會導(dǎo)致結(jié)果產(chǎn)生偏差�；谝陨锨闆r,本文在分析了缺失數(shù)據(jù)的機制以及缺失數(shù)據(jù)處理方法之后,根據(jù)統(tǒng)計領(lǐng)域中的經(jīng)典算法EM算法(Expectation-maximization Algorithm,又譯作最大期望化算法)原理,探討了當(dāng)變形監(jiān)測數(shù)據(jù)出現(xiàn)缺失時利用EM算法對其進行處理的方法。本文針對EM算法在不完全監(jiān)測數(shù)據(jù)處理中的研究主要做了以下的工作:(1)論述了變形監(jiān)測中常用的數(shù)據(jù)處理方法,并對這些方法進行了總結(jié)比較,分析各種方法在測繪數(shù)據(jù)處理中的適用情形和優(yōu)缺點。(2)根據(jù)數(shù)據(jù)缺失機制介紹了測量中常用的不完全測量數(shù)據(jù)的處理方法,通過對比各種缺失數(shù)據(jù)處理方法,分析了各種方法的適用性。(3)對EM算法的原理和性質(zhì)進行了介紹,詳細的介紹了EM算法同常用的預(yù)報模型AR(p)模型結(jié)合處理不完全監(jiān)測數(shù)據(jù)的步驟。通過對比刪除法和回歸填補法在單一缺失和多重缺失情況下的預(yù)報效果,證實了EM算法用于變形監(jiān)測不完全數(shù)據(jù)處理中的可靠性。(4)在完全數(shù)據(jù)情況下分別采用GM(1,1)灰色模型和BP神經(jīng)網(wǎng)絡(luò)模型對沉降數(shù)據(jù)進行預(yù)測,對比在單一缺失數(shù)據(jù)與多重缺失情況下采用EM算法估計的AR(p)模型的預(yù)測結(jié)果。通過對比分析發(fā)現(xiàn),4種方法的預(yù)測效果相差不大,綜合比較EM算法估計的AR(p)模型的預(yù)測精度較高。
[Abstract]:As we all know, the survey work will be affected by the terrain conditions, weather, environment, human factors and other factors, these factors will often lead to the lack of observation data or contain gross error, make the observation data become incomplete. Nowadays, most of the data processing methods for deformation monitoring are based on complete data. If the missing data is not processed, the accuracy of the results will be affected. In the case of missing data, deletion method, general filling method, fitting method or prediction method are often used to process the missing data, and then the data are modeled and analyzed by the conventional method. However, these methods have some limitations. Deletion method is simple and fast to implement, but it leads to the waste of resources. When there are more missing data or in a more important position, the method may lead to the error of the result. The common filling method, the fitting method and the prediction method can improve the processing quality of deformation monitoring data to some extent, but the result must be the best, because these methods are to fill the missing data first. Then the modeling analysis and prediction are carried out. Due to the limitations of these methods there are some uncertainties in the data filled by these methods. Using them for modeling and analysis may lead to the deviation of the results. Based on the above situation, this paper analyzes the mechanism of missing data and the methods of processing missing data, and according to the principle of EM algorithm, a classical algorithm in the field of statistics, which is translated as maximum expectation algorithm, The method of using EM algorithm to deal with deformation monitoring data when it is missing is discussed. In this paper, the research of EM algorithm in incomplete monitoring data processing has been done as follows: (1) the data processing methods commonly used in deformation monitoring are discussed, and these methods are summarized and compared. The application of various methods in surveying and mapping data processing and their advantages and disadvantages are analyzed. (2) according to the mechanism of missing data, the common methods of incomplete measurement data processing are introduced, and the methods of missing data processing are compared. The applicability of various methods is analyzed. (3) the principle and properties of the EM algorithm are introduced, and the steps of processing incomplete monitoring data by combining the EM algorithm with the commonly used prediction model AR (p) model are introduced in detail. By comparing the prediction results of deletion method and regression filling method in the case of single deletion and multiple deletions, The reliability of EM algorithm used in incomplete data processing of deformation monitoring is confirmed. (4) in the case of complete data, GM (1k-1) grey model and BP neural network model are used to predict the settlement data, respectively. The prediction results of AR (p) model estimated by EM algorithm under the condition of single missing data and multiple deletions are compared. By comparison and analysis, it is found that the prediction effect of the four methods is not different, and the prediction accuracy of the AR (p) model estimated by comprehensive comparison with EM algorithm is higher.
【學(xué)位授予單位】：成都理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：P207

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