發(fā)布時(shí)間：2018-10-29 19:56

【摘要】：半?yún)?shù)模型把非參數(shù)分量加入觀測(cè)方程中,一方面使得建立的數(shù)學(xué)模型與真實(shí)情況更為接近,另一方面能在數(shù)值上分別求出系統(tǒng)誤差和偶然誤差的估值。本文探討了半?yún)?shù)模型的若干問(wèn)題,討論了幾種傳統(tǒng)模型與半?yún)?shù)模型的結(jié)合,分析采用補(bǔ)償最小二乘準(zhǔn)則與最小二乘準(zhǔn)則的區(qū)別,探討了幾種數(shù)據(jù)處理方法與半?yún)?shù)模型相結(jié)合的優(yōu)點(diǎn),并用算例驗(yàn)證,傳統(tǒng)模型與半?yún)?shù)模型結(jié)合得到的參數(shù)估值精度明顯提高。本文主要內(nèi)容如下:1.基于半?yún)?shù)模型與補(bǔ)償最小二乘估計(jì)方法,分析了正規(guī)矩陣R和平滑因子α的選取方法。對(duì)比分析了傳統(tǒng)參數(shù)模型與半?yún)?shù)模型對(duì)于系統(tǒng)誤差的穩(wěn)定性,鑒于傳統(tǒng)平滑因子選取方法偏于復(fù)雜且計(jì)算量大,提出了一種新的更加簡(jiǎn)便的平滑因子選取方法——基于效率最優(yōu)準(zhǔn)則的平滑因子選取方法。2.研究了基于半?yún)?shù)模型的灰色預(yù)測(cè)建模方法,并通過(guò)改進(jìn)傳統(tǒng)正規(guī)矩陣的選取方法,分析不同正規(guī)矩陣對(duì)參數(shù)估值的影響及其精度變化,結(jié)合變形監(jiān)測(cè)數(shù)據(jù),探討補(bǔ)償最小二乘準(zhǔn)則下的灰色預(yù)測(cè)與最小二乘準(zhǔn)則下的灰色預(yù)測(cè)精度的變化。3.對(duì)于半?yún)?shù)模型及其嶺估計(jì),探討了當(dāng)法矩陣病態(tài)時(shí)模型的解法,探討了嶺參數(shù)的選取方法,分析了半?yún)?shù)模型嶺估計(jì)與泛補(bǔ)償最小二乘估計(jì)之間的聯(lián)系。通過(guò)算例分析了半?yún)?shù)模型與半?yún)?shù)嶺估計(jì)解算病態(tài)模型對(duì)參數(shù)估值的影響。4.考慮到最小二乘估計(jì)不具備抗差性,所以補(bǔ)償最小二乘估計(jì)也不具備抗差性,研究了半?yún)?shù)模型抗差估計(jì),探討了抗差估計(jì)權(quán)因子的選取方法,推導(dǎo)了基于選權(quán)迭代法的半?yún)?shù)抗差估計(jì)的計(jì)算公式,通過(guò)算例對(duì)比分析了幾種模型解的精度以及對(duì)精度的影響。
[Abstract]:The semi-parametric model adds nonparametric components into the observation equation on the one hand makes the established mathematical model closer to the real situation on the other hand it can numerically calculate the estimates of the system error and the accidental error respectively. This paper discusses some problems of semi-parametric model, discusses the combination of several traditional models and semi-parametric models, and analyzes the differences between the compensatory least square criterion and least square criterion. This paper discusses the advantages of combining several data processing methods with semi-parametric model and verifies by an example that the precision of parameter estimation obtained by combining traditional model with semi-parametric model is obviously improved. The main contents of this paper are as follows: 1. Based on the semi-parametric model and the compensated least square estimation method, the selection method of normal matrix R and smoothing factor 偽 is analyzed. The stability of the system error between the traditional parameter model and the semi-parametric model is compared and analyzed. In view of the complexity of the traditional smoothing factor selection method and the large amount of calculation, In this paper, a new and more convenient method for selecting smoothing factors is proposed, which is based on the optimal efficiency criterion. 2. The grey prediction modeling method based on semi-parametric model is studied. By improving the traditional normal matrix selection method, the influence of different normal matrices on parameter estimation and its accuracy change are analyzed, and the deformation monitoring data are combined. This paper discusses the variation of grey prediction accuracy under the least square criterion and the least square criterion. 3. For the semi-parametric model and its ridge estimation, this paper discusses the solution of the model when the normal matrix is ill-conditioned, discusses the selection method of the ridge parameter, and analyzes the relationship between the semi-parametric model ridge estimation and the universal compensated least square estimation. The effects of semi-parametric model and ill-conditioned model of semi-parametric ridge estimation on parameter estimation are analyzed by an example. 4. Considering that the least square estimation is not robust, so the compensated least squares estimation is not robust, so the robust estimation of semi-parametric model is studied, and the method of selecting the weight factor of robust estimation is discussed. The calculation formula of semi-parameter robust estimation based on weight selection iteration method is derived. The accuracy of several model solutions and their effects on accuracy are analyzed by examples.
【學(xué)位授予單位】：東華理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：P207

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 周敏;周世健;譙婷;池其才;;半?yún)?shù)模型自然樣條函數(shù)法與時(shí)間序列法分析[J];江西科學(xué);2017年01期

2 潘雄;呂玉婷;汪耀;羅靜;徐景田;;基于半?yún)?shù)平差模型的粗差定位與定值研究[J];武漢大學(xué)學(xué)報(bào)(信息科學(xué)版);2016年11期

3 周敏;周世健;王奉偉;;正規(guī)矩陣選取半?yún)?shù)灰色模型改進(jìn)的預(yù)測(cè)建模[J];測(cè)繪科學(xué);2016年08期

4 王康;周世健;;初始條件改進(jìn)全概括灰色預(yù)測(cè)模型研究[J];測(cè)繪科學(xué);2014年12期

5 潘申運(yùn);;補(bǔ)償最小二乘法改進(jìn)灰色預(yù)測(cè)模型的應(yīng)用分析[J];測(cè)繪科學(xué);2014年11期

6 陶肖靜;朱建軍;田玉淼;;半?yún)?shù)模型中影響正則化參數(shù)的因素分析[J];武漢大學(xué)學(xué)報(bào)(信息科學(xué)版);2012年03期

7 高寧;崔希民;高彩云;王果;趙萬(wàn)東;;變形平差系統(tǒng)模型誤差的半?yún)?shù)補(bǔ)償方法[J];大地測(cè)量與地球動(dòng)力學(xué);2012年01期

8 王成勇;;半?yún)?shù)回歸模型研究綜述[J];數(shù)理統(tǒng)計(jì)與管理;2009年05期

9 周命端;郭際明;文鴻雁;汪偉;;基于優(yōu)化初始值的GM(1,1)模型及其在大壩監(jiān)測(cè)中的應(yīng)用[J];水電自動(dòng)化與大壩監(jiān)測(cè);2008年02期

10 丁士俊;張松林;張洪波;陶本藻;;半?yún)?shù)模型穩(wěn)健估計(jì)及其應(yīng)用[J];測(cè)繪科學(xué)技術(shù)學(xué)報(bào);2007年01期

相關(guān)博士學(xué)位論文 前3條

1 丁士俊;測(cè)量數(shù)據(jù)的建模與半?yún)?shù)估計(jì)[D];武漢大學(xué);2005年

2 潘雄;半?yún)?shù)模型的估計(jì)理論及其應(yīng)用[D];武漢大學(xué);2005年

3 胡宏昌;半?yún)?shù)模型的估計(jì)方法及其應(yīng)用[D];武漢大學(xué);2004年

相關(guān)碩士學(xué)位論文 前5條

1 陶肖靜;半?yún)?shù)平差模型的平差準(zhǔn)則研究[D];中南大學(xué);2011年

2 樂(lè)科軍;基于Helmert方差分量估計(jì)的半?yún)?shù)回歸模型若干算法研究[D];中南大學(xué);2009年

3 劉運(yùn)航;半?yún)?shù)模型理論及其在大地測(cè)量中的應(yīng)用[D];解放軍信息工程大學(xué);2008年

4 尹遜震;灰色模型的改進(jìn)及其應(yīng)用[D];南京信息工程大學(xué);2007年

5 周曉衛(wèi);基于虛擬觀測(cè)的若干測(cè)量數(shù)據(jù)處理方法研究[D];中南大學(xué);2007年

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